Volume of a Cone Calculator

A cone’s volume is exactly one third of the cylinder that would enclose it. Enter the radius and height to get the volume, the slant height, and both surface areas.

Results

Formula

Volume, slant and surfaces:
V = ⅓ π r² h  ·  Slant = √(r² + h²)  ·  Total area = πr(r + slant)

How to use this calculator

  1. Enter the base radius.
  2. Enter the perpendicular height (not the slant).
  3. Press Calculate for volume and the related measures.
Volume of a Cone Calculator — how the calculation works, illustratedacb
Volume of a Cone Calculator — how the calculation works, illustrated

Worked example

Radius 3, height 4.

  1. Slant height: √(9 + 16) = 5.
  2. Volume: ⅓ × π × 9 × 4 = 12π ≈ 37.699.
  3. Total area: π × 3 × (3 + 5) = 24π ≈ 75.398.

Result: Volume ≈ 37.699 cubic units, slant height 5.

Frequently asked questions

Why one third of a cylinder?

A cone and cylinder with the same base and height have volumes in an exact 1:3 ratio — demonstrable by filling a cone with water and pouring it into the matching cylinder three times.

Height vs slant height — which do I enter?

The perpendicular (vertical) height. The slant height — measured along the surface — is calculated for you from the Pythagorean theorem.

What is lateral surface area?

The area of the curved side only, excluding the circular base. Total surface area includes the base.

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