LMTD (Log Mean Temperature Difference) Heat Exchanger Calculator

Enter any two of voltage, current, resistance, or power — the calculator solves for the other two using V = IR and P = VI.

Enter any two of distance, time and speed to get the third — with km/h, mph, m/s, km, miles, hours and minutes supported.

Compute density from mass and volume (ρ = m / V), or solve for the missing variable. Built-in reference table for 19 common substances.

Enter launch speed, angle and height to compute projectile range, peak height and flight time (no air resistance). Pick from Earth, Moon, Mars and more.

Compute the wind chill (feels-like temperature) from air temperature and wind speed using the 2001 Environment Canada / US NWS formula, with frostbite risk levels.

Compute dew point from air temperature and relative humidity using the Magnus formula — handy for HVAC, photography and weather analysis.

Compute kinetic energy KE = ½ m v² with mixed units (kg / g / lb and m/s / km/h / mph) and see the result in joules, kilojoules, food calories, foot-pounds and watt-hours.

Enter any three of initial amount, remaining amount, elapsed time and half-life to solve for the fourth — useful for radioactive decay, drug pharmacokinetics and radiometric dating.

Pick the colour bands and instantly read the resistance and tolerance — 4-band and 5-band notations supported, with Ω / kΩ / MΩ formatting and a closest E12 / E24 preferred-value check.

Enter two latitude/longitude pairs to compute the great-circle distance using the haversine formula (km, miles, nautical miles), with bearing and midpoint.

Solve any one of C₁, V₁, C₂, V₂ from the dilution equation C₁V₁ = C₂V₂ — a daily lab essential for chemistry, biology and pharmacy work.

Two 80 dB sound sources do not equal 160 dB. Enter multiple dB values to compute the combined SPL, and subtract background noise to recover the signal alone.

Enter up to 8 resistor values to see the series total (R₁ + R₂ + …) and the parallel total (1 / Σ(1/Rᵢ)) at the same time.

Convert between electromagnetic wavelength and frequency via c = λf, with the matching spectrum band (radio / microwave / visible / X-ray / γ) and photon energy.

Compute the capacity of vertical or horizontal cylindrical, rectangular and spherical tanks, including partial-fill volumes at a given liquid level.

Enter the pendulum length and local gravity to get the period, frequency and angular frequency, with Earth/Moon/Mars/Jupiter presets — and reverse-solve for the length needed to hit a target period.

Enter air temperature and relative humidity to get the apparent temperature (NOAA Rothfusz heat index) and the corresponding heat-stress risk band.

Enter speed, reaction time and road friction to estimate reaction, braking and total stopping distance.

Enter the refractive indices of two media and an angle of incidence — get the refraction angle and critical angle from Snell's law (n₁ sin θ₁ = n₂ sin θ₂).

Enter capacitance (F, mF, µF, nF, pF) and voltage to compute the stored energy (E = ½CV²) and charge (Q = CV) on a capacitor.

Enter altitude to compute the boiling point of water (°C / °F) and local air pressure using the ICAO standard atmosphere and the Antoine equation — useful for hiking, cooking and high-altitude baking.

Solve Q = m × c × ΔT for any one of heat energy, mass, specific heat capacity or temperature change — with presets for water, aluminium, iron, copper, glass, air and more.

Convert between pH, pOH, hydrogen-ion concentration [H⁺] and hydroxide concentration [OH⁻] — with acid / neutral / alkaline classification.

Pick the unknown (P, V, n or T), enter the other three and PV = nRT is solved instantly — works in Pa / kPa / atm / bar / mmHg / psi, m³ / L / mL, mol / mmol / kmol and K / °C / °F.

Enter two point charges and the separation distance to compute the electrostatic force between them via F = kₑ·q₁·q₂/r² (attractive or repulsive).

Enter two masses and the distance between them to compute the gravitational attraction via F = G·m₁·m₂/r².

Given any two of the three quantities (object distance u, image distance v, focal length f), solve for the remaining one and the lateral magnification.

Enter the observer eye height above the surface to compute the distance to the geometric and refraction-corrected horizon.

Given any two of spring constant k, displacement x or restoring force F, solve for the third and the elastic potential energy U = ½kx².

Enter fluid density, submerged volume and gravitational acceleration to compute the buoyant force F = ρ V g, plus whether the object floats, sinks or stays neutral.

Enter the input voltage and two series resistor values to find the divider output voltage, current and power dissipated in each resistor.

Enter the mass and radius of a celestial body (or pick Earth, Moon, Mars and other presets) to compute the minimum surface launch speed v = √(2GM/r) needed to escape its gravity.

Enter the source frequency, observer/source velocities and wave speed (sound or light) to compute the observed frequency shift due to the Doppler effect.

