Fleiss' Kappa (Multi-rater Agreement) Calculator

Percent of, percent change, and percent add/subtract in one.

Enter 2–6 positive integers to get the greatest common divisor (HCF / GCD) and least common multiple (LCM), with the Euclidean step chain shown.

Enter a list of numbers to get the mean, median, mode, range plus standard deviation, variance and total.

Enter the coefficients of ax² + bx + c = 0 to find the real or complex roots, discriminant and vertex.

Estimate a password's bit entropy, brute-force time and strength tier. All computation happens in your browser.

Convert between standard decimal numbers and scientific notation, with significant figures and order of magnitude.

Compute permutations P(n,r), combinations C(n,r) and factorial n! — useful for probability problems, lottery odds and combinatorics homework.

Paste a list of numbers to compute mean, median, sample and population variance and standard deviation — with the working shown.

Solve a triangle from 3 sides, 2 sides + 1 angle, or 2 angles + 1 side — area, perimeter and remaining parts via the law of sines / cosines.

Given any two sides of a right triangle (two legs, or one leg plus the hypotenuse), instantly find the third side, area, perimeter and the two non-right angles.

Enter any one of radius, diameter, circumference or area to get the other three — useful for design, engineering and DIY.

Two-way conversion between Arabic numbers (1–3999) and Roman numerals (I, V, X, L, C, D, M) — handy for typesetting, chapter titles and homework.

Enter two points (x₁, y₁) and (x₂, y₂) to instantly get the slope, y-intercept, line equation y = mx + b, distance, and midpoint — a classroom staple for algebra and coordinate geometry.

Enter group size n to see the probability that at least two people share a birthday — the classic birthday problem.

Compute logₐ(x) for any base — natural log (ln), common log (log₁₀), binary log (log₂) and a custom base, with the change-of-base steps shown.

Enter a value, the mean and the standard deviation to compute the z-score and the corresponding normal-distribution percentile and probabilities.

Enter the screen resolution and diagonal size to get pixel density (PPI), real width/height, dot pitch and total pixel count.

Enter the number of tickets / selections and see the actual probability of hitting first, second … prizes in a Mark Six (6-of-49) draw.

Convert any decimal (including repeating decimals) to a simplified fraction and a mixed number.

Give a sphere any one of radius, diameter, surface area or volume and instantly get the other three — plus the great-circle circumference and area.

Enter the radius and height of a cylinder to get volume (π r²h), lateral surface, base area and total surface area.

Compute nPr — the number of ordered arrangements of r items chosen from n — alongside n!, r! and the related combination nCr.

Factor any integer from 2 up to 10¹² into primes, see the canonical exponent form, count and list all divisors.

Compute the n-th root of the product of n positive numbers — the right average for growth rates, returns and ratios — alongside the arithmetic mean for comparison.

Enter any integer n from 0 to 1500 to instantly compute F(n) and F(n−1) with BigInt precision, the consecutive-term ratio (converging to the golden ratio φ) and the first 30 terms of the sequence.

Pick the number of dice, sides (d4 / d6 / d8 / d10 / d12 / d20) and a target sum to compute the probability of rolling exactly that total, at least, or at most.

Enter first term a, common difference d and number of terms n to compute the nth term aₙ and the partial sum Sₙ = n/2·(2a + (n − 1)d).

Enter confidence level, margin of error, expected proportion (and optional population size) to compute the survey sample size you need.

Enter the first term a, common ratio r and number of terms n to find the sum of the first n terms of a geometric series — plus the infinite-series sum when |r| < 1.

Enter base radius and height to get the cone volume, slant height, lateral, base and total surface area.

Pick a note (C, C♯, D, …), octave and tuning reference A4 (440 Hz by default) and the tool returns the frequency in Hz, the wavelength in air and the MIDI note number via f = A4 × 2^((n − 69)/12).

Enter two known points (x₁, y₁) and (x₂, y₂) and a target x to instantly read off y via y = y₁ + (x − x₁)(y₂ − y₁)/(x₂ − x₁) — the tool flags whether your x sits inside the two points (interpolation) or outside (extrapolation).

Enter the two parallel sides and height of a trapezoid to get its area, midsegment length and perimeter when the legs are known.

Enter the number of trials n, the per-trial success probability p and a target number of successes k to get P(X = k), P(X ≤ k), P(X ≥ k) along with the distribution mean and standard deviation.

Paste two parallel data series (X and Y) and get the Pearson correlation coefficient r, r², the best-fit line slope and intercept, and the sample means and standard deviations.

Enter the sample mean, sample standard deviation, sample size and confidence level to compute a confidence interval for the population mean using the t (or z) distribution, with margin of error and standard error.

Enter the means, standard deviations and sample sizes of two groups to compute Cohen's d and Hedges' g effect sizes, classified per Cohen 1988 as trivial / small / medium / large.

Enter dividend a and divisor n to compute the quotient and remainder a mod n. The truncated (C / JavaScript %), floored (Python / mathematical) and Euclidean conventions are shown side by side so the negative-input differences are obvious.

Toggle read/write/execute for user, group and other to instantly get both octal (e.g. 755) and symbolic (e.g. rwxr-xr-x) notations.

Enter 2D or 3D vector components (x, y, z) to compute the magnitude, unit vector and direction angles.

Enter experimental and theoretical (accepted) values to get absolute percent error, signed relative error, and absolute error. Switch to percent-difference mode to compare two measurements where neither is the accepted value.

Enter the mean event rate λ and an event count k to get P(X = k), P(X ≤ k), P(X ≥ k), the mean, variance and standard deviation — useful for queueing, call-centre staffing and rare-event modelling.

Enter the prior P(A), the sensitivity P(B|A) and the false-positive rate P(B|¬A); the tool applies Bayes’ theorem to give the posterior P(A|B) — handy for medical tests, spam filters and any classification decision.

Enter a circle’s radius and central angle (degrees or radians) to compute the arc length s = r·θ, sector area A = ½·r²·θ and chord length — useful for geometry, machining and architectural layout.

Enter the entries of a 2×2 or 3×3 matrix and instantly get the determinant det(A) via ad − bc or cofactor expansion along the first row, with an invertibility check and the step-by-step 2×2 minors shown for linear-algebra study.

Enter two 2D or 3D vectors and instantly compute the dot product, included angle, scalar projection and vector projection — with hints for orthogonal, parallel and anti-parallel cases.

Enter two numeric vectors of any dimension and compute cos θ = (a·b) / (|a|·|b|), plus the angular distance — the staple similarity metric in NLP, recommender systems and document-similarity scoring.

Enter two values and compute the symmetric percent difference |a − b| / ((|a| + |b|) / 2) alongside the directional percent change (b − a)/a — a common source of confusion in lab reports and news headlines.

Enter two 3D vectors a and b, compute the cross product a × b together with its magnitude (the area of the parallelogram they span) and sin θ — the workhorse of physics torque, computational geometry and 3D graphics.

Enter two points in the plane or in 3D space and the tool returns the straight-line Euclidean distance √Σ(Δᵢ)², each axis delta and the midpoint — handy for geometry homework, CAD measurements and planar GIS work.

Enter a dataset and the tool returns the coefficient of variation CV = σ / μ × 100% (standard deviation divided by mean) — the standard yardstick for comparing dispersion across datasets with different units or magnitudes (lab repeatability, portfolio risk).

Enter a dataset and the tool sorts it and returns the median, first and third quartiles, the inter-quartile range (IQR) and Tukey 1.5×IQR outlier fences — the five-number summary behind every box plot.

Enter a set of positive numbers and compute the harmonic mean HM = n / Σ(1/xᵢ) alongside the arithmetic and geometric means — the right average when the data behaves like rates or denominators (speeds, P/E ratios, flow rates).

Enter a list of class probabilities or frequencies and compute Shannon entropy H = −Σ pᵢ log₂ pᵢ (bits) alongside the maximum entropy and the normalised entropy — the foundation of information theory, decision-tree splits and password analysis.

Enter the side count n and side length s of a regular polygon and the tool returns the interior and exterior angles, the apothem and circumradius, the area and the perimeter in one shot — works for triangles, squares, pentagons, hexagons and beyond.

Enter n and the tool returns the n-th Catalan number Cₙ = (2n)! / ((n+1)! · n!) — the textbook count for balanced parentheses, binary tree shapes, Dyck paths and many other combinatorics problems.

Enter a column of actual values and a column of predicted values; the tool computes MAE, MSE, RMSE, R² and MAPE side-by-side — the staple set of regression-error metrics in machine learning, forecasting and lab-vs-model comparisons — and explains how each one weights outliers differently.

Enter the 6 coefficients of ax + by = e and cx + dy = f. The tool applies Cramer's rule to return x, y, the determinant D and the system's classification (unique solution / no solution / infinitely many), showing the working out so it doubles as a homework check.

Enter a per-trial probability p and a trial count n; the tool returns the probability of at least one success 1 − (1 − p)ⁿ, the expected count np, and the trials needed to reach a target probability — the maths behind raffles, gacha pulls, A/B tests and redundancy design.

Enter observed and expected counts; the tool computes the chi-square statistic χ² = Σ (O − E)² / E, degrees of freedom and the p-value to test whether the observed distribution deviates significantly from theory — the standard test for die fairness, Mendelian ratios and categorical A/B counts.

Enter outcome values x and matching probabilities p; the tool returns the expected value E[X] = Σ p·x, variance Var(X) and standard deviation σ — the foundational metric for casino games, insurance pricing, investment decisions and A/B-test analysis.

Enter sample size n, sample proportion p (or sample standard deviation) and a confidence level (90 / 95 / 99 %); the tool computes the margin of error MOE = z·√(p(1−p)/n) and the matching confidence interval — the core statistic behind political polls, A/B tests and market research.

Enter a list of numbers; the tool returns the mean absolute deviation (MAD = average of |xᵢ − mean|) — a more intuitive spread measure than standard deviation, used in school statistics and demand-forecasting accuracy.

Paste (x, y) data points; the tool fits an ordinary least-squares regression and reports the coefficient of determination R², slope, intercept and Pearson r — the standard "how much variance is explained" measure.

Enter base dimensions and height; the tool returns volume, base area, slant height, lateral surface area and total surface area for square, rectangular, equilateral-triangular or regular n-gon based right pyramids using V = ⅓ × base area × height.

Enter base and height, or two side lengths and the included angle; the tool returns the parallelogram area, perimeter and both diagonals via A = b · h or A = a · b · sin θ.

Enter the semi-major axis a and semi-minor axis b; the tool returns the area A = π a b and uses Ramanujan's second approximation for the perimeter — relative error below 4 × 10⁻⁵ across all eccentricities.

