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Cone Volume Calculator

How do I find the volume of a cone?

How it is calculated

A cone is described by its base radius r and its vertical height h, in the same unit. The tool computes the slant height s = √(r² + h²), the volume V = (1/3) × π × r² × h and the total surface area A = π × r × (r + s), which includes the circular base. The volume is exactly one third of a cylinder with the same base and height. Radius and height must both be greater than zero. Results are given in cubic and square units of whatever you entered, rounded to two decimals, with no unit label added, so keep track of whether you used cm, m or inches.

Worked example

A cone with r = 3 and h = 4. Slant height s = √(9 + 16) = 5.00. Volume = (1/3) × π × 9 × 4 = 12π = 37.70. Surface area = π × 3 × (3 + 5) = 24π = 75.40. A 3-4-5 triangle makes the numbers clean.

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Common mistakes

  • Entering the diameter as the radius: halve it first, because the volume depends on the square of r.
  • Using the slant height as the vertical height h, which inflates the volume.
  • Reading the surface area as the lateral area only; the figure here also includes the base.
  • Mixing units, such as a radius in centimetres and a height in metres.
  • Forgetting the one third factor when checking by hand and getting the volume of a cylinder.

About this calculator

This calculator finds a cone's volume (one-third of π × r² × h — exactly a third of a cylinder with the same base and height), surface area, and slant height (the distance along the cone's side from apex to base edge, found from radius and height via the Pythagorean theorem) using just the radius and height as inputs. The one-third relationship to a cylinder's volume is a classic geometry result that surprises many people the first time they see it demonstrated.

It's used in manufacturing and construction to work out material needed for conical parts — funnels, hoppers, traffic cones, roof spires — and in geometry courses to apply the volume, surface area and slant height formulas to a concrete shape rather than working with them abstractly.

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Comments (1)

  • Editorial team

    The surface figure includes the circular base. For something open at the bottom, like a paper party hat or a pointed roof, you want only the side, which is the total minus π × r². With r = 5 and h = 12 the total is 282.74, but the side alone is 204.20. A heap of gravel or sand is also roughly a cone. What shape are you measuring, and in which unit?

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