Enter initial temperature, ambient temperature, cooling constant and elapsed time to estimate an object's temperature with T(t) = T∞ + (T₀ − T∞)·e^(−kt), plus half-cooling time and time constant.

Enter mass and radius, then linear speed, angular speed or period, and instantly read off centripetal force F = m·v²/r, centripetal acceleration, tangential speed, angular speed, period and frequency.

Enter inductance L (H) and capacitance C (F) to compute the resonant frequency f = 1 / (2π√(LC)) of an LC tank circuit, plus its period and angular frequency.

Enter the air temperature and compute the speed of sound in dry air using v = 331.3 × √(1 + T/273.15) — output in m/s, km/h, mph, ft/s plus the "count-the-seconds" thunder distance rule.

Enter fluid density, velocity, characteristic length and viscosity to compute the Reynolds number and classify the flow as laminar, transitional or turbulent.

Enter the spring constant k and displacement x to instantly compute the elastic potential energy stored in a Hookean spring via U = ½·k·x², with conversions to kJ, kcal, ft·lbf and Wh for easy comparison.

Use A = ε·c·ℓ to compute absorbance, transmittance and concentration — any three of the four inputs determines the fourth.

Compute orbital period from semi-major axis and central body mass via T² = 4π²·a³/GM, or invert to recover the semi-major axis — with presets for the Sun, Earth, Moon and Jupiter.

Enter fluid density, velocity, drag coefficient Cd and frontal area and compute the drag force from Fd = ½·ρ·v²·Cd·A — handy for cycling, automotive, ballistic and skydiving scenarios.

Compute the hydrostatic pressure P = ρ·g·h from fluid density, depth and gravity, and convert it to kPa, bar, psi, atm, mmHg and metres of water — useful for diving, aquariums and piping.

Enter pKa together with the conjugate-base [A⁻] and weak-acid [HA] concentrations and apply the Henderson–Hasselbalch equation to compute buffer pH, the buffer ratio and the effective buffering range.

Enter mass, incline angle and friction coefficients (or pick a preset like steel-on-steel or rubber-on-concrete) to compute normal force N, maximum static friction fs,max = μs·N, kinetic friction fk = μk·N and the critical angle θc — and instantly see whether the block stays at rest or slides down the slope.

Enter driving and driven gear tooth counts plus input RPM and torque to compute gear ratio, output RPM, output torque and mechanical advantage.

Enter solute mass, molecular weight and solution volume to compute molarity (mol/L); solve for any one unknown.

Convert moment magnitude (Mw) to released energy (joules and TNT equivalent) via the Gutenberg–Richter relation log₁₀E = 1.5M + 4.8, with a comparison to landmark historical earthquakes.

Enter the actual mass of product recovered and the theoretical yield to compute % yield = actual ÷ theoretical × 100%, with an indicative classification (poor / moderate / good / excellent).

Pick a common shape (solid sphere, hollow sphere, solid cylinder, thin-walled cylinder, thin disk, slender rod about centre or end, rectangular plate) and enter mass and dimensions to get the rotational moment of inertia I = k·m·r² / k·m·L².

Enter air temperature, barometric pressure and relative humidity to compute air density (kg/m³) via the CIPM partial-pressure form and the Magnus-Tetens saturation vapour pressure — useful for cyclists, runners, pilots and aerodynamics estimates.

Enter a fall height (and optional mass / gravity) to compute fall time, impact velocity and kinetic energy via h = ½·g·t² and v = √(2·g·h). Preset gravities for Earth, Moon, Mars and more.

Enter a chemical formula (e.g. H2SO4, Ca(OH)2, CuSO4·5H2O) and the tool sums the IUPAC standard atomic weights element by element to return the molar mass in g/mol — useful for chemistry homework and lab weighing.

Enter any two of force, mass and acceleration and the tool solves for the third — handy for high-school physics, machine design, vehicle braking and elevator safety factors.

Enter mass and molar mass (g/mol), or moles, and the tool converts via n = m / M, also reporting the particle count N = n · Nₐ — the everyday workhorse of chemistry lab weighing and stoichiometry problems.

Enter a velocity v (as a fraction of c or in m/s) and compute the special-relativity Lorentz factor γ = 1/√(1 − v²/c²), together with the time-dilation factor, the length-contraction ratio and the relativistic kinetic energy.

Enter surface area A, temperature T (kelvin) and emissivity ε, then compute the radiant power P = ε σ A T⁴ under the Stefan–Boltzmann law — the standard formula for thermal radiation, the solar constant and stellar luminosity estimates.

Enter the moles (or mass + molar mass) of each component in a mixture and compute the mole fraction xᵢ = nᵢ / Σ nⱼ for every component, with the total checked to equal 1 — used in Raoult's law, gas mixtures and thermodynamic analysis.