Enter a Z-score; the tool returns the one-sided (left / right) and two-sided p-values, and flags significance against α = 0.05 / 0.01 / 0.001 — the missing step of nearly every hypothesis test.

Enter the sphere radius R and cap height h; the tool returns V = πh²(3R − h)/3 and the curved surface area A = 2πRh — useful for partial spherical tanks, domes and lens segments.

Paste a list of values; the tool scans the dataset and reports the most-frequent value(s), handling unimodal, bimodal and multimodal cases, with the full frequency table — the standard intro-statistics tool for categorical and discrete data summaries.

Enter initial value N₀, continuous rate constant k and elapsed time t; the tool returns N(t) = N₀·e^(kt), the per-period change, and the doubling time (k > 0) or half-life (k < 0) — the universal model for populations, bacteria, radioactive decay, first-order pharmacokinetics and continuously compounded interest.

Enter any positive integer n; the tool iterates the Collatz rule (even → n/2, odd → 3n+1) until it reaches 1 and lists the full sequence, the number of steps and the peak value reached — a classic number-theory and programming exercise.

Enter a positive integer n and the tool returns the n-th triangular number Tₙ = n(n+1)/2, or inversely: given any positive integer N, identify whether N is triangular (and at which index) — staple of combinatorics, the handshake problem and math competitions.

Enter a positive integer n; the tool applies Σᵢ₌₁ⁿ i² = n(n+1)(2n+1)/6 to return the sum of the first n squared positive integers, along with the sum of cubes ([n(n+1)/2]²) and the arithmetic sum — fundamental identities for induction, series and statistics problems.

Enter any length and the tool splits it into long / short parts so that a/b = (a+b)/a using the golden ratio φ ≈ 1.6180339887, or inversely: input two segments and see how closely their ratio approaches φ — a staple of design, photography, layout and mathematics.

Enter two sides and the included angle (SAS) or three sides (SSS); the tool applies c² = a² + b² − 2ab·cos C to solve the unknown side or angle and reports all three sides and angles — a core surveying, construction and navigation tool.

Enter board thickness (in), width (in) and length (ft); the tool applies BF = (T × W × L) ⁄ 12 to return board feet per piece, total board feet, volume (ft³ / m³) and total cost — used by woodworkers, furniture makers and DIY hobbyists for lumber budgeting.

Enter the three sides a, b, c of a triangle; the tool applies r = A ⁄ s (inradius) and R = abc ⁄ (4A) (circumradius) to return both circle radii, plus triangle area via Heron's formula — a workhorse for geometry homework, mechanical layout and architectural design.

Enter base a, exponent b and modulus n; the tool uses the square-and-multiply fast-exponentiation algorithm with BigInt support to compute a^b mod n — the core operation behind RSA cryptography, hashing and modular-arithmetic homework.

Enter a and modulus n; the tool uses the extended Euclidean algorithm to return the modular inverse (a·x ≡ 1 mod n), gcd(a, n) and the Bézout identity — required for RSA private-key generation, the Chinese Remainder Theorem and solving linear congruences.

Enter an IPv4 address and CIDR prefix length (e.g. 192.168.1.10/24); the tool returns the subnet mask, network address, broadcast address, usable host range and total host count — a daily tool for network admins and SREs.

Enter a numerator and denominator (e.g. 48 ⁄ 60); the tool reduces to lowest terms via the greatest common divisor (4 ⁄ 5) and also shows the mixed-number, decimal and percent equivalents — a workhorse for primary and middle-school maths homework.

Enter a row index n (starting at 0); the tool prints the binomial coefficients C(n,0) C(n,1) … C(n,n) for that row, along with the row sum 2ⁿ, the maximum value and the matching (a+b)ⁿ expansion — a quick reference for combinatorics, binomial distributions and the binomial theorem.

Enter two angles + one side (AAS / ASA) or two sides + one non-included angle (SSA — including the ambiguous case); the tool applies sin A ⁄ a = sin B ⁄ b to solve the unknown side or angle and reports all three sides, angles and area. Pair with the existing Law of Cosines tool to cover every SAS / SSS / AAS / ASA / SSA triangle-solving case.

Paste a dataset (comma-separated); the tool returns mean, median, mode, sample standard deviation, plus Pearson's First skewness coefficient (uses the mode) and Second skewness coefficient (uses the median, 3·(mean − median) ⁄ SD) — the standard quick measure of distribution asymmetry in data science, quality control and psychometrics.

Paste a dataset; the tool returns Q1, Q3 and the IQR, then applies Tukey's 1.5 × IQR rule to flag mild outliers (beyond ±1.5 IQR of the quartiles) and extreme outliers (beyond ±3 IQR), reporting the box-plot whisker range. A standard step in exploratory data analysis, quality control and data cleaning.

Enter each group's mean, standard deviation and sample size; the tool returns the t statistic, degrees of freedom and two-sided p-value under both Welch's test (no equal-variance assumption) and the Student pooled t-test. The most-used inferential test for controlled experiments, A/B tests and clinical trial outcome comparisons.

Enter two paired numeric arrays; the tool converts each to ranks (averaging ties) and applies Pearson's formula on the ranks to return Spearman's ρ. A non-parametric measure of monotonic association, robust to outliers and with no normality assumption.

Enter the periodic growth rate r (in %); the tool returns t = ln 2 ⁄ ln(1+r), the exact number of periods needed for a quantity to double. More accurate than the Rule of 72, and applies to population, GDP, investment returns, bacterial cultures and any exponential-growth process.

Enter the sample standard deviation and sample size; the tool returns SEM = s ⁄ √n and the 95% confidence interval (μ ± 1.96 × SEM). The standard calculation behind error bars in scientific charts, A/B-test reporting and journal articles.

Common questions: "100 is 40% of what?" "After +8% it is 540 — what was the original?" The tool handles all three classic reverse-percentage cases: original from percent, percent from base, and pre-markup or pre-discount value.

Enter the win probability p, net odds b and bankroll; the tool returns the Kelly-optimal stake fraction f* = (bp − q) ⁄ b and the suggested bet size (with optional ¼ / ½ fractional-Kelly). The standard bankroll-management framework for sports betting, poker and quant investing.

Enter any time on a 12-hour clock; the tool returns the angle between the hour and minute hands using |30·H − 5.5·M|, reported as the smaller angle in the 0 – 180° range. A classic interview / math-olympiad question and a useful teaching aid for analog-clock instruction.

Enter the number of sides n; the tool returns the sum of interior angles (n − 2) × 180°, the per-vertex interior angle in a regular polygon (sum ÷ n) and the per-vertex exterior angle (360° ÷ n). A standard high-school geometry tool and useful for tiling / tessellation design.

Enter two points (or a slope plus a point); the tool returns all three canonical forms of the same line: slope-intercept y = mx + b, standard Ax + By = C (integer coefficients) and point-slope y − y₁ = m(x − x₁). The bread-and-butter conversion drilled in US Algebra I, SAT and SSAT.

Enter (x, y) coordinates of three points; the tool computes the unique circumscribed circle's centre (h, k) and radius r, plus the standard-form equation (x − h)² + (y − k)² = r². Handy for geometry classes, CAD layouts, drafting and reverse-engineering arcs.

Enter any two of long-run arrival rate λ, time-in-system W, or average number in the system L; the tool returns the third via Little's Law L = λ × W — the foundational identity for queueing theory, WIP management in Agile/Kanban, and capacity planning for support desks and restaurants.

Enter bandwidth and round-trip time (RTT); the tool returns BDP = Bandwidth × RTT (bits in flight) and converts to bytes and KB/MB. The fundamental sizing parameter for TCP socket buffers, congestion window targets and CDN prefetch tuning.

Enter two strings; the tool returns the minimum number of single-character edits (insert / delete / substitute) needed to turn one into the other, plus a similarity percentage — the foundational algorithm for spellcheck, fuzzy matching, plagiarism detection and DNA sequence comparison.

Enter total operating hours and number of failures; the tool returns MTBF = total hours ÷ failures, failure rate λ, and exponential reliability R(t) = e^(−t ⁄ MTBF) — the standard reliability-engineering metrics for hardware, servers and production lines.

Enter two equal-length strings or bit sequences; the tool compares them position by position and returns the Hamming distance (count of differing positions) — the foundational metric for error-correcting codes, DNA sequence comparison, hash similarity and coding theory.

Enter the (x, y) vertex coordinates of a simple polygon (clockwise or counter-clockwise); the tool applies Gauss's shoelace formula A = ½|Σ(xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)| to return the enclosed area — used in surveying, cartography, GIS, CAD and game-development geometry.

Enter two points (x₁, y₁) and (x₂, y₂); the tool instantly returns the midpoint M = ((x₁+x₂)⁄2, (y₁+y₂)⁄2), the Euclidean distance d = √((Δx)² + (Δy)²) and the slope m = Δy⁄Δx — handy for geometry homework, surveying, GIS and CAD work.

Enter the edge length a of a regular tetrahedron; the tool returns volume V = a³ ⁄ (6√2), total surface area A = √3·a², height h = a·√(2⁄3) and the inscribed / circumscribed sphere radii — handy for crystallography, molecular geometry (methane CH₄), organic chemistry and pure geometry problems.

Enter the larger radius R, smaller radius r and height h of a cone frustum; the tool returns volume V = πh(R² + Rr + r²) / 3, slant height ℓ, lateral surface area, the two circular faces and total surface area — useful for paper cups, lampshades, funnels and water tanks.

Enter the radicand x and the root index n; the tool returns the real nth root x^(1/n), handling negative x with odd n, fractional roots and complex-only cases with a clear warning — for cube roots, fifth roots, principal roots and inverse-power problems.

Enter a digit string; the tool validates it with the Luhn (mod-10 doubling) algorithm and computes the trailing check digit that makes the first N − 1 digits valid — the same scheme used by credit cards (Visa, Mastercard, Amex), phone IMEIs and Canadian SINs.

Enter an ISBN-13 (with or without the trailing digit); the tool computes the correct check digit using the (1, 3) weighted mod-10 formula and validates the entire string — useful for librarians, publishers and bookshops managing catalogues.

Enter any positive integer; the tool repeatedly sums its digits until a single digit remains — showing each iteration, the numerology life-path equivalent and the mod-9 identity.

Enter carrying capacity K, initial value N₀, intrinsic growth rate r and time t; the tool applies the Verhulst logistic equation N(t) = K / (1 + ((K−N₀)/N₀)·e^(−rt)) and reports current value, instantaneous growth rate and half-saturation time — universal model for population dynamics, epidemic spread, start-up adoption curves and any growth limited by a carrying capacity.

