Sphere Volume Calculator
With diameter 3 ft, sphere volume comes to 14.137 cu ft — volume. It is reached in 5 steps, the last of which is 4 / 3 * pi * pow(1.5, 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 and surface area of a sphere from its diameter, in cubic feet, cubic inches and gallons, with the radius shown as its own