Enter mass, frontal area, drag coefficient and air density and the tool returns the terminal velocity v_t = √(2mg / (ρ·A·Cd)) — the speed at which drag balances gravity, with presets for skydivers, raindrops, baseballs and feathers.

Enter applied force, cross-sectional area, original length and the change in length. The tool returns the engineering stress σ, strain ε, Young's modulus E = σ/ε and the elongation, alongside a reference table of common materials (steel, copper, aluminium, concrete, rubber).

Enter a mass (or energy) and the tool uses Einstein's E = mc² to compute the other side, expressing the result in joules, kilowatt-hours, megatonnes of TNT and electron-volts — and showing just how staggering even 1 g of fully-converted matter is.

Enter elevation, velocity and pressure at two points and the tool applies P + ½ρv² + ρgh = constant from Bernoulli's equation to solve for the missing variable — the foundation of pipe flow, Venturi meters, Pitot tubes and aerofoil lift.

Enter the spring constant k and mass m; the tool returns the simple-harmonic period T = 2π√(m/k), frequency f and angular frequency ω, and can also solve for k — the foundation of physics labs, mechanical vibration and MEMS sensor design.

Enter resistance R and capacitance C; the tool returns the RC circuit time constant τ = R × C, the 63.2% / 99.3% charging times (1τ / 5τ) and the voltage percentage at any time t during charging or discharging — the workhorse for electronics design, RC filters, oscillator timing and Arduino debounce.

Enter hot-reservoir temperature T_h and cold-reservoir T_c (units auto-handled in °C / K / °F); the tool returns the Carnot maximum efficiency η = 1 − T_c / T_h, the thermodynamic upper bound for any real heat engine — IC engines, thermal power stations and refrigerators.

Enter any one of linear speed, radius, period, frequency or RPM; the tool interconverts angular velocity ω (rad/s), frequency f (Hz), period T, revolutions per minute (RPM) and rim speed v — for circular motion problems, motor specs, orbital mechanics, centrifuges and any spinning object.

Enter two particle masses m₁ and m₂; the tool applies the reduced-mass formula μ = m₁·m₂ / (m₁ + m₂) to give the effective inertial mass for two-body problems — the building block that reduces orbital mechanics, Keplerian motion, vibrational spectroscopy and collision analysis to single-body equations.

Enter a wavelength or frequency; the tool applies the Planck relation E = hf = hc/λ to return the energy of a single photon in joules and electron-volts (eV), plus the visible-light colour band where applicable — the foundation of physics, chemistry and spectroscopy problems.

Enter a blackbody temperature in kelvin; the tool applies Wien's displacement law λ_max·T = b to return the peak wavelength and corresponding frequency, and can invert to estimate temperature from a measured wavelength — the foundation of solar spectra, thermal imaging and CMB analysis.

Enter initial length L₀, temperature change ΔT and the linear expansion coefficient α (or pick a preset material); the tool returns ΔL = α·L₀·ΔT and the new length — used for bridge expansion joints, rail track gaps, pipework thermal allowances and more.

Enter initial and final angular velocity plus the time interval (or tangential acceleration and radius); the tool returns the angular acceleration α and converts between rad/s² and rpm/s — a basic quantity in rotational dynamics, rotor engineering and motor analysis.

Enter any three of plane spacing d, diffraction angle θ, order n and wavelength λ; the tool solves Bragg's law nλ = 2d sinθ for the missing one — the cornerstone of X-ray crystallography and materials characterisation.

Enter initial velocity u, final velocity v and elapsed time t; the tool returns the average acceleration a = (v − u) / t along with the displacement s = ½(u + v)·t — the entry-point of Newtonian kinematics.

Enter a particle's mass and speed; the tool applies the de Broglie relation λ = h / (mv) to return the matter-wave wavelength, momentum and kinetic energy — the cornerstone of intro quantum mechanics, electron-microscope resolution and cold-neutron experiments.

Enter a mass in kilograms, solar masses or Earth masses; the tool applies r_s = 2GM/c² to return the Schwarzschild radius (event horizon) and equivalent density — the headline number for any black-hole conversation in astrophysics, GR intro courses and pop-science Q&A.

Enter battery capacity (in Wh or Ah + voltage), load power, depth of discharge and inverter efficiency; the tool returns the realistic usable runtime in hours. Use it to size UPS units, solar-storage banks, portable power stations and 12 V car fridges.

Enter the total current and two parallel resistor values; the tool applies the current-divider rule I₁ = I·R₂/(R₁+R₂) to compute each branch current, the equivalent resistance, the shared voltage and the power dissipated in each resistor — a staple for circuit analysis, PCB design and EE coursework.

Enter inductance L and frequency f; the tool returns the inductive reactance X_L = 2πfL and the angular frequency ω — used in filter design, impedance matching and AC circuit analysis.