Enter a 2×2 matrix [[a, b], [c, d]]; the tool applies the closed-form A⁻¹ = 1/det(A) × [[d, −b], [−c, a]] to return the inverse together with the determinant (det = ad − bc) — and reports "singular" when det = 0.

Enter two points (x₁, y₁) and (x₂, y₂) — with optional z to extend to 3D — and the tool applies M = ((x₁ + x₂)/2, (y₁ + y₂)/2) to give the midpoint, the Euclidean distance and the slope (in 2D). Used in high-school coordinate geometry, CAD drafting and game-coordinate math.

Pick a solid shape (sphere, cube, cylinder, cone) and enter its dimensions; the tool returns the surface area (sphere 4πr², cube 6a², cylinder 2πr² + 2πrh, cone πr² + πrl) and the volume — useful for estimating paint, packaging, wrap film and insulation requirements.

Enter the number of defects and total opportunities — or DPMO directly — and the tool returns the yield (1 − DPMO / 10⁶), the long-term sigma level (without shift) and the short-term Six Sigma level (with the conventional 1.5 σ shift) — the standard Motorola / Lean Six Sigma process-capability score.

Enter the torus major radius R (centre of ring to centre of tube) and the tube radius r; the tool applies V = 2π²Rr² and SA = 4π²Rr to give the volume and surface area of the torus (donut shape) — useful for pipe elbows, rubber O-rings, inner tubes and magnetic ring cores.

Enter the four coefficients of ax³ + bx² + cx + d = 0; the tool applies the Cardano-Tartaglia formula to return all three roots (real or conjugate-complex), the discriminant Δ and the type of root configuration.

Enter multiple value + weight pairs; the tool returns the weighted mean Σ(xᵢwᵢ) ⁄ Σwᵢ — unlike a simple arithmetic mean, heavier-weighted entries count more. Common uses: course grades, portfolio returns, survey scores.

Enter an upper bound N for the hypotenuse c; the tool uses Euclid's formula a = m²−n², b = 2mn, c = m²+n² to enumerate every primitive Pythagorean triple (gcd(a,b,c) = 1) up to that bound, with an option to list non-primitive multiples too.

Enter the radius r and height h of a cylinder; the tool returns the total surface area (two circular caps + lateral surface), the lateral surface alone, and a single cap, expressed in cm², m², in² and ft².

Enter outer radius R and inner radius r; the tool returns the annular area, the outer disk area, the inner hole area and the ring width in mm², cm², m², in² and ft² — useful for washers, gaskets, running tracks and tree-ring growth.

Enter the two parental genotypes (e.g. Aa × Aa); the tool draws the 2×2 Punnett square and reports the offspring genotype and phenotype ratios.

Enter the recessive-phenotype frequency q² (or the dominant allele frequency p); the tool applies p + q = 1 and p² + 2pq + q² = 1 to back out the expected fractions of homozygous-dominant, heterozygous and homozygous-recessive genotypes, plus carrier frequency among the unaffected.

Enter the target score, current score, overs bowled and total overs; the tool returns the required run rate (RRR), current run rate (CRR), balls remaining and runs-per-ball needed — useful for cricket fans tracking a chase.

Enter the pitcher's earned runs (ER) and innings pitched (IP); the tool applies ERA = (ER × 9) / IP to give the normalised "earned runs per nine innings" — the universal pitching benchmark used by MLB, NPB, KBO, CPBL and the WBSC.

Enter the pin counts for all ten frames; the tool applies World Bowling / USBC rules for strike (X) and spare (/) bonuses, including the tenth-frame fill balls, and gives the running per-frame total and final score.

Enter pass attempts (ATT), completions (CMP), passing yards (YDS), touchdowns (TD) and interceptions (INT); the tool applies the four-component formula the NFL has used since 1973 to give the 0–158.3 passer rating, the tier (perfect 158.3 down to poor) and the four sub-scores.

Enter planned production time, actual run time, ideal cycle time and total / good unit counts; the tool computes OEE = Availability × Performance × Quality — the universal manufacturing KPI (world-class ≥ 85 %) used in lean management and TPM — and breaks out each of the three component factors.

Enter the bowler's average, the league's base score (commonly 200 or 220) and the handicap percentage (typically 80 %, 90 % or 100 %); the tool applies handicap = max(0, ⌊(base − average) × percent / 100⌋) for the per-game handicap — the standard USBC, World Bowling and league formula — plus the multi-game handicap series total.

Enter up to 20 recent scores plus the course's Course Rating and Slope Rating; the tool applies the World Handicap System (WHS, USGA / R&A 2020) Rule 5 — average the best N of the last 20 score differentials — to give the official Handicap Index.

Enter a base font size (px / rem) and a scale ratio (minor third 1.2, major third 1.25, perfect fourth 1.333, golden ratio 1.618, etc.); the tool generates a complete typographic scale (h1–h6, small, caption) — essential for designers and developers.

Enter a decimal value and a bit width (8 / 16 / 32 / 64 bit); the tool returns the two's-complement binary and hexadecimal representation plus the representable range — essential for computer-science students and embedded developers.

Enter two 2D or 3D vectors; the tool applies cos θ = (u · v) / (|u| × |v|) to give the angle in degrees and radians, along with the dot product and magnitudes — essential for graphics, physics, mechanics and robotics.

Enter two 2D or 3D vectors u and v; the tool applies proj_v(u) = ((u · v) / |v|²) × v to give the vector and scalar projections of u onto v — essential for resolving forces in mechanics and 3D graphics.

Paste a set of (x, y) data points; the tool uses ordinary least squares to compute the best-fit line y = m × x + b, including slope, intercept, Pearson r, R², standard errors of slope and intercept, and a prediction for any x — essential for experimental data, A/B-test trends and engineering fits.

Enter f(x), integration limits a, b and an even subinterval count n; the tool applies composite Simpson's 1/3 rule (h/3)[f₀ + 4·Σf_odd + 2·Σf_even + fₙ] to estimate the definite integral with O(h⁴) error — the standard numerical-integration recipe in engineering, physics and statistics.

Enter group A and B sample sizes and successes; the tool returns the pooled proportion, Z statistic, two-sided P-value and a (1−α) confidence interval for the difference — essential for A/B-test, market-research and clinical-trial significance decisions.

Enter TP, FP, FN, TN counts from a 2×2 contingency table; the tool gives sensitivity, specificity, positive / negative predictive values, likelihood ratios, Youden's J and overall accuracy — essential for diagnostic-test and ML-classifier evaluation.

Enter f(x), its derivative f′(x), an initial guess x₀ and a tolerance; the tool applies Newton iteration x_{n+1} = x_n − f(x_n)/f′(x_n) to find a root of f(x) = 0, listing the iterates and convergence diagnostic — the classic numerical-analysis root-finder.

Enter successes x and sample size n; the tool returns the Wilson score 95 % confidence interval for the binomial proportion — far more reliable than the Wald (normal-approx) interval for small samples or extreme proportions, and used in A/B-test reporting, polling and ranking systems.

Enter the (x, y) coordinates of a triangle's three vertices; the tool returns the centroid G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3), the three side lengths, the three median lengths and the area (shoelace formula) — essential for geometry teaching, CAD and structural balance-point work.

Enter a continuous function f(x), an interval [a, b] with f(a)·f(b) < 0, and a tolerance; the tool applies the bisection method (repeatedly halving the interval) to converge on a root of f(x) = 0, listing each midpoint and sign change — linear-rate but extremely robust, the textbook root-finder taught alongside Newton–Raphson.

Enter an integrand f(x), an interval [a, b] and number of subdivisions n; the tool applies the composite trapezoidal rule ∫f ≈ (h/2)·(f₀ + 2f₁ + … + 2f_{n-1} + f_n) to estimate the definite integral, with a side-by-side error comparison vs Simpson and midpoint rules — a numerical-methods staple alongside Simpson and Romberg.

Enter the two diagonals (or side length + angle) of a rhombus; the tool applies A = ½ d₁ d₂ and A = s² sin θ to give the area, perimeter and side length — a standard DSE / IGCSE / SAT geometry tool.

Enter length (L), width (W) and height (H); the tool returns the volume V = LWH, surface area S = 2(LW + WH + LH), space diagonal d = √(L² + W² + H²) and all face diagonals — the most fundamental geometry calculation for boxes, packaging, shipping crates and furniture sizing.

Enter radius and central angle (degrees or radians) to get sector area, arc length, perimeter, chord length and sagitta — handy for design, mechanical layout, radar coverage and geometry homework.

Enter radius and central angle to compute the area of a circular segment (the region between a chord and the arc), plus chord length, sagitta (height) and perimeter — useful for mechanical layout, partial-fill of pipes / tanks and arc-shaped civil components.

Enter the straight-section length L and semicircle radius r; the tool applies A = πr² + 2rL and P = 2πr + 2L to give the stadium (discorectangle) area, perimeter and total length — essential geometry for athletic tracks, gym layouts and pill-shaped objects.

Enter the per-trial success probability p and a trial number k; the tool applies P(X=k) = (1−p)^(k−1)·p and P(X≤k) = 1−(1−p)^k to give the PMF, CDF, mean 1/p and variance (1−p)/p² of the geometric distribution — the standard model for "trials until first success".

Enter population size N, success-class size K, sample size n and observed successes k; the tool applies P(X=k) = C(K,k)·C(N−K,n−k) / C(N,n) to give the hypergeometric PMF, CDF, mean and variance — the foundation for poker hands, defect sampling, lotteries and capture-recapture estimates.

Enter the sample sizes n₁, n₂ and standard deviations s₁, s₂ of two groups; the tool applies s_p = √[((n₁−1)·s₁² + (n₂−1)·s₂²) / (n₁ + n₂ − 2)] to return the pooled standard deviation, pooled variance and degrees of freedom — the standard preprocessing step for two-sample t-tests, Cohen's d effect size and meta-analysis.

Enter the edge length a of a regular octahedron; the tool applies V = (√2/3)·a³ for volume, A = 2√3·a² for surface area, and the formulas for the inscribed and circumscribed sphere radii — one of the five Platonic solids, common in crystallography, dice design and geometry teaching.

Enter x; the tool applies sinh x = (eˣ − e⁻ˣ)/2, cosh x = (eˣ + e⁻ˣ)/2, tanh x = sinh x / cosh x to return sinh, cosh, tanh, coth, sech and csch — common in relativistic Lorentz transforms, catenary curves and neural-network activations.

Enter a positive integer n; the tool factorises n and applies φ(n) = n · ∏(1 − 1/p) over its distinct prime divisors p to return the count of integers in [1, n] coprime to n — the foundation of RSA cryptography, Euler's theorem and elementary number theory.

