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Cone Volume Calculator

Volume of a cone from its diameter and height, in cubic feet, cubic inches and gallons, with the radius and the base area shown separately.

With base diameter 4 ft, height 6 ft, cone volume comes to 25.13 cu ft — volume. It is reached in 6 steps, the last of which is base_area * height / 3, and each one is printed on the page with its numbers filled in. The formula is the one published by Wolfram MathWorld, not an approximation fitted to it.

Formula and sources checked · How we check

Base diameter 4 ft, Height 6 ft

25.13 cu ft

Volume for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.

It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.

Volume
25.13 cu ft
Radius
diameter / 22 ft
Base area
pi * pow(radius, 2)12.566 sq ft
Volume
base_area * height / 325.133 cu ft
Volume in cubic inches
volume * 172843,429.377 cu in
Capacity in US gallons
volume * 7.48052188.006 gal
A cylinder of the same base and height
base_area * height75.398 cu ft

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Worked example

A cone 4 ft across and 6 ft tall holds 25.13 cu ft, or 188 US gallons. A cylinder with the same base and height holds 75.40 cu ft — exactly three times as much, which is the whole content of the formula.

How to work it out yourself

  1. 1.Measure straight across the widest part of the base for the diameter, and halve it for the radius.
  2. 2.Multiply π by the radius squared for the base area.
  3. 3.Multiply the base area by the height, then divide by three.
  4. 4.For gallons, multiply the cubic feet by 7.48052.

The formula

  1. Radiusdiameter / 2
  2. Base areapi * pow(radius, 2)
  3. Volumebase_area * height / 3
  4. Volume in cubic inchesvolume * 1728
  5. Capacity in US gallonsvolume * 7.48052
  6. A cylinder of the same base and heightbase_area * height

Source: Wolfram MathWorld — cone, NIST Digital Library of Mathematical Functions

Questions people actually ask

Why divide by three?
A cone occupies exactly one third of the cylinder that shares its base and height. That ratio is exact and holds for any cone, which is why the formula needs no other constant.
Does a slanted cone hold the same?
Yes. An oblique cone with the same base and the same perpendicular height has the same volume — only the height measured square to the base matters, not the slant.

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