VolLab

Cylinder Volume Calculator

Radius × radius × height × π — plus surface area.

Radius

Height

Volume

502.655

V = π · r² · h

Surface area: 351.858

What you entered

Radius: 4Height: 10

1
Volume
π × 4² × 10= 502.6548
2
Surface area
2π × 4 × (4 + 10)= 351.8584

Result

Volume: 502.655

A cylinder with radius 4 and height 10 has a volume of 502.655 and a surface area of 351.858.

Cylinder volume and surface area

Volume is pi r squared times height. Surface area includes both circular ends plus the curved side.

Radius x Height	Volume	Total surface area
1 x 2	6.28	18.85
2 x 5	62.83	87.96
3 x 6	169.65	169.65
4 x 10	502.65	351.86
5 x 12	942.48	534.07
6 x 15	1696.46	791.68
10 x 20	6283.19	1884.96

The 3 x 6 row shows volume and surface area matching exactly, which happens whenever the height is twice the radius and both are 3 - a numerical coincidence rather than a rule. Radius matters far more than height: doubling the radius quadruples the volume while doubling the height only doubles it, which is why a short wide tank holds much more than a tall narrow one of the same surface area. For a tank or pipe, use the internal radius rather than the external one.

A stack of circles

A cylinder's volume is just its circular cross-section (πr²) stacked up over the height — the same logic as a rectangular box's volume being its footprint times height.

Where this comes up

Cans, pipes, water tanks, and cylindrical containers of every kind rely on this formula to determine capacity or the material needed to build them.

Frequently asked questions

How do I calculate the volume of a cylinder?

Volume = π × r² × h (pi times radius squared times height). A cylinder with radius 5 cm and height 10 cm: V = π × 25 × 10 = 785.4 cm³. If you have the diameter, halve it first to get the radius.

How many gallons does a cylindrical tank hold?

Calculate volume in cubic inches (π × r² × h), then divide by 231 (1 US gallon = 231 in³). A tank 24 inches in diameter and 48 inches tall: V = π × 12² × 48 = 21,715 in³ ÷ 231 = 94 gallons.

What is the surface area of a cylinder?

Total surface area = 2πr² + 2πrh. The first term is the two circular ends, the second is the curved side (imagine unrolling it into a rectangle of width 2πr and height h). For an open-top tank, subtract one πr².