Enter two integers a and b; the tool runs the extended Euclidean algorithm to return gcd(a, b) together with Bézout coefficients (x, y) satisfying a·x + b·y = gcd(a, b), plus the modular inverse a⁻¹ mod b whenever gcd = 1 — essential for RSA, Diffie–Hellman and modular arithmetic.

Enter a positive integer n; the tool uses Stirling's formula ln(n!) ≈ n·ln n − n + ½·ln(2πn) to approximate ln(n!) and n!, and shows the exact value plus the relative error for small n — useful in statistical physics, combinatorics and probability.

Convert between decimal, binary and reflected-binary Gray code (G = N ⊕ (N >> 1)) — a staple for rotary encoders, Karnaugh maps, qubit ordering and fault-tolerant counters.

Enter an upper bound on the hypotenuse and the tool uses Euclid's formula a = m² − n², b = 2mn, c = m² + n² to list every integer triple a² + b² = c² (primitives + multiples), highlighting the primitives.

Choose the wheel (European 0, American 0/00, French 0 + en prison), bet amount and bet type (red/black, even/odd, column, street, split, straight up …); the tool returns the expected value per spin, the house edge percentage and the long-run expected loss — the canonical casino-mathematics teaching tool.

Enter the nine entries of a 3×3 matrix; cofactor (Laplace) expansion instantly returns the determinant det(A), the adjugate matrix and — whenever det ≠ 0 — the inverse A⁻¹, alongside a Sarrus-rule diagonal walkthrough. The everyday tool for linear algebra, Jacobian change-of-variables, signed volume / area and Cramer's rule.

Enter a system of congruences x ≡ a₁ (mod m₁), x ≡ a₂ (mod m₂), …; the tool uses the extended Euclidean algorithm to handle any moduli (no pairwise-coprime requirement) and returns the unique smallest non-negative solution x and the combined modulus M = lcm(m₁, m₂, …), explicitly flagging inconsistent systems. The core algorithm behind classical "Sun Tzu / Han Xin counting soldiers", RSA / cryptography and calendar arithmetic.

Enter an integer n; the tool returns the exact rational H_n = 1 + 1/2 + 1/3 + … + 1/n (BigInt numerator/denominator), its decimal value, and the Euler-Mascheroni approximation H_n ≈ ln(n) + γ + 1/(2n) − 1/(12n²) for comparison — fundamental in algorithm analysis (quicksort, the coupon-collector problem) and divergent-series theory.

Enter f(x), two starting guesses x₀ and x₁ and a tolerance; the tool iterates the secant rule x_{n+1} = x_n − f(x_n)·(x_n − x_{n−1})/(f(x_n) − f(x_{n−1})) — no analytic derivative needed and no bracketing required, the practical middle ground between Newton-Raphson and bisection.

Enter a first-order ODE dy/dx = f(x, y), the initial point (x₀, y₀), step h and end x_end; the tool integrates forward with the explicit Euler rule and tabulates every (x_n, y_n) — the canonical teaching tool for numerical methods, physics simulations and population models.

Enter a set of (x, y) data points and a target x; the tool builds the unique degree n − 1 polynomial passing through all points using the Lagrange basis P(x) = Σ y_i · ∏_{j≠i}(x − x_j)/(x_i − x_j) and evaluates P(x) — the textbook approach to fitting experimental data and filling missing values.

Enter a real number x to get σ(x) = 1/(1+e⁻ˣ) and its derivative σ′(x) = σ(x)(1−σ(x)), or enter a probability p ∈ (0,1) to recover logit(p) = ln(p/(1−p)) — the canonical link between log-odds and probability used in logistic regression, neural networks, Bayesian statistics and epidemiology.

Enter a multiplier k (≥ 1) of standard deviations; the tool returns Chebyshev's bound that for *any* distribution with finite variance, P(|X − μ| ≥ k σ) ≤ 1 / k² — a distribution-free tail estimate used in statistics, machine learning and risk management when normality cannot be assumed.

Enter two sets A and B (separated by commas, semicolons or newlines); the tool deduplicates, computes Jaccard similarity J(A, B) = |A ∩ B| / |A ∪ B| and distance 1 − J, and lists the intersection, A − B and B − A — the standard metric for text similarity, recommenders, ecological diversity, image-segmentation IoU and A/B-test control overlap.

Enter the nine entries of a 3×3 matrix A; the tool computes the determinant by the rule of Sarrus and returns the inverse A⁻¹ = adj(A) / det(A) via the adjugate formula, flagging singular matrices when det(A) = 0 — a standard utility for linear algebra, 3-D transforms and least-squares work.

Enter the four entries of a 2×2 matrix [[a, b], [c, d]]; the tool solves the characteristic equation λ² − (a + d)λ + (ad − bc) = 0 for both eigenvalues (real or complex-conjugate) and returns the corresponding eigenvectors — a foundational tool for dynamical-system stability, PCA and Markov-chain steady-state analysis.

Enter two n-dimensional vectors a, b (comma, whitespace or semicolon separated); the tool computes the Manhattan (taxicab / L¹) distance d = Σ|aᵢ − bᵢ| and contrasts it with the Euclidean (L²) and Chebyshev (L∞) distances — the foundational metric for ML feature distance, grid path-finding, city travel, Lasso regularisation and k-nearest-neighbour search.

Enter the start (lat₁, lon₁) and end (lat₂, lon₂) coordinates in decimal degrees; the tool applies the standard spherical-trigonometry formula to return the initial great-circle bearing (° clockwise from true north), the reverse bearing and the nearest 16-point compass cardinal — a basic navigation metric for marine, aviation, drone, hiking and radio direction-finding work.

Enter the first term a₁, common difference d and term count n (or last term aₙ); the tool applies Sₙ = n/2 · (a₁ + aₙ) = n/2 · (2a₁ + (n−1)d) to return the sum of the first n terms, the last term, the mean and the first 10 terms for verification — bedrock of secondary-school maths, loan-instalment cumulative accounting, training-block planning and complexity analysis.

Supply P(A), P(B) and any one of P(A∩B), P(A|B) or P(B|A); the tool uses P(A|B) = P(A∩B)/P(B) and Bayes' theorem to derive the other quantities, also returning P(A∪B) and an independence check — the foundational operation behind statistical inference, machine learning, diagnostic-test interpretation and Naive Bayes classification.

Enter a 3×3 coefficient matrix A and the constant vector b; the tool applies Cramer's rule x_i = det(A_i) / det(A) to return the unique solution (x, y, z), and shows the main determinant and each substituted determinant — the standard pedagogical method for school-level linear algebra and engineering systems of equations.

Enter a first-order ODE dy/dx = f(x, y), the initial point (x₀, y₀), step h and end x_end; the tool applies the classical fourth-order Runge-Kutta method (four k-values per step, weighted average) to tabulate every (x_n, y_n) — about four orders of magnitude more accurate than Euler at the same step size, and the industry-standard ODE integrator for physics simulations, orbit propagation and control engineering.

Enter a sheet thickness (typical A4 0.1 mm) and number of folds N; the tool applies the exponential formula thickness × 2^N to compute the final stack height and compares it to real-world heights (a person, buildings, mountains, the Earth–Moon distance) — a striking visualization of exponential growth.

Enter the triangular distribution parameters min a, mode c and max b; the tool returns the mean (a+b+c)/3, variance, standard deviation, PDF / CDF and P(X ≤ x) — the standard continuous distribution behind PERT three-point estimates and lightweight risk analysis.

Enter the lower bound a and upper bound b of a continuous uniform distribution; the tool returns the mean (a+b)/2, variance (b−a)²/12, standard deviation, PDF 1/(b−a), CDF and P(X ≤ x) plus interval probability P(c ≤ X ≤ d) — the baseline distribution for simulation, sampling and Monte Carlo work.

Enter index n; the tool returns the Lucas number L(n) — same recurrence as Fibonacci, L(n) = L(n−1) + L(n−2), but with starting values L(0)=2 and L(1)=1. Widely used in number theory, combinatorics and Fibonacci identity proofs.

Enter n; the tool returns the number of derangements !n — permutations where no element stays in its original position — using !n = n! · Σ_{k=0..n} (−1)ᵏ/k! and reports the limiting probability !n / n! → 1/e ≈ 0.3679, the answer to the classic hat-check / letter-mismatch puzzle.

Enter a line in general form Ax + By + C = 0 and a point (x₀, y₀); the tool returns the perpendicular distance d = |Ax₀ + By₀ + C| / √(A² + B²) — the staple geometry formula used in high-school maths, CAD, mechanical engineering and computer graphics.

Enter a positive integer N; the tool computes π(N), the number of primes ≤ N, exactly via a sieve of Eratosthenes and compares the result against the Prime Number Theorem estimate N / ln(N) and the logarithmic integral li(N) — a staple tool for number theory, cryptography and contest mathematics.

Enter three known values of the proportion A : B = C : X; the tool cross-multiplies X = B × C / A (direct) or X = A × B / C (inverse) to solve for the unknown fourth term — the oldest, most-taught technique for recipe scaling, map distances, currency conversion, worker-days and any everyday proportion problem.

Enter the integrand f(x), the limits [a, b] and the number of subintervals n; the tool applies the midpoint rule (evaluate f at the centre of each subinterval and sum) to return the approximate definite integral — O(h²) accuracy makes it the standard "first quadrature method" taught alongside the trapezoid and Simpson rules.

Enter positive integers n₁, n₂, …, nₖ; the tool returns the multinomial coefficient C(n; n₁, n₂, …, nₖ) = (n₁ + n₂ + … + nₖ)! / (n₁! n₂! ⋯ nₖ!) — the generalisation of the binomial coefficient and the building block of multinomial expansions, combinatorial counting and the multinomial distribution.

Enter n (items) and k (boxes); the tool applies the *stars-and-bars* theorem to count the ways to distribute n identical items into k boxes — C(n + k − 1, k − 1) if boxes may be empty, C(n − 1, k − 1) if every box must be non-empty — the foundational counting trick behind generating functions, choosing-with-replacement and Diophantine enumeration.

Enter two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in 3D space; the tool returns the Euclidean distance √((Δx)² + (Δy)² + (Δz)²), the squared distance, the per-axis deltas and the unit direction vector — a workhorse for CAD, 3D modelling, robotics, drone path planning, game development and physics simulation.

Enter a dataset and a target value; the tool applies the NIST-standard formula PR = (B + 0.5 · E) / N × 100 to return the target's percentile rank within the data — used for exam scores, growth charts, performance reviews, income rankings and ML feature scaling.

