Cone Volume Calculator
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 12.566371 * 6 / 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.
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.
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.
- Radius
4 / 22 ft- Base area
pi * pow(2, 2)12.566 sq ft- Volume
12.566371 * 6 / 325.133 cu ft- Volume in cubic inches
25.132741 * 172843,429.377 cu in- Capacity in US gallons
25.132741 * 7.48052188.006 gal- A cylinder of the same base and height
12.566371 * 675.398 cu ft
Several at once
A job is rarely one of anything. Work out the first, add it, change the figures and add the next — the list keeps what each line was, and totals them.
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.Measure straight across the widest part of the base for the diameter, and halve it for the radius.
- 2.Multiply π by the radius squared for the base area.
- 3.Multiply the base area by the height, then divide by three.
- 4.For gallons, multiply the cubic feet by 7.48052.
The formula
- Radius
4 / 2 - Base area
pi * pow(2, 2) - Volume
12.566371 * 6 / 3 - Volume in cubic inches
25.132741 * 1728 - Capacity in US gallons
25.132741 * 7.48052 - A cylinder of the same base and height
12.566371 * 6
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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