Cylinder Volume Calculator

Enter the radius and height of a cylinder to get its volume, surface area and lateral area, drawn to scale. Click the diameter or height on the drawing to change it.

Dimensions

Cylinder
Blueprint · Isometric Click an amber dimension to edit it · isometric, not to printed scale

Result

Volume of a cylinder

A cylinder is a circular prism: the area of its circular base, πr², multiplied by its height. The curved side unrolls into a rectangle of width equal to the base circumference, giving the lateral area 2πrh.

Editing on the drawing

Click the diameter to set the size across, or the height to set how tall it is — the radius is updated for you and the cylinder redraws to scale.

How to find the volume of a cylinder

A cylinder is a prism with a circular base — think of a pipe, a tank or a column. Two measurements set it: the radius of the circular end and the height. From those, the volume and the surface areas all follow.

The formulas

Volume is the circular base area times the height. The curved side, unrolled, is a rectangle as tall as the cylinder and as wide as the base circumference, which gives the lateral area; adding the two circular ends gives the total surface area.

V = πr²h
A = 2πr² + 2πrh

Worked example

Take a cylinder with radius 34 and height 84.

Step 1 — base area

Area of the circular end.

πr² = π × 34² = π × 1,156 ≈ 3,631.7
Step 2 — volume

Base area times height.

V = 3,631.7 × 84 ≈ 305,061
Step 3 — surface area

Two ends plus the curved side.

A = 2(3,631.7) + 2π(34)(84) ≈ 7,263 + 17,944 ≈ 25,208

What else the calculator returns

You also get the lateral (curved) area on its own, the base area and the diameter. Many practical problems start from the diameter rather than the radius, so you can type the diameter straight onto the figure and the radius is set for you.

Where it comes up

Cylinder volumes cover pipe and bore capacities, storage tanks and drums, structural columns and concrete cores. To convert a volume in cubic millimetres to litres, divide by 1,000,000 — a litre is exactly 1,000 cubic centimetres.

Frequently asked questions

How do you find the volume of a cylinder?

Multiply the area of the circular base, πr², by the height: V = πr²h.

I only have the diameter — what do I do?

Halve it to get the radius (r = d/2) and then use πr²h. On this tool you can also type the diameter directly on the figure and it sets the radius for you.

What is the difference between lateral and total surface area?

The lateral area is just the curved side, 2πrh. The total surface area adds the two circular ends, giving 2πr² + 2πrh.

How do I find the height from the volume?

Rearrange the volume formula: h = V / (πr²).

How much liquid does a cylinder hold?

Its volume. Working in millimetres, divide the result by 1,000,000 for litres; in centimetres, divide by 1,000.