Enter the object speed and the local air temperature (the tool derives a from temperature); returns the Mach number M = v ⁄ a and classifies the regime as subsonic, transonic, supersonic or hypersonic — a standard tool for aviation and fluid dynamics.

Pick a pulley configuration (fixed, single movable, block-and-tackle or differential), enter the load; the tool returns the input force required, ideal & actual mechanical advantage and the rope length pulled — staple tool for physics class and rigging.

Enter the enthalpy change ΔH, entropy change ΔS and absolute temperature T; the tool applies ΔG = ΔH − TΔS to give the free-energy change and flags whether the reaction is spontaneous (ΔG < 0), at equilibrium (ΔG = 0) or non-spontaneous (ΔG > 0) — a staple of chemical thermodynamics, biochemistry and materials science.

Enter specific impulse Isp, initial mass m₀ and final (dry) mass m_f; the tool applies Δv = Isp · g₀ · ln(m₀ ⁄ m_f) to give the ideal velocity change a rocket can deliver — fundamental for mission planning, orbital mechanics and Kerbal Space Program players alike.

Enter the wavelength or frequency of incident light plus the metal's work function φ; the tool applies Einstein's photoelectric equation KE = hf − φ to give the maximum kinetic energy of ejected electrons, the stopping voltage V₀ and whether the threshold frequency is met.

Enter the material thermal conductivity k, area A, thickness L and temperature difference ΔT; the tool applies Fourier's law Q = k·A·ΔT / L to give the steady-state heat flow (W) and derives the R-value (thermal resistance) — fundamental for wall insulation, glazing, CPU heatsink and energy-audit calculations.

Enter the parallel fraction p of a program and the number of processors N; the tool applies Amdahl's law S = 1 / ((1 − p) + p ⁄ N) to give the theoretical maximum speedup — essential for parallel computing, GPU programming, HPC capacity planning and data-engineering decisions.

Enter the signal and noise power (or voltage); the tool applies SNR(dB) = 10·log₁₀(P_s ⁄ P_n) or 20·log₁₀(V_s ⁄ V_n) and classifies the result for communications, audio or instrumentation use — fundamental for telecom, recording and measurement.

Enter the activation energy Eₐ, pre-exponential factor A and temperature T; the tool returns the reaction rate constant k via Arrhenius k = A·exp(−Eₐ ⁄ RT) and the rate ratio between two temperatures — the standard tool for chemical kinetics, food shelf-life and drug stability.

Enter the intensity at one distance; the tool applies I₂ = I₁ × (d₁ ⁄ d₂)² to return intensity at any other distance, along with the equivalent dB change (ΔL = 20·log₁₀(d₁ ⁄ d₂)) — a workhorse for photography, stage lighting, audio engineering, radiation safety and radio link planning.

Enter current, one-way wire length, conductor size (AWG) and system type (single-phase / three-phase); the tool returns voltage drop and % drop via V_drop = 2·I·R·L (1-φ) or √3·I·R·L (3-φ) and warns when it exceeds the NEC 3% guideline — essential for home wiring, solar runs and long-distance equipment feeds.

Enter capacitance C and frequency f; the tool returns the capacitive reactance X_C = 1/(2πfC) and the angular frequency ω — used for filter design, AC circuit analysis and impedance matching, complementing the existing inductor reactance tool.

Enter mass, incline angle and coefficient of friction; the tool applies Newton's second law to return net force along the slope, acceleration, normal force and the push needed to hold or move the object — a staple for high-school / first-year physics and basic mechanical design.

Enter the two masses m₁ and m₂ hung from a fixed pulley; the tool returns the system acceleration via a = (m₁ − m₂)g ⁄ (m₁ + m₂), the rope tension T and the heavier-mass direction — the standard quick-reference for a classic mechanics textbook problem.

Enter the drop height h and the rebound height h′; the tool applies e = √(h′ ⁄ h) to compute the coefficient of restitution (COR), the energy-loss percentage and the post-impact/pre-impact speed ratio — the standard tool for physics labs and sports engineering (tennis, basketball, golf).

Enter two masses m₁, m₂ and pre-collision velocities v₁, v₂; the tool applies momentum conservation m₁v₁ + m₂v₂ = (m₁ + m₂)v′ to find the common post-collision velocity, plus energy lost (to heat/sound/deformation) and pre/post kinetic energies — the standard tool for physics class and accident-reconstruction.

Enter two temperatures plus one saturation vapor pressure (and the molar enthalpy of vaporisation ΔHvap); the tool applies ln(P₂ ⁄ P₁) = −ΔHvap ⁄ R × (1 ⁄ T₂ − 1 ⁄ T₁) to return the vapor pressure at the other temperature, or the boiling point at altitude. A staple of chemistry, HVAC, brewing, cooking and meteorology.

