Cylinder Volume Calculator

Volume of a cylinder formula

A cylinder is a prism whose base is a circle. Its volume is therefore the area of that circle multiplied by how far the shape extends, which gives one of the shortest formulas in solid geometry.

V = π × r² × hr is the radius of the circular base, h is the height, and π ≈ 3.14159.

The radius is squared because the base area grows with the square of the radius, while the height enters only once. That has a practical consequence: doubling the radius makes the volume four times larger, whereas doubling the height only doubles it.

How to calculate the volume of a cylinder

1. Measure the radius of the base, which is the distance from the centre of the circle to its edge. If you only know the diameter, halve it first.
2. Measure the height, the straight distance between the two circular faces.
3. Type both numbers into the calculator and choose the unit they are measured in. Use the same unit for both.
4. Press Calculate. The answer is given in that unit cubed, for example cm³ or ft³, and is rounded to six decimal places.

The calculator does not convert units for you. Whatever unit you select is applied to the radius, the height and the result. To express the answer in litres or gallons, use the volume converter afterwards.

Example: find the volume of a cylinder

A small tin. The base radius is 5 cm and the height is 10 cm. V = π × 5² × 10 = π × 250 ≈ 785.398 cm³, which is roughly 0.785 litres.

A water tank. A tank is 1.2 m across and 1.5 m tall. The radius is 0.6 m, so V = π × 0.6² × 1.5 = π × 0.54 ≈ 1.69646 m³. Because one cubic metre holds 1,000 litres, the tank holds about 1,696 litres.

The table shows how fast the volume rises with the radius when the height stays at 10 cm.

Finding the height or the radius from a known volume

When you need a container of a given capacity, rearrange the formula for the missing dimension.

h = V ÷ (π × r²)

r = √( V ÷ (π × h) )

Example: a cylinder of 2,000 cm³ with a radius of 8 cm needs a height of 2,000 ÷ (π × 64) ≈ 9.95 cm. A cylinder of 500 cm³ that is 12 cm tall needs a radius of √(500 ÷ (π × 12)) ≈ 3.64 cm.

Hollow cylinders and related solids

For a pipe or tube, subtract the empty core from the outer cylinder: V = π × (R² − r²) × h, where R is the outer radius and r the inner radius. A pipe with an outer radius of 5 cm, an inner radius of 4 cm and a length of 100 cm holds π × (25 − 16) × 100 ≈ 2,827.43 cm³ of material.

• A cone with the same base and height has exactly one third of the cylinder's volume. For the 5 cm by 10 cm example that is about 261.8 cm³; see the cone volume calculator.
• A sphere that just fits inside a cylinder (height equal to its diameter) fills two thirds of it. A sphere of radius 5 cm has a volume of about 523.6 cm³, which is two thirds of the 785.4 cm³ cylinder around it. Try the sphere volume calculator.
• A slanted (oblique) cylinder has the same volume as an upright one with the same base and the same perpendicular height, so measure the height at right angles to the base, not along the slanted side.

Practical applications

• Storage: sizing water tanks, silos, drums and gas bottles.
• Plumbing and building: the amount of water in a length of pipe, or concrete needed for a round column or a post hole.
• Cooking and packaging: the capacity of cans, glasses and jars.
• Engineering: displacement of a piston or the material in a rod or shaft.

For rectangular containers use the box volume calculator, and for cubes the cube volume calculator.