Enter a message and a shift N (1–25); the tool applies the classical Caesar cipher E(x) = (x + N) mod 26 to encrypt or decrypt instantly, preserving case and leaving non-alphabetic characters (punctuation, spaces, digits) unchanged.

Paste a list of numbers (comma- or newline-separated); the tool returns the median, MAD = median(|xᵢ − median|), the robust σ̂ ≈ 1.4826 × MAD, and flags outliers using the 3·MAD rule (Hampel 1974, Leys 2013) — a far more robust dispersion estimator than the standard deviation when your data has outliers.

Enter a percentile p ∈ (0, 1) (e.g. 0.975); the tool uses the Acklam approximation (1.5 × 10⁻⁹ accuracy) to return the corresponding standard-normal z-score (z = Φ⁻¹(p)) and shows the equivalent cut-off in μ ± σ units — useful for hypothesis testing, confidence intervals, A/B-test sample sizing and SPC control charts.

Enter any number and a target precision (1–15 significant figures); the tool rounds via IUPAC round-half-up to that precision and returns the standard, scientific (mantissa × 10ⁿ) and decimal forms — used for physics / chemistry lab write-ups, engineering measurements and keeping significant-figure rules consistent across a calculation chain.

Enter a service availability target (e.g. 99 %, 99.9 %, 99.99 %, 99.999 %); the tool returns the allowed downtime per year, month, week and day, alongside the familiar "Nines" reference (99 % = 3.65 d/yr, 99.9 % = 8.77 h/yr, 99.999 % = 5.26 min/yr) — handy for SREs, cloud architects and contract negotiation.

Enter jackpot amount, win probability (e.g. 1 / 292,201,338) and ticket price; the tool returns EV = (Jackpot × P) − Ticket Price, with optional tax-rate and jackpot-share adjustments — works for Powerball, Mega Millions, EuroMillions, Mark Six and other lotteries.

Enter coin head probability p, number of flips n and target streak length k; the tool uses Feller’s run-of-k recurrence to compute the exact probability of seeing at least one streak of length k — useful for analysing winning streaks, hitting streaks and A/B-test streak bias.

Enter slope in any one of percent (%), degrees (°), ratio (1 : n) or rise/run, and the tool instantly returns the other three — useful for hiking, cycling grade, ADA / BS 8300 ramp compliance and roof drainage.

Enter the outer frame opening, the photo window size, and the border style (centred or museum bottom-weighted) and get the four mat border widths so you can cut a custom mat or order a standard size.

Enter your and opponent Elo ratings, match result (win / draw / loss) and K-factor (10 / 20 / 40); the tool returns rating change and expected score using FIDE's standard Elo formula.

Enter unanswered questions, options per question and the penalty rule (no penalty / −¼ per wrong / −1/(n−1) per wrong); the tool returns expected score from pure guessing and a strategy recommendation — useful for SAT / GRE / TOEFL / HKDSE.

Enter the lottery number pool size (n) and how many numbers you pick (k, with optional bonus ball); the tool returns combinations and a "1 in X" jackpot probability. Works for Powerball, Mega Millions, UK Lotto, Mark Six and more.

Enter a positive integer n to evaluate 1³ + 2³ + … + n³ using the closed-form (n(n+1)/2)².

Enter coefficients a, b, c of a quadratic to find the parabola's vertex (h, k), axis of symmetry, discriminant, y-intercept and real roots (if any).

Enter two roots r₁, r₂ and a leading coefficient a — the tool expands into standard form y = ax² + bx + c and reports the vertex, axis of symmetry and the sum/product of roots (Vieta's formulas).

Two-way bijective base-26 conversion between spreadsheet column letters (A, Z, AA, AMJ) and column numbers (1, 26, 27, 1024) — handy for macros, formula offsets and CSV column references.

Enter two complex numbers a + bi and c + di to get the sum, difference, product and quotient, plus modulus, argument (in degrees and radians) and polar form.

Enter the number of disks n and seconds per move to get the minimum moves needed (2ⁿ − 1), total time and a quick reference table for the Tower of Hanoi puzzle.

Enter a positive integer n and Legendre's formula ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + … instantly returns how many trailing zeros n! ends with — no need to compute the factorial, works for arbitrarily large n.

Enter a message and a keyword to instantly get the Vigenère polyalphabetic substitution ciphertext / plaintext — the classic 16th-century "unbreakable" cipher used today to teach intro cryptography.

Enter offered traffic A in Erlangs (calls/hour × avg call minutes / 60) and a target blocking probability (e.g. 1 %); the Erlang B formula returns the minimum number of trunks / channels needed.

Enter pixel width × height, bits per pixel (8 / 16 / 24 / 32) and buffer count (single / double / triple) — get the frame-buffer memory size in KB, MB and MiB.

Enter available shift time, breaks and customer demand to get the *takt time* (seconds per unit), units per hour and units per minute — the lean-manufacturing pace required to match demand without over- or under-producing.

Enter process mean, standard deviation and upper / lower specification limits (USL / LSL) to compute Cp, Cpk, Cpu, Cpl and the implied sigma level — the staple Six Sigma / SPC capability indices.

Enter hour:minute (e.g. 3:15) to get the angle between hour and minute hands in degrees (with reflex angle) — the classic interview / olympiad problem.

Enter numerator p and denominator q to get the decimal expansion of p / q, the non-repeating prefix length, the repetend (cycle) length and the actual repeating digit string.

Compute the area A = (d₁ × d₂)/2 of a kite from its two diagonals, and the perimeter P = 2(a + b) from the two adjacent-side lengths.

Enter triangle base, height and prism length to get the volume, base area and total surface area (two triangles plus three rectangles) of a triangular prism.

Compute the volume of a pyramid frustum (truncated pyramid) from bottom area, top area and height via V = h/3 × (A₁ + A₂ + √(A₁·A₂)) — handy for sand piles, hoppers and stepped foundations.

Enter an upper limit N (≤ 1,000,000) and use the ancient Greek Sieve of Eratosthenes to list every prime ≤ N, with total count, largest prime, and the first 100 shown.

Enter a decimal or fraction (π, 3.14159, 22/7, 355/113…) and instantly get its simple continued-fraction expansion [a₀; a₁, a₂, …], the first 10 convergents and the error of each.

Enter the regular-hexagon side length a and prism height h to get volume (3√3/2 · a² · h) and total surface area (3√3 · a² + 6 · a · h) — useful for honeycomb panels, pencils and battery-cell sizing.

Enter any two of cone slant ℓ, height h or base radius r — solve for the third via the Pythagorean ℓ² = r² + h² and also get lateral surface area, apex angle and the flat-pattern sector angle.

Given base delay, multiplier, cap and retry count — list each attempt’s wait time (with jitter range) plus cumulative total wait. Used by API clients, SRE retry policies and distributed-system design.

Enter an ISBN-10 (with or without the trailing digit); the tool computes the correct check digit using the mod-11 weighted formula (the result may be "X" meaning 10) and validates the whole string. Handles books from the 1972–2006 era and the second-hand / antiquarian trade.

Enter the length, width and height of a cuboid (rectangular box) — the calculator returns volume V = l · w · h, surface area SA = 2 (lw + wh + hl) and the space diagonal d = √(l² + w² + h²).

Enter the main pool n and picks k (optionally a bonus pool m + bonus picks b); the calculator returns the single-ticket jackpot odds = 1 ÷ C(n,k) [× C(m,b)] and includes presets for Powerball, EuroMillions, Mark Six, Lotto Max and more.

Enter a real-world dimension and a scale ratio (e.g. 1:48) — the tool returns the matching model size; works in reverse too (measure the model → recover the real size). 19 common scale presets included (action figures 1:6, die-cast cars 1:24, HO rail 1:87, architecture 1:100 …). Useful for aircraft kits, model railways, armour, cars, architecture, Gundam and 3D-print rescaling.

Enter beats per minute (BPM) to look up the matching Italian tempo marking (Largo, Adagio, Andante, Moderato, Allegro, Vivace, Presto, Prestissimo …), or pick a marking to see the typical BPM range. Standard in classical scores, music-theory exams and DAW / Spotify tempo metadata.

Enter the 2×2 to 5×5 contingency table for two raters scoring the same items; the tool returns Cohen's κ — the chance-corrected agreement statistic — with its standard error, 95 % confidence interval and the Landis & Koch (1977) benchmark label (poor / slight / fair / moderate / substantial / almost perfect).

Enter song duration (mm:ss or seconds), tempo (BPM) and time signature (4/4, 3/4, 6/8, etc.); the tool converts both directions to total measures and total beats — useful for composing, arranging, podcast scoring, 30-second jingles and aligning sections when cutting video soundtracks.

Enter your number of *outs* (unseen cards that complete your hand) and which streets remain (turn-only, river-only or turn + river); the tool returns the *rule of 2 & 4* shorthand alongside the exact hypergeometric probability — the standard outs-to-equity teaching tool for Texas Hold'em, Omaha and stud variants.

Enter either a SMPTE timecode (HH:MM:SS:FF) or a total frame count, pick a frame rate (24 / 25 / 29.97 drop-frame / 30 fps), and the tool converts both ways. The staple of video editing, broadcast and animation pipelines.

Enter a log value y and a base b (10, e or custom), and the tool computes x = b^y — the inverse of log. Indispensable for unwinding pH, decibels, Richter, entropy and other log-scale formulas back to the underlying quantity.

Enter the cone's base radius and height (or slant height), and the tool applies SA = πr² + πr·ℓ (with ℓ = √(r² + h²)) to return the base, lateral and total surface area — the natural pair for the existing cone volume calculator.

Enter the size of two or three sets and their pairwise (and triple) intersections, and the tool applies the inclusion–exclusion principle |A∪B| = |A| + |B| − |A∩B| (extended to three sets) to return the union size — useful for Venn diagrams, probability, and SQL count queries.

Enter two parallel series of actual vs forecast values, and the tool computes MAPE = mean(|actual − forecast| ÷ |actual|) × 100% — the workhorse error metric in sales forecasting, demand planning and ML regression. Also returns SMAPE and MAE for comparison.

Enter probabilities P(A) and P(B), pick independent / mutually exclusive / custom dependence, and the tool returns P(A ∧ B), P(A ∨ B) and P(A | B) — bread-and-butter of high-school probability, interview questions and decision trees.

Enter the mean μ and standard deviation σ of a normal distribution; the tool returns the 1σ / 2σ / 3σ intervals with their coverage percentages (68.27% / 95.45% / 99.73%) and lets you look up the z-score of any value — staple of intro statistics, quality control and exam-score analysis.