Enter the solute mass, molar mass, solvent mass, the solvent freezing-point depression constant Kf and the van't Hoff factor i; the tool applies ΔTf = i · Kf · m to return the temperature drop and the new freezing point. A staple of general chemistry, food science, road de-icing and antifreeze formulation.

Enter the redshift z and the Hubble constant H₀ (default Planck 2018 value 67.4 km/s/Mpc); the tool returns recession velocity v = cz, comoving distance d = v ⁄ H₀, and the relativistic-Doppler form v_rel = c · ((1+z)² − 1) ⁄ ((1+z)² + 1) for high-z work. The standard back-of-the-envelope tool for estimating cosmological distances.

Enter two or more independent sound levels (dB); the tool combines them using L_total = 10 log₁₀(Σ 10^(Lᵢ ⁄ 10)). Explains why two equally loud machines together produce only a 3 dB increase rather than double — essential for engineering acoustics and noise assessments.

Enter real power P (kW) plus either apparent power S (kVA) or the power factor cos φ; the tool computes the missing two using S² = P² + Q² and PF = cos φ, and returns the phase angle. Essential for industrial loads, motor sizing and UPS planning.

Enter the incident photon wavelength and scattering angle; the tool returns the Compton shift Δλ = (h ⁄ m_e c)(1 − cos θ), the scattered-photon wavelength and the photon energy loss. Cornerstone result of quantum mechanics, X-ray scattering and radiation physics.

Enter primary / secondary turns (or voltages); the tool returns the turns ratio V₁ ⁄ V₂ = N₁ ⁄ N₂ = I₂ ⁄ I₁, the output voltage, the output current and the impedance reflection (N₁ ⁄ N₂)². Cornerstone of electrical engineering, audio output transformer design and power-distribution planning.

Enter a distance (km, AU, light-years or parsecs); the tool uses c = 299 792 458 m/s to return the one-way light-travel time, with quick references for Earth–Moon, Earth–Sun and Earth–Mars distances. Useful for astronomy, deep-space communications and intro relativity classes.

Enter one-way distance (km or mi), vehicle class (small / medium / large petrol, diesel, hybrid, PHEV, BEV, motorbike), passenger count and whether the trip is return-only or round-trip; the tool applies DEFRA 2024 well-to-wheel emission factors to return total vehicle CO₂, per-passenger share, annualised (× 250 commuting-day) emissions and a tree-month offset.

Enter panel area, panel efficiency (%), average peak sun hours and the system performance ratio; the tool applies E = A × η × H × PR to return daily, monthly and annual kWh — the first sizing tool for any rooftop PV project.

Enter the moles available for two reactants plus their stoichiometric coefficients from the balanced equation; the tool identifies the limiting reagent, returns the theoretical yield of product (mol) and the excess reagent remaining. The canonical homework calculation in A-level, AP and first-year university chemistry.

Enter rotor diameter, wind speed, air density and the power coefficient Cp (Betz limit 0.593); the tool applies P = 0.5 × ρ × A × v³ × Cp to return instantaneous electrical power (kW), an annual-energy estimate and an equivalent number of households powered. The first-cut sizing tool for small wind turbines and off-grid systems.

Enter altitude (and optionally sea-level pressure/temperature); the tool applies the ISA barometric formula p(h) = p₀ × (1 − Lh ⁄ T₀)^(gM ⁄ RL) to return ambient pressure in hPa, atm and psi. Standard reference for hiking, drones, mountaineering, aviation and cooking corrections at altitude.

Enter any three of initial pressure/volume and final pressure/volume of an isothermal gas; the tool returns the fourth via P₁V₁ = P₂V₂ — the foundational formula for scuba tank compression, syringes, engine pistons and air springs.

Enter solute concentration, temperature and the van 't Hoff factor i; the tool returns osmotic pressure via π = i·M·R·T — the foundational equation for cell osmosis, reverse-osmosis desalination membranes and isotonic IV fluid tonicity.

Enter the focal length, f-number, and sensor circle-of-confusion; the tool returns the hyperfocal distance via H = f² ⁄ (N × c) + f — the defining number for landscape, street and astro photography focus-point selection.

Enter up to 8 capacitances and pick series or parallel; the tool returns the equivalent capacitance via C_parallel = ΣCᵢ or 1⁄C_series = Σ(1⁄Cᵢ) — the basic tool for circuit design and filter calculations.

Enter flow rate Q, total head H, fluid density and pump efficiency; the tool returns the required electrical power via P_shaft = ρ·g·Q·H ⁄ η in kW and HP — fundamental sizing equation for water supply, irrigation, fire-fighting and HVAC system design.

