Volume of a Cylinder: Base Area × Height

Updated September 26, 2026•Geometry & Mensuration

Calculate cylinder volume from the circular base area and perpendicular height, with unit checks and common mistakes.

The structure of the formula

A cylinder is a prism-like solid with the same circular cross-section all the way through. Volume equals base area × perpendicular height.

V = πr²h

Example: Radius 4 cm, height 10 cm.

V = π × 4² × 10 = 160π cm³ ≈ 502.65 cm³

Halve it before squaring. A diameter of 12 cm means a radius of 6 cm, so r²=36, not 144.

Volume measures three-dimensional space, so the unit is cubed: mm³, cm³, m³ and so on. Convert lengths into a common unit before using the formula.

Rearrange V=πr²h to h=V/(πr²). Rearranging first keeps the structure visible and reduces calculator errors.

Estimate π as about 3. A radius of 4 gives base area around 3×16≈48. Multiply by height 10 to get about 480, so 502.65 is plausible.

Try one yourself

A cylinder has radius 3 and height 5. What is the coefficient of π in its exact volume?

For another problem using related ideas, return to the Geometry & Mensuration page.