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Cone Volume Calculator

Cone Volume Calculator is part of Toolspire and is ready as soon as this page loads. A cone with the same radius and three times the height of a unit cylinder matches that cylinder’s volume, because the one-third and the extra height cancel. Slant height is not the height.

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On this page

What you can do here

The one-third is visible

People forget it and report a cylinder. The sample is chosen so the cone equals a known cylinder only because the height is tripled.

Radius of the base

The apex has no radius. Do not average the base with zero.

No slant-height box

If you measured the side, find the perpendicular height before you type.

The sequence

How to use the Cone Volume Calculator

  1. 1

    Use the base radius

    Diameter across the base must be halved.

  2. 2

    Use the upright height

    The slanted side is longer and is not this input.

  3. 3

    Check 3.1416

    Radius 1, height 3, volume π.

Worth knowing

  • Cone Volume Calculator on Toolspire: volume = (1/3) π r² h.
  • Radius 1 and height 3 give π, about 3.1416.
  • That equals a unit cylinder of radius 1 and height 1, because 1/3 × 3 = 1.
  • The height is the perpendicular height, not the slant from the rim to the apex.

A third of the cylinder with the same base and height

A right circular cone has one third the volume of a cylinder with the same base radius and the same perpendicular height. The page multiplies π r² h by 1/3. Radius 1 and height 3 therefore match π r² h for a cylinder of height 1, which is a useful cross-check against the cylinder page. An oblique cone is not modelled.

FAQ

Questions about Cone Volume Calculator

Where does Cone Volume Calculator run?

Cone Volume Calculator runs in this tab on Toolspire. What you type or drop in is not sent to us and is not stored on a server.

What is the volume for radius 1 and height 3?

π, about 3.1416.

Why those dimensions?

So the one-third and the height of 3 cancel to the unit cylinder’s volume. If you drop the one-third you will not get π.

Is the slant height the height?

No. Height is the perpendicular drop from the apex to the base plane.

What about the lateral surface?

This page is volume only. Lateral area needs the slant height, which is not an input.

Keep going

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