Heat pump COP = heat output Q ÷ electrical work input W. Enter the heat delivered and electricity used; the tool returns the COP and contrasts it with the Carnot upper bound COP_max = T_hot ⁄ (T_hot − T_cold) — useful for sizing AC, heat pumps, underfloor heating and water heaters.

The Sabine formula RT60 = 0.161·V / A (metric) estimates the time it takes for sound to decay 60 dB inside a room. Enter the room volume and the total effective absorption (Σ Sᵢ·αᵢ); the tool returns RT60 and compares it against recommended ranges for studios, classrooms and concert halls.

Enter the standard cell potential E°, number of electrons transferred n, reaction quotient Q and temperature; the tool returns the actual cell potential via the Nernst equation E = E° − (RT/nF) ln Q — used in electrochemistry, battery design, corrosion analysis and nerve-membrane potentials.

Enter solute mass / volume and total solution mass / volume; the tool returns mass percent (% w/w), mass-volume percent (% w/v) and volume percent (% v/v) — standard in chemistry class, food labelling and pharmaceutical formulation.

Enter initial pressure, volume, temperature and the heat-capacity ratio γ; the tool applies the isentropic relations PVγ = const and TVγ−1 = const to give the new P, V and T — standard for internal-combustion engines, compressors and rocket nozzles.

Enter air temperature and relative humidity (and optionally leaf temperature); the tool applies the Tetens saturation-vapor-pressure formula to return the vapor pressure deficit in kPa — the single most-used environmental metric for indoor hydroponics, commercial greenhouses, cigar humidors and fruit ripening rooms.

Enter the diameters of the two pulleys and the center-to-center distance; the tool returns the V-belt length via the standard closed-form L = 2C + π(D₁ + D₂)/2 + (D₁ − D₂)² / (4C) and shows the wrap angles on each pulley. Useful for industrial fans, lathes and any open belt drive.

Enter field elevation, QNH altimeter setting and OAT; the tool applies the standard FAA Pilot's Handbook formula and reports pressure altitude (PA), the ISA standard temperature, the deviation from ISA and the density altitude (DA) — essential for takeoff performance, high-altitude training and drone lift planning.

Enter focal length, aperture, focus distance and sensor format; the tool returns the hyperfocal distance, near-limit, far-limit and total depth of field — the core tool landscape, product and portrait photographers use to plan how much of a scene will be acceptably sharp.

Enter the installation latitude; the tool applies the standard NREL Landau / Heliene rules to give the year-round optimal fixed tilt, the summer tilt and the winter tilt — the headline number every rooftop PV, off-grid system and solar-thermal installer sizes by.

Enter any two of frequency f, wavelength λ and wave speed v; the tool applies v = f × λ to return the third together with the period T, angular frequency ω and angular wavenumber k. Built-in presets cover sound in air, fresh water, sea water and steel, plus EM in vacuum, water and glass — the most basic wave relation used across acoustics, radio, optics and ocean waves.

Enter the seconds between seeing the flash and hearing the thunder; the tool uses the speed of sound (≈ 343 m/s, light arrives essentially instantly) to compute distance in km and miles, with NOAA "30/30 rule" guidance on when to seek shelter.

Enter the balloon diameter and the payload weight; the tool applies lift ≈ (ρ_air − ρ_He) × V to give the net lift per balloon (≈ 1 g per litre at sea level), how many balloons you need, and notes on envelope weight and altitude density effects.

Enter antenna gain in dBi (or as a linear ratio); the tool applies G = 10^(dBi/10) to convert between dBi and ratio, with reference ranges for common antenna types (whip, Yagi, parabolic, patch, WiFi router) — essential for picking WiFi, two-way radio or satellite antennas.

Enter skid mark length and road surface friction coefficient μ; the tool applies v = √(2μgd) to estimate the minimum entry speed when braking began (km/h and mph) — used in crash reconstruction, insurance assessment and driving safety analysis.

Enter aperture f-number, shutter time and ISO; the tool returns EV = log₂(N²/t) − log₂(ISO/100), maps it to a typical scene (sunny day, indoor, moonlight) and lists five equivalent-exposure pairs (same EV, different aperture / shutter combinations) — handy for Sunny-16, night and moonlight photography.

Enter sample rate (Hz), bit depth (8 / 16 / 24 / 32 bit), channel count (mono / stereo / 5.1 / 7.1 / Atmos) and duration; the tool instantly returns the Nyquist limit, raw PCM bitrate, bytes-per-second and the uncompressed WAV file size.

Enter latitude (° N or S); the tool applies v = (2π · R · cos φ) ÷ T (where R is Earth's equatorial radius and T = 86 164 s, one sidereal day) to compute the linear speed of the ground at that latitude in m/s, km/h and mph — explains why equatorial launch sites (Cape Canaveral, Kourou) get a "free kick" for rocket launches.