Enter two integers (decimal, hex or binary); the tool computes AND, OR, XOR, NOT, left-shift and right-shift — for programmers, embedded engineers and CS exam prep.

Enter singles, doubles, triples, home runs and at-bats; the tool computes Slugging Percentage SLG = (1B + 2·2B + 3·3B + 4·HR) ÷ AB — a core sabermetric stat.

Enter 2-point makes, 3-point makes and total shot attempts; the tool returns eFG% = (FGM + 0.5·3PM) ÷ FGA — a fairer basketball shooting metric that weights 3-pointers.

Enter an integer; the tool checks whether it is a perfect number (the sum of its proper divisors equals itself — e.g. 6 = 1+2+3, 28 = 1+2+4+7+14) and lists all perfect numbers up to a chosen ceiling.

Enter any real number; the tool returns the value in scientific notation (a × 10ⁿ), engineering notation (exponent constrained to multiples of 3, a × 10³ᵏ) and the SI prefix form (kilo, mega, micro, nano…) — essential for engineering, electronics and physics work.

Enter n; the tool returns the n-th Tribonacci number (T₀=0, T₁=1, T₂=1, Tₙ = Tₙ₋₁ + Tₙ₋₂ + Tₙ₋₃) and lists the first n+1 terms. Successive ratios converge to the Tribonacci constant ≈ 1.83929.

Enter a positive integer; the tool repeatedly replaces it by the sum of the squares of its digits and checks whether the sequence reaches 1 (a *happy* number) or falls into the 8-cycle 4 → 16 → 37 → 58 → 89 → 145 → 42 → 20 → 4 (an *unhappy* number). The full iteration chain is shown.

Enter a positive integer; the tool checks whether it is a *narcissistic* (or *Armstrong*) number — its digits, each raised to the power equal to the digit count, sum back to the number itself. Example: 153 = 1³ + 5³ + 3³. It also lists all narcissistic numbers up to a chosen ceiling.

Enter a positive integer; the tool checks whether it is a *Harshad* (a.k.a. *Niven*) number — divisible by the sum of its own digits, e.g. 12 (1+2=3, 12 ÷ 3 = 4) or 1729 (1+7+2+9=19, 1729 ÷ 19 = 91). It also lists every Harshad number up to a chosen ceiling.

Enter a list of values (comma- or newline-separated); the tool sorts them descending, computes the cumulative percentage and highlights the "vital few" items that make up the first 80 % (or a configurable threshold) of the total — the standard Pareto-rule workflow for ABC inventory, sales contribution and bug triage.

Enter any 4-digit integer (not all the same digit). The tool repeatedly subtracts the ascending arrangement of its digits from the descending arrangement; in ≤ 7 steps the sequence always reaches *Kaprekar's constant* 6174. The full iteration chain is displayed.

Enter a positive integer n. The tool computes the aliquot sum m = σ(n) − n and then σ(m) − m; if the result equals n, the pair (n, m) is *amicable* (e.g. 220 ↔ 284, 1184 ↔ 1210). It also lists every amicable pair within a chosen ceiling.

Enter a positive integer n. The tool computes n² and checks whether its last digits reproduce n itself — for example 5² = 2*5*, 25² = 6*25*, 76² = 57*76*, 625² = 390*625*. These are the *automorphic* (or *curious*) numbers — finite truncations of the two non-trivial 10-adic idempotents.

Enter a positive integer. The tool repeatedly reverses its digits and adds the result back to the original until a palindrome appears or the iteration cap is reached. 196 is the smallest Lychrel candidate — no palindrome has been found despite > 10⁹ iterations.

Enter a positive integer n. The tool computes the divisor sum σ(n) and compares it to 2n: σ(n) < 2n is *deficient*, = is *perfect*, > is *abundant*. It also enumerates how many of each class appear below a chosen ceiling.

Enter a positive integer n. The tool checks whether n is a *Smith number* — a composite whose digit sum equals the digit sum of its prime factors counted with multiplicity. Example: 4937775 = 3 × 5 × 5 × 65837 (digit sum 42 = 3 + 5 + 5 + (6+5+8+3+7)).

Enter a positive integer n. The tool checks whether n is a *vampire number* — its digits can be rearranged into two equal-length "fangs" whose product is n, with the fangs not both ending in zero. Example: 1260 = 21 × 60.

Enter a positive integer n. The tool checks whether n is a *sphenic number* — a product of *exactly three distinct primes* (e.g. 30 = 2 × 3 × 5, 42 = 2 × 3 × 7, 66 = 2 × 3 × 11) — and lists all sphenic numbers up to a chosen ceiling.

Enter three side lengths a, b and c; the tool applies Heron's formula to compute the triangle's area without needing a height — handy for surveying, mapping, civil-engineering checks and homework.

Enter the number of sides n of a convex polygon; the tool returns vertex count, total diagonals (n(n−3)/2), interior-angle sum and each interior angle — useful for geometry homework and CAD polygon design.

Enter the number of distinct items n (e.g. card pack rarities or sticker types); the tool returns the expected number of draws to collect them all using E = n·Hₙ, plus its standard deviation — essential for gacha, trading-card and prize-collection planning.

Enter the total number of doors n and the number of empty doors the host reveals k; the tool returns the win probability for *switching* vs *staying* (covers classic 3-door and generalised variants) — a staple of probability courses.

Enter a positive integer n; the tool returns the Möbius function μ(n) — μ(1) = 1, μ(n) = 0 if n has a squared prime factor, otherwise (−1)^(number of distinct prime factors). Cornerstone of analytic number theory.

Enter n; the tool computes the Bell number B(n) — the number of ways to partition a set of n distinct elements into any number of non-empty subsets, evaluated with Bell's triangle recurrence. A staple of combinatorics.

Enter a positive fraction a/b (0 < a/b ≤ 1). The tool decomposes it into a sum of distinct unit fractions (1/n) using the Fibonacci–Sylvester greedy algorithm — the way fractions were written in the Rhind papyrus.

Enter a positive integer n. The tool computes p(n) — the number of ways to write n as a sum of positive integers ignoring order — via Euler's pentagonal-number-theorem recurrence. A classic of combinatorics.

Enter n and k. The tool computes S(n,k) — the number of ways to partition n distinct elements into exactly k non-empty subsets — using S(n,k) = k·S(n−1,k) + S(n−1,k−1). The row sums are Bell numbers.

Enter a positive integer n. The tool greedily writes n as a sum of non-consecutive Fibonacci numbers. Zeckendorf's theorem guarantees the representation exists and is unique — the basis of Fibonacci coding used in data compression.

Enter a starting string (typically "1"). The tool repeatedly "reads off" each run of identical digits as count-then-digit: 1 → 11 → 21 → 1211 → 111221 → … — Conway's audio-active sequence.

Enter index n. The tool computes the Padovan number via P(n) = P(n−2) + P(n−3) — Fibonacci-like but skipping one term: 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, … . Growth ratio is the plastic constant ρ ≈ 1.3247.

Enter n and k. The tool computes c(n,k) — the number of permutations of n elements with exactly k cycles — via the recurrence c(n,k) = (n−1)·c(n−1,k) + c(n−1,k−1). Row sums equal n!.

Enter a positive integer n. The tool computes the Carmichael function λ(n) — the smallest exponent such that a^λ(n) ≡ 1 (mod n) for every a coprime to n. λ is the "reduced totient" used in modern RSA.

Enter the edge length a. The tool returns volume V = (√2/3)·a³, surface area S = 2√3·a², circumradius R, inradius r and midradius ρ for the regular octahedron — useful for geometry, crystallography and 3D modelling.

Enter a positive integer n and an order k. The tool computes σ_k(n) = Σ_{d|n} d^k — at k=0 it equals the number of divisors d(n); at k=1 it equals the divisor sum σ(n), the building block of perfect / abundant / deficient classification.

Enter a positive integer n. The tool computes the Liouville function λ(n) = (−1)^Ω(n), where Ω(n) is the number of prime factors counted with multiplicity — deeply tied to the Riemann zeta function and a workhorse of analytic number theory.

Enter the modulus n. The tool computes the Pisano period π(n) — the period of the Fibonacci sequence modulo n, first noted by Leonardo Pisano (Fibonacci, 1202) and tabulated as OEIS A001175.

Enter a positive integer n. The tool decides whether n is a *practical number* — every integer 1 ≤ m ≤ n can be written as a sum of distinct positive divisors of n. Famous examples include 12 (the clock face) and 1, 2, 4, 6, 8, 12, 16, ….

Enter an index n. The tool uses BigInt to compute the Pell number P_n and half-companion H_n — the convergents H_n/P_n give the best rational approximations to √2 (OEIS A000129 and A001333).

Enter a positive integer p. The tool decides whether p is a *Sophie Germain prime* — both p and 2p+1 are prime. These primes power Diffie–Hellman / safe-prime RSA groups in modern cryptography and underpin the first partial results on Fermat's Last Theorem.

Enter a positive integer n. The tool decides whether n is a *highly composite number* — its divisor count d(n) strictly exceeds d(m) for every m < n. Studied systematically by Ramanujan in 1915, the sequence starts 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, … (OEIS A002182).

Enter the item average rating R, vote count v, overall site average C and the minimum-votes threshold m. The tool applies the IMDb Top 250 Bayesian weighted formula WR = (v/(v+m))·R + (m/(v+m))·C to return a credible weighted score — preventing a handful of 5-star votes from dominating rankings.

Enter a non-negative integer m. The tool decides whether m is a *pentagonal number* (there exists positive integer k with m = k(3k − 1)/2), and if so reports the index k and lists neighbouring pentagonal numbers. Pentagonal numbers power Euler's pentagonal number theorem and the O(√n) recurrence for the partition function p(n).

Enter a non-negative integer m. The tool decides whether m is pronic (the product of two consecutive integers, m = n(n+1)), returns the index n, the neighbouring pronic values and the identity P_n = 2·T_n where T_n is the n-th triangular number. OEIS A002378.

Enter the edge length a of a regular dodecahedron. The tool uses the closed form V = (15 + 7√5)/4 · a³ and S = 3·√(25 + 10√5) · a² and reports the volume, surface area, circumscribed-sphere radius R = a·√3·(1+√5)/4 and inscribed-sphere radius r = a·√(250+110√5)/20. The dodecahedron is the Platonic solid used in D12 dice, soccer-ball geometry and many viral capsids.

Enter the new observation x_t, the previous EMA_{t−1} and a smoothing factor α (or an equivalent period N, with α = 2/(N+1)). The tool computes EMA_t = α·x_t + (1−α)·EMA_{t−1} — the standard recurrence used in stock technical analysis, IoT signal smoothing and forecasting models.

