Cylinder Volume & Surface Area Calculator
Enter the base radius r and height h of a right circular cylinder to instantly get the volume V = πr²h, lateral (curved) surface area 2πrh, base area πr², total surface area, diameter and base circumference — handy for tank / can / pipe capacity and geometry homework.
Both radius and height must be positive numbers.
Volume V
785.3982
Lateral area A_l
314.1593
Base area A_b
78.5398
Total surface area A_t
471.2389
Diameter d
10
Base circumference C
31.4159
Formula
V = πr²h ; A_l = 2πrh ; A_b = πr² ; A_t = 2πr(h + r)
Units are up to you (cm, m, in, ft, m all fine). Radius and height share one linear unit; areas use that unit squared; volume uses that unit cubed. 1 litre = 1000 cubic centimetres.
Formula
V = π r² h | lateral A_l = 2π r h | base A_b = π r² | total A_t = 2π r (h + r)
- · The tool computes a right circular cylinder — parallel circular bases with the axis perpendicular to them.
- · Pick any unit you like (cm, m, in, ft, m). Radius and height share one linear unit; areas use that unit squared; volume uses that unit cubed.
- · 1 litre = 1000 cubic centimetres = 0.001 cubic metres; 1 US gallon ≈ 3.78541 litres.
- · Total surface area includes BOTH circular ends (A_t = 2πrh + 2πr²). For an open-top container (a bucket, an open tank) subtract one πr² yourself.
- · Pure geometric volume only — wall thickness and head-space are not accounted for.
- · Sources: CRC Standard Mathematical Tables and Formulae, 31st ed., §4.10 "Right Circular Cylinder"; Archimedes, On the Sphere and Cylinder.
Frequently asked
How big is a 330 ml soda can?
A standard Euro 330 ml can is roughly 66 mm outer diameter (r ≈ 3.3 cm) and 11.5 cm tall. Plug it in: V = π × 3.3² × 11.5 ≈ 393 cm³. The ~60 cm³ overhead above 330 ml is head-space — gas room left between the liquid and the lid for thermal expansion.
A pipe 25 mm in diameter and 3 m long holds how many litres?
Convert first: r = 12.5 mm = 1.25 cm, length 300 cm. V = π × 1.25² × 300 ≈ 1473 cm³ ≈ 1.47 L. In the tool, enter r = 1.25 and h = 300 (cm) and you’ll get the same 1473 cm³.
What happens to the volume if I double the height? Or the radius?
Volume scales linearly with height: double h, double V. Radius is different — the formula has r squared (V = πr²h), so doubling r quadruples the volume (2² = 4). That is why "making the cup wider" affects capacity far more than "making it taller" by the same factor.
Why does the total surface area count the base TWICE?
A closed cylinder has TWO circular ends — one top, one bottom — so A_t = lateral + 2 × base. For an open-top container (a tumbler, an open tank) use A_l + 1 × A_b instead; for an open-ended pipe wall just A_l = 2πrh. The tool reports the closed-cylinder total — adjust by hand if your shape is open.
Related tools
Percentage Calculator
Percent of, percent change, and percent add/subtract in one.
GCD & LCM Calculator
Enter 2–6 positive integers to get the greatest common divisor (HCF / GCD) and least common multiple (LCM), with the Euclidean step chain shown.
Average Calculator (Mean / Median / Mode)
Enter a list of numbers to get the mean, median, mode, range plus standard deviation, variance and total.
Quadratic Equation Solver
Enter the coefficients of ax² + bx + c = 0 to find the real or complex roots, discriminant and vertex.
Password Strength (Entropy) Calculator
Estimate a password's bit entropy, brute-force time and strength tier. All computation happens in your browser.
Scientific Notation Converter
Convert between standard decimal numbers and scientific notation, with significant figures and order of magnitude.
Permutations & Combinations (nPr / nCr) Calculator
Compute permutations P(n,r), combinations C(n,r) and factorial n! — useful for probability problems, lottery odds and combinatorics homework.
Standard Deviation Calculator
Paste a list of numbers to compute mean, median, sample and population variance and standard deviation — with the working shown.
Triangle Calculator (SSS / SAS / ASA)
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.
Pythagorean Theorem Calculator
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.
Circle Calculator (radius / diameter / circumference / area)
Enter any one of radius, diameter, circumference or area to get the other three — useful for design, engineering and DIY.
Roman Numeral Converter
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.
Slope & Line Equation Calculator (y = mx + b from Two Points)
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.
Birthday Paradox Calculator
Enter group size n to see the probability that at least two people share a birthday — the classic birthday problem.
Logarithm Calculator (log / ln / log₂ / any base)
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.
Z-Score (Standard Score) Calculator
Enter a value, the mean and the standard deviation to compute the z-score and the corresponding normal-distribution percentile and probabilities.
Screen Pixel Density (PPI) Calculator
Enter the screen resolution and diagonal size to get pixel density (PPI), real width/height, dot pitch and total pixel count.
Hong Kong Mark Six Odds Calculator
Enter the number of tickets / selections and see the actual probability of hitting first, second … prizes in a Mark Six (6-of-49) draw.
Decimal to Fraction Converter
Convert any decimal (including repeating decimals) to a simplified fraction and a mixed number.
Sphere Volume & Surface Area Calculator
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.
Prime Factorization Calculator
Factor any integer from 2 up to 10¹² into primes, see the canonical exponent form, count and list all divisors.
Geometric Mean Calculator
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.
Fibonacci Sequence Calculator
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.