Right Cylinder Calculator

Background.

Water tanks, tins, pipes, round concrete columns and straight-sided glasses are all right circular cylinders: a circle carried straight upward, so every horizontal slice is the same size and the side meets the base at a right angle. That uniformity is what makes the shape so easy to measure. Its volume is simply the area of the base, πr², multiplied by the height.

The formula's real lesson is how unevenly the two dimensions count. Height enters once; radius enters squared. Make a tank twice as tall and it holds twice as much; make it twice as wide and it holds four times as much. The same imbalance applies to mistakes — a radius measured 5% too large overstates the volume by about 10%, while a 5% error in height costs only 5%.

Working backwards is often the more useful direction. A water tank must hold 1,000 litres, which is 1 cubic metre, and stand no taller than 1.2 m: what radius does it need? Rearranged, the same equation gives r = √(V ÷ πh), here about 0.515 m, so a tank a little over a metre across. Know the radius and the volume instead, and h = V ÷ πr² gives the height or the length of pipe.

Whichever quantity you solve for, the page also reports the diameter and the total surface area of the closed shape, 2πr(r + h): both round ends plus the curved side. That is the figure for painting or wrapping a sealed drum. An open-topped tank has one end fewer and a length of pipe has none, so subtract those yourself. The shape is treated as solid, with no wall thickness; for a container's capacity, measure the inside.

What is right cylinder calculator?

A right circular cylinder is the solid formed by two identical, parallel circular bases joined by a curved surface, with the line through the centres of the bases perpendicular to them. Its size is fixed by two lengths: the radius r of the base and the height h between the bases. Volume, the space enclosed, is πr²h in cubic units; total surface area, the two ends plus the side, is 2πr(r + h) in square units.

How to use this calculator.

1. 01Choose what to solve for: Volume, Radius or Height. The field for that quantity is ignored, so you only need to fill in the other two.
2. 02Use one length unit throughout. Volume then comes out in that unit cubed and surface area in that unit squared — centimetres give cm³ and cm², metres give m³ and m².
3. 03If you measured a diameter, halve it before entering it as the radius; if you wrapped a tape round the outside, divide the circumference by 2π, about 6.283.
4. 04For a container's capacity, measure the inside diameter and depth rather than the outside, so that wall thickness is not counted as space.
5. 05Read the diameter and surface area beside the main answer. The area includes both ends; subtract πr² for each end that is open.

The formula.

V = πr²h. The base is a circle of area πr², where π ≈ 3.14159 is the ratio of any circle's circumference to its diameter, and the cylinder stacks that area uniformly up the height h. Solving for the other dimensions rearranges the same equation: r = √(V ÷ πh) and h = V ÷ πr². Total surface area is 2πr² for the two ends plus 2πrh for the curved side, which unrolls into a rectangle whose width is the circumference 2πr; together that is 2πr(r + h). Because r is squared in the volume, it dominates: increasing the radius by 10% raises the volume by 21%, the same as raising the height by 21%. Inputs must be positive lengths and a positive volume.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.