Enter the frequencies of a set of symbols. The tool constructs the optimal prefix code by Huffman's greedy algorithm and returns each symbol's code length, the average code length L̄ = Σ p_i·ℓ_i and the Shannon entropy H = −Σ p_i·log₂ p_i — the standard pedagogical tool for data compression and coding theory.

Enter the family size m and the desired family-wise significance level α (typically 0.05). The tool returns the Bonferroni-corrected per-test critical value α_corrected = α/m and can transform a raw p-value into the corrected p_corr = min(1, m·p) — the most conservative classical correction for multiple-comparison testing.

Enter the two base radii r₁, r₂ and height h of a conical frustum. The tool returns volume V = πh/3·(r₁² + r₁r₂ + r₂²), lateral and total surface area, and slant height s — useful for cups, buckets, hoppers and stockpile estimates.

Enter the edge length a. The tool returns volume V = (5/12)(3+√5)·a³, surface area S = 5√3·a², and the circumscribed / inscribed / midsphere radii of a regular icosahedron — completing the Platonic-solid set.

Enter an integer n and the tool returns the Jacobsthal number J(n) — defined by J₀ = 0, J₁ = 1, J(n) = J(n−1) + 2·J(n−2) (OEIS A001045), with closed form J(n) = (2ⁿ − (−1)ⁿ) / 3.

Enter a z value. The tool returns the standard-normal CDF Φ(z) = P(Z ≤ z), the upper tail 1 − Φ(z) and the two-tailed 2(1 − Φ(|z|)) probability — using the Abramowitz & Stegun 7.1.26 erf approximation, accuracy < 1.5 × 10⁻⁷.

Enter two strings and the tool returns the Jaro score and the Jaro–Winkler similarity (0 = completely different, 1 = identical). Winkler's tweak rewards a common *prefix*, making it the go-to fuzzy-matching metric for names and addresses.

Enter a positive integer n. The tool lists the Farey sequence F(n) — every fraction in lowest terms between 0/1 and 1/1 whose denominator is ≤ n, in ascending order (OEIS A005728 counts each order's length).

Enter the radius r and the tool returns hemisphere volume V = (2/3)·π·r³, curved surface area 2πr², base-circle area πr² and total surface 3πr² — handy for domes, tank caps and hemispherical bowls.

Enter a recurring decimal (e.g. 0.1(6), 0.142857…); the tool applies the standard "multiply-by-10-and-subtract" algebra to convert it to its lowest-terms fraction p/q — handy for students, music theory (note subdivisions) and number theory.

Enter significance level α (or confidence 1 − α), degrees of freedom df and tail choice (one- or two-tailed); the tool returns the critical t* value — the workhorse number for hypothesis tests, confidence intervals and regression-coefficient significance; converges to the standard-normal z as df → ∞.

Enter numerator df₁, denominator df₂ and significance level α; the tool returns the right-tail F critical value F* — the standard cutoff for ANOVA, overall regression significance and variance-ratio hypothesis tests.

Enter degrees of freedom df and significance level α (right tail); the tool returns the χ²₍α,df₎ critical value via the Wilson–Hilferty cube-root approximation — used for goodness-of-fit, contingency-table independence and variance-confidence-interval tests.

Enter sample sizes n₁, n₂ and significance level α; the tool returns the Mann–Whitney U two-tailed / one-tailed critical value via the normal-approximation z = (U − μ_U) / σ_U — the standard non-parametric test of medians from two independent samples.

Enter regression R², sample size n and number of predictors k; the tool returns adjusted R² = 1 − (1 − R²)(n − 1) / (n − k − 1) — the model-comparison metric that penalises the spurious fit gained from simply adding more predictors.

Enter a reference and a hypothesis transcript; the tool computes WER = (Substitutions + Deletions + Insertions) / reference words via the Levenshtein edit distance — the gold-standard accuracy metric for speech recognition, machine translation and OCR systems.

Enter two paired data series; the tool returns the Spearman rank correlation ρ ∈ [−1, 1] — a non-parametric measure of monotonic association that needs no normality assumption and resists outliers.

Enter a dataset and the tool returns the *sample skewness* — both the Fisher–Pearson moment coefficient g₁ and the Excel / SPSS / SAS adjusted G₁, together with the skewness direction, the Bulmer interpretation band, mean and standard deviation.

Enter two paired columns (X, Y per row); the tool returns *Kendall τ-b* — concordant minus discordant pairs over total pairs (with the tie correction) — the rank-based companion to Spearman’s ρ, robust to outliers and recommended for small samples and tied data.

Enter the chi-square statistic χ², sample size N, and rows × columns; the tool returns Cramér’s V = √(χ² / (N · min(r−1, c−1))) — the standard *effect size* for a chi-square test of independence, bounded 0–1 and independent of N, complementing the raw p-value with the actual strength of association.

Enter the two group means, standard deviations and sample sizes; the tool returns both Cohen’s d and *Hedges’ g = d × J* where the bias correction J = 1 − 3/(4·df − 1) — the standard effect size used in systematic reviews and meta-analyses, fairer than raw Cohen’s d when any study has n < 20.

Enter two discrete probability distributions P and Q over the same bins; the tool returns D_KL(P‖Q) = Σ P(x) · log(P(x)/Q(x)) — the standard information-theoretic "information lost when Q is used to approximate P", reported in nats (natural log) and bits (log₂), as used across machine learning, Bayesian inference and information theory.

Enter a confusion matrix (TP / FP / FN / TN); the tool returns Precision, Recall, F1, configurable F-β, Accuracy and Specificity — the one-stop evaluator for any binary classifier.

Enter a confusion matrix (TP / FP / FN / TN); the tool returns the Matthews Correlation Coefficient — a balanced binary-classification metric on [−1, +1], more robust to class imbalance than F1 or accuracy, and recommended as the default binary metric by BMC Genomics (2020).

Enter x; the tool computes the Gauss error function erf(x) = (2/√π) ∫₀ˣ e⁻ᵗ² dt and the complementary erfc(x) = 1 − erf(x) — the core integral underpinning the normal-distribution CDF, the heat / diffusion equation and signal processing. Also returns the inverse erfInv(y).

Enter an observation vector x, a mean vector μ and a covariance matrix Σ (or a sample dataset); the tool returns D² = (x − μ)ᵀ Σ⁻¹ (x − μ) — the variable-scale-aware multivariate distance behind outlier detection, Hotelling's T² and Quadratic Discriminant Analysis.

Enter shape parameters α and β plus x ∈ [0,1]; the tool returns the Beta PDF f(x) = x^(α−1)·(1−x)^(β−1) / B(α,β) and its CDF (the regularised incomplete beta function) — the conjugate prior for proportions and the workhorse of Bayesian A/B testing.

Enter a dataset and a trim proportion p (e.g. 0.1 = drop 10% from each tail); the tool sorts, trims and averages what remains — a robust central-tendency estimate used by Olympic judging, sports refereeing and the trimmed-mean CPI.

Enter shape k, scale λ and x ≥ 0; the tool returns the Weibull PDF f(x) = (k/λ)·(x/λ)^(k−1)·e^(−(x/λ)^k) and CDF F(x) = 1 − e^(−(x/λ)^k) — the standard model for reliability, wind-speed distributions and insurance loss severity.

Enter total factor productivity A, labour L, capital K and the elasticities α, β; the tool returns Y = A · L^α · K^β, the marginal products MPL and MPK, and the returns-to-scale verdict (α + β > / = / < 1) — the workhorse production function of macroeconomics.

Enter calls per hour, average handle time (AHT) and number of agents; the tool applies the Erlang C formula to return the wait probability, average speed of answer (ASA), service level (% answered within X seconds) and agent occupancy — the textbook staffing model used by call centres, emergency rooms and IT support desks.

Enter location μ and scale σ (the mean and SD of ln X) plus x > 0; the tool returns the lognormal PDF f(x) = 1 / (xσ√(2π)) · exp(−(ln x − μ)² / (2σ²)), CDF Φ((ln x − μ) / σ) and the mean, median, mode and variance — the standard model for incomes, stock prices, biological measurements and reliability life-times.

Enter rate λ > 0 and x ≥ 0; the tool returns the exponential PDF f(x) = λ·e^(−λx), CDF F(x) = 1 − e^(−λx), mean 1/λ and median ln(2)/λ — the canonical waiting-time distribution for Poisson processes, queueing and memory-less reliability.

Enter values xᵢ and weights wᵢ; the tool returns the weighted mean x̄_w = Σ(wᵢ·xᵢ) / Σwᵢ — the right average when each value should count proportionally to its weight (course credits, portfolio holdings, survey strata).

Enter two sets (comma-separated); the tool returns the Jaccard similarity coefficient J(A, B) = |A ∩ B| / |A ∪ B| and the Jaccard distance 1 − J — the workhorse similarity metric for NLP token overlap, recommendation systems, clustering and plagiarism detection.

Enter the expectation E[X] of a non-negative random variable and a threshold a; the tool returns Markov's inequality bound P(X ≥ a) ≤ E[X]/a — the simplest distribution-free upper bound on the tail of a non-negative random variable.

Enter a real number x; the tool returns the sigmoid σ(x) = 1/(1+e^(−x)), its complement 1−σ(x), the derivative σ′(x) = σ(x)·(1−σ(x)) and the inverse logit(p) = ln(p/(1−p)) — the core transform behind logistic regression, neural-network activation functions and probability ↔ log-odds conversion.

Paste a list of numbers (comma- or newline-separated); the tool returns the median, MAD = median(|xᵢ − median|), the robust σ̂ ≈ 1.4826 × MAD, and flags outliers using the 3·MAD rule (Hampel 1974, Leys 2013) — a far more robust dispersion estimator than the standard deviation when your data has outliers.

Enter the true value y, the predicted value ŷ and the threshold δ; the tool returns the Huber loss — ½·(y − ŷ)² for |y − ŷ| ≤ δ and δ·(|y − ŷ| − ½·δ) otherwise — plus the residual, gradient and a comparison against MSE / MAE. Peter Huber's 1964 hybrid L2 / L1 loss is the workhorse of robust regression, scikit-learn's HuberRegressor, PyTorch's nn.HuberLoss, and the *Smooth L1* used in Fast R-CNN / Faster R-CNN bounding-box regression.

Enter a target number of successes r, a per-trial success probability p and a failure count k; the tool returns the negative binomial PMF P(X = k) = C(k + r − 1, k)·pʳ·(1 − p)ᵏ and its CDF — the distribution of failures before reaching r successes in a Bernoulli process, and the workhorse alternative to Poisson when count data is over-dispersed.

Enter two discrete probability distributions P and Q; the tool returns the *Bhattacharyya coefficient* BC(P, Q) = Σ√(p_i · q_i) ∈ [0, 1] and the *Bhattacharyya distance* D_B = −ln(BC), along with the *Hellinger distance* √(1 − BC) and the angle between √P and √Q on the unit hypersphere — the textbook overlap measure for image retrieval, feature selection and speech recognition, and a more numerically robust alternative to KL divergence when supports may be disjoint.

Enter two discrete probability distributions P and Q; the tool returns the Jensen-Shannon divergence JSD(P‖Q) = ½·KL(P‖M) + ½·KL(Q‖M) with M = ½(P + Q) — the symmetric, bounded (∈ [0, ln 2]) cousin of KL divergence, used as a distance metric in t-SNE, GAN evaluation and NLP topic modelling.

Enter a list of real-valued logits and a temperature T; the tool returns the *softmax* σ(z_i) = exp(z_i / T) / Σ exp(z_j / T), the argmax class, the probability sum (a numerical sanity check) and the Shannon entropy in nats and bits — converting any real vector into a probability distribution that sums to 1, the standard output layer of multinomial logistic regression and neural-network classifiers.

Enter precision P, recall R and a weighting factor β; the tool returns *F_β = (1 + β²) · P · R / (β² · P + R)* — the generalisation of F1 (β = 1) where β > 1 weights recall higher (disease screening, fraud detection) and β < 1 weights precision higher (spam filtering, recommender systems).

Enter two frequencies f₁ and f₂; the tool applies *n (cents) = 1200 · log₂(f₂ / f₁)* to give the *cents* interval between them (one semitone = 100 cents, one octave = 1200 cents) — the international unit used in instrument tuning, just-intonation vs equal-temperament comparison and microtonal music analysis.

Enter two binary fingerprint vectors; the tool returns the *Tanimoto coefficient T(A, B) = c / (a + b − c)*, where a, b are the number of 1-bits in each vector and c the number of common 1-bits — the de-facto standard for chemical-similarity search and pharmaceutical virtual screening (Morgan / ECFP fingerprints, with T ≥ 0.85 typically flagged as bioactivity-similar).

Enter a list of numbers and a winsorisation fraction k %; the tool *replaces* the bottom-k % and top-k % extreme values with the k-th and (1 − k)-th percentile values, then averages — a *robust* location estimate that, unlike the trimmed mean, preserves the original sample size and is widely used in SPC, psychology and insurance-claim analysis.

Enter a list of numbers; the tool returns the *sample excess kurtosis g₂ = m₄ / m₂² − 3* and the Fisher bias-corrected estimator *G₂* (the Excel KURT formula) — the standard measure of *tail heaviness* relative to a normal distribution, used in financial tail-risk, QC outlier detection, insurance claim modelling and ML data diagnostics.

Enter two paired columns (before / after) — or a single column of differences directly; the tool returns the mean and SD of the differences, the *t = d̄ ⁄ (s_d ⁄ √n)* statistic, df = n − 1, and the two-tailed p-value — the standard hypothesis test for within-subject before/after comparisons (drug response, training effect, taste panel, A/B with the same users).

Enter the (n, mean, SD) of two independent samples; the tool returns Welch's *t = (x̄₁ − x̄₂) ⁄ √(s₁² ⁄ n₁ + s₂² ⁄ n₂)*, the Welch–Satterthwaite degrees of freedom and the two-tailed p-value — the robust drop-in replacement for Student's t-test that does not assume equal variances, and the default of R, SPSS and SciPy `ttest_ind(equal_var=False)`.

Enter k ≥ 2 independent groups of data (or each group's (n, mean, SD) summary); the tool returns *F = MS_between ⁄ MS_within*, df₁ = k − 1, df₂ = N − k, the right-tail p-value, plus effect-size η² and Hays' ω² — the standard hypothesis test for comparing the means of two or more groups, the workhorse of experimental design, agricultural trials, A/B/C marketing tests and dose-response clinical studies.

Enter a model's log-likelihood ln L, sample size n and number of parameters k; the tool returns *AIC = 2k − 2 ln L*, the small-sample corrected *AICc* and *BIC = k · ln n − 2 ln L* — the gold-standard model-selection criteria, with smaller values better and ΔAIC > 10 typically enough to rule out the weaker model.

Enter two independent samples (any ordinal data); the tool computes the *U statistic* from joint ranks, the tie-corrected standard error, the *z* score and the two-sided p-value — the distribution-free alternative to Student's t-test for comparing the location of two groups.

Enter an N × k matrix of N subjects × k conditions (the tool ranks row-by-row); it returns the *Friedman Q statistic*, df = k − 1, the chi-square approximate p-value and Kendall's W concordance — the non-parametric alternative to repeated-measures ANOVA and the standard test for sensory ratings, Likert scores and paired three-or-more condition designs.

Enter k ≥ 2 independent samples; the tool returns the tie-corrected *Kruskal–Wallis H statistic*, df = k − 1 and the chi-square approximate p-value — the distribution-free alternative to one-way ANOVA, robust to outliers and the standard multi-group test in ecology, medicine and the social sciences.

Enter a 2×2 paired-binary table (a, b, c, d); the tool returns *McNemar χ² = (b − c)² ⁄ (b + c)*, the Edwards continuity-corrected form, the exact binomial p-value, the χ²(1) p-value and the discordant-pair odds ratio OR = b ⁄ c — the standard hypothesis test for paired binary outcomes (before / after treatment, two diagnostic tests on the same patients, item answered right ⁄ wrong).

Enter a 2×2 contingency table (a, b, c, d); the tool uses the *hypergeometric distribution P = C(a+b,a)·C(c+d,c) ⁄ C(N,a+c)* to enumerate every configuration consistent with the marginal totals, returning the one- and two-tailed exact p-values plus the odds ratio OR — Fisher's (1922) gold-standard small-sample test, used whenever any expected cell drops below 5 and χ² loses validity.

Enter a list of numbers; the tool computes the skewness S, excess kurtosis K and the *JB = (n ⁄ 6) · (S² + K² ⁄ 4)* statistic with its χ²(2) p-value — Jarque & Bera's (1980) joint *skewness + kurtosis* normality test, the default residual diagnostic in EViews, STATA and R `tseries::jarque.bera.test`, widely used in econometrics regression diagnostics.

Enter the degrees of freedom df and the significance level α (or a confidence level like 95 %); the tool returns the two-tailed critical value *t_(α/2, df)* and the one-tailed *t_(α, df)* — Student's (Gosset, 1908) t-distribution inverse CDF used to construct confidence intervals *x̄ ± t · s ⁄ √n* and the rejection boundaries of every t-test.

Enter wins, losses and ties; the tool returns the winning percentage (W + 0.5·T) ⁄ (W + L + T) in baseball .XXX and percentage form, plus the ties-excluded rate W ⁄ (W + L).

Enter points scored and allowed; the tool uses Bill James’ Pythagorean formula expected win% = RS^e ⁄ (RS^e + RA^e) to estimate a team’s "deserved" win rate and projected season wins.

Enter your remaining score (2–170); the tool looks up the standard double-out checkout table and returns a suggested 2- or 3-dart finish, flagging the bogey numbers that cannot be checked out.

Enter the decimal odds of several legs and your stake; the tool multiplies the legs to give the combined parlay odds, total payout, profit, implied probability and American odds.

Enter a batting line (hits, walks, hit-by-pitch, total bases, etc.) to compute on-base percentage (OBP), slugging (SLG) and their sum, OPS.

Enter a pitcher's walks, hits allowed and innings pitched to get WHIP = (walks + hits) ÷ innings pitched, a core measure of how many baserunners a pitcher allows.

Enter the pot size and the amount to call to get your pot odds, the break-even equity needed, and — from your number of outs — your chance of hitting, so you can tell whether a call is profitable.

Enter the total games in a season, the leader's wins and the trailing team's losses to get the "magic number" — the combined leader-wins-plus-rival-losses that clinches a division or playoff spot.

Enter a Dungeons & Dragons 5e ability score to get its modifier = floor((score − 10) / 2), plus the standard point-buy cost for building a character.

Enter any three known terms of the proportion a/b = c/d and solve for the missing value x by cross-multiplication.

Enter two known concentrations and a desired concentration to get the mixing ratio of the two using the alligation (cross) method.

Enter two fractions (mixed numbers allowed) and an operator to get the result as a simplified fraction, mixed number and decimal.

Reduce a square root (or any nth root) to simplest radical form, e.g. √72 = 6√2, with the decimal approximation.

Enter two paired data series to get the sample and population covariance and see how the variables move together.

Enter a total amount and a ratio (e.g. 2:3:5) to split it into each share, with the simplified ratio and each part's percentage.

Allocate seats to parties from vote counts and total seats using the D'Hondt highest-averages method.

Allocate seats using the Sainte-Laguë (Webster) divisor method from vote counts and total seats.

Allocate seats by the largest-remainder method using a Hare or Droop quota.

Show Benford's Law expected first-digit distribution and compare it with your own data set.

From each hole’s strokes, par and handicap strokes received, compute Stableford points and the total score.

Compute a goalie or keeper save percentage (Sv%) from saves and goals against, plus the saves needed to reach a target Sv%.

Compute a team’s Net Run Rate (NRR) for standings from runs scored, runs conceded and overs, including the full-quota rule when a side is bowled out.

Find your probability of winning at least one prize from the total tickets, the tickets you hold and the number of prizes drawn.

Compute every binomial coefficient in the nth row of Pascal's triangle, along with the row sum (2ⁿ).

From each voter’s weight and the passing quota, compute the Banzhaf power index — each voter’s share of swing (critical) votes.

Estimate the GPU VRAM needed to run a large language model from its parameter count, quantization, context length and batch size.

Compute the volume and approximate surface area of an ellipsoid from its three semi-axes a, b and c.

Compute the nth Bernoulli number Bₙ as an exact rational (numerator and denominator).

From home runs, walks, hit-by-pitch, strikeouts and innings pitched, compute FIP — an ERA-scale metric that strips out defence and luck.

Compute BABIP from hits, home runs, at-bats, strikeouts and sacrifice flies to gauge how much of a hitter or pitcher line is luck.

Work out Isolated Power (ISO = SLG − AVG) from doubles, triples, home runs and at-bats to measure a hitter’s raw extra-base power.

Estimate the runs a player creates for their team using Bill James’ basic Runs Created formula from on-base, total bases and at-bats.

Compute the root mean square (quadratic mean) of a set of numbers, with the arithmetic mean, peak value and crest factor.