Enter initial volume V₁, initial temperature T₁ and final temperature T₂ (in °C or K); the tool applies Charles's Law V₁/T₁ = V₂/T₂ (at constant pressure) to find the final volume V₂. Any one variable can be left blank to solve for it.

Enter snow depth (cm or inches) and snow density (kg/m³, or pick a preset for fresh / powder / wet / packed snow); the tool returns the equivalent water-column height after melting (mm or inches) and the mass per square metre (kg) — used for avalanche risk, roof load and irrigation water supply.

Two modes: (1) compute μ = F/N from friction force F and normal force N; (2) compute static coefficient μ_s = tan θ from the incline angle θ at which an object just starts to slip. A staple of physics labs and engineering classes.

Enter Young's modulus E, cross-section (solid round / rectangle / pipe), length L and an effective-length factor K (0.5 fixed-fixed, 0.7 fixed-pinned, 1.0 pinned-pinned, 2.0 fixed-free); the tool computes the minimum moment of inertia, radius of gyration, slenderness ratio and the critical buckling load P_cr — the foundation tool for slender-column stability design.

Enter the cutter diameter and recommended surface speed (SFM or m/min); the tool applies RPM = (SFM × 12) ⁄ (π × D) to give the spindle speed — the standard machinist conversion used for drills, end mills and lathes.

Enter filament diameter (1.75 mm or 2.85 mm), length in metres and material (PLA / PETG / ABS / TPU / Nylon / PC — density auto-fills); the tool applies m = π·(d/2)²·L·ρ to give the mass in grams, and inverts to answer "how many metres on a 1 kg spool".

Enter roof snow depth (cm or in) and snow type (fresh 50 kg/m³, settled 200, wet 400, ice 917); the tool computes the surface load in kPa, psf and kg/m² so you can compare to local building codes (IBC, NBC, Eurocode 1).

Enter daily high and low temperatures and a crop base temperature (corn 10 °C, wheat 4 °C, cotton 15 °C, etc.); the tool applies the standard ((Tmax + Tmin) ⁄ 2) − Tbase formula to give the day's GDD and a running cumulative total — used by growers, gardeners and IPM scouts to predict bloom, harvest and pest emergence windows.

Enter your Earth age; the tool uses each planet's orbital period around the Sun (Mercury 87.97 d, Venus 224.7 d, Mars 686.97 d, Jupiter 11.86 yr…) to compute your equivalent age on each of the other seven planets plus Pluto.

Enter water volume (litres), starting temperature and the kettle wattage; the tool applies Q = m·c·ΔT to give the energy (kJ / Wh) and time needed to reach 100 °C (or a custom target) and also reports the latent heat needed to fully evaporate.

Enter tank volume (litres / gallons), incoming and target water temperature, heater rated power (W or BTU/h) and efficiency; the tool applies Q = m·c·ΔT to give the time needed to bring a full tank up to temperature.

Enter the initial and final principal quantum numbers n₁ and n₂; the tool applies E_n = −13.6/n² eV and the Rydberg formula 1/λ = R(1/n₁² − 1/n₂²) to give the energy levels, transition energy, photon wavelength and frequency (Lyman / Balmer / Paschen series).

Enter the transmit frequency (MHz / GHz) and the distance (m / km / mi); the tool applies the Friis free-space path loss formula FSPL(dB) = 20·log₁₀(d) + 20·log₁₀(f) + K, useful for Wi-Fi, LoRa, 4G/5G and satellite link-budget estimates.

Enter the battery system voltage (12 / 24 / 48 V), chemistry (LiFePO₄, Li-Ion NMC, lead-acid / AGM) and measured open-circuit voltage; the tool linear-interpolates the standard rest-voltage SoC table to give the percent state of charge, remaining headroom to low-voltage cut-off, and warns when you are at the floor.

Enter the surface air temperature and dew point; the tool applies the standard aviation approximation 125 m per °C of dew-point spread to estimate the cumulus cloud base (lifting condensation level, LCL).

Enter the lens focal length (mm) and sensor size (full-frame, APS-C, M4/3, 1-inch, etc.); the tool returns the horizontal, vertical and diagonal angle of view in degrees — useful for lens choice, framing estimates and landscape / portrait planning.

Enter the supply voltage, the LED forward voltage (per colour, per series count) and the target current (mA); the tool applies Ohm's law to give the limiting resistor value (Ω), the minimum wattage and the closest standard E12 value.

Enter the native focal length and the sensor format (full-frame 1.0×, APS-C 1.5/1.6×, M4/3 2.0×, 1-inch 2.7×, etc.); the tool returns the 35 mm-equivalent focal length and the depth-of-field-equivalent aperture, making cross-system lens comparisons straightforward.

Enter the span L, Young's modulus E, second moment of area I and the load type (centre point P or uniformly distributed w) for a simply supported beam; the tool applies δ = PL³/(48EI) or δ = 5wL⁴/(384EI) to give the mid-span deflection and maximum bending moment — a quick sanity check for woodworking, civil and mechanical work.

Enter the current (A), allowable temperature rise ΔT (°C), copper weight (oz/ft², typically 0.5 / 1 / 2) and whether the trace is on an external or internal layer; the tool applies the IPC-2221 formula I = k·ΔT^0.44·A^0.725 to give the required trace width (mm / mil) — a quick PCB layout sanity check.

Enter a note name (C, C♯, D … ) and octave (e.g. A4, C5); the tool applies the 12-tone equal-temperament formula f = 440 × 2^((n − 69)/12) to give the frequency (Hz). Reverse mode: enter a Hz value and the tool reports the nearest note and cents deviation — useful for tuning, synth design and acoustics work.

Enter the VSWR (voltage standing-wave ratio) or the return loss in dB; the tool applies Γ = (VSWR − 1)/(VSWR + 1) and RL = −20·log₁₀|Γ| in both directions, and reports the reflected/transmitted power percentages — a quick sanity check for antenna, RF and transmission-line work.

Enter the telescope aperture (mm), main focal length, eyepiece focal length and Barlow factor; the tool returns magnification M = f_tel × Barlow ÷ f_eye, exit-pupil diameter (D ÷ M), focal ratio, maximum useful magnification (~ 2 × aperture mm), minimum useful power (~ aperture ÷ 7 mm dark-adapted) and the Dawes / Rayleigh diffraction limits — the numbers that decide whether an eyepiece (or planned purchase) is the right match.

Enter the string length (mm), tension (N) and linear mass density (g/m); the tool applies f₁ = (1/2L)·√(T/μ) to give the fundamental and the first 8 harmonics — useful for guitar, violin or piano string tuning and for classroom demonstrations of standing waves.

Enter the cylinder bore (mm), stroke (mm) and cylinder count; the tool applies V = π · (bore/2)² · stroke · cylinders to give engine displacement in cc, L and cubic inches — useful for motorcycles, car tuning and mechanical-engineering teaching.

Enter the driver pulley diameter, driven pulley diameter and input RPM; the tool applies RPM_out = RPM_in × (D_drive / D_driven) to give output RPM, reduction ratio and belt linear speed (m/s) — useful for mechanical, agricultural and CNC retrofits.

Enter the runway heading (°T), wind direction and wind speed (kt or m/s); the tool applies crosswind = V·|sin α| and headwind = V·cos α to give orthogonal components — used by pilots, gliders and UAV operators to assess take-off and landing risk.

Enter vehicle power (hp) and total weight (lb or kg); the tool applies Hale's empirical formulas ET = 5.825 × (W/HP)^(1/3) and trap-speed = 234 × (HP/W)^(1/3) to estimate the 1/4-mile elapsed time and terminal speed — a drag-strip rule-of-thumb.

Enter the waterline length (LWL, ft or m); the tool applies the Froude-derived hull_speed = 1.34 × √LWL (kn) to estimate the theoretical top speed of a displacement hull — a quick benchmark for sailboats, fishing boats and small yachts; exceeding it requires a semi-planing or planing hull form.

Enter the thread's major diameter (mm or in) and pitch or TPI; the tool applies tap_drill = D − (%/100) × 1.0825 × pitch to give the required drill — the everyday tap-drill chart for tapping, machining and DIY woodworking, with 50–100 % engagement adjustment.

Enter the bolt diameter (mm or in), target clamp load (preload, kN or lbf) and nut friction factor K (dry 0.20, oiled 0.15, anti-seize 0.10); the tool applies T = K·F·d to give the recommended tightening torque — essential for mechanical assembly and maintenance.

Enter aircraft (or UAV) mass and wing area; the tool returns W/S (N/m² or lb/ft²) — a fundamental performance parameter: high W/S = stable cruise but long takeoff and high stall speed; low W/S = short takeoff and agile, but gust-sensitive.

Enter two apparent magnitudes; the tool applies Pogson's law m₁ − m₂ = −2.5 × log₁₀(F₁/F₂) to give the brightness (flux) ratio between any two stars, planets or deep-sky objects, and can convert apparent to absolute magnitude given distance.

Enter resistance (Ω) and either voltage (V) or current (A); the tool applies P = V²/R = I²R to give power dissipation (W) and recommends the next-up standard 1/8 W, 1/4 W, 1/2 W, 1 W or 2 W package (with a 50 % safety margin).

Enter the feedback resistor Rf and input resistor Rin, choose inverting or non-inverting topology; the tool returns the closed-loop gain (V/V and dB) using G = −Rf / Rin (inverting) or G = 1 + Rf / Rin (non-inverting) — essential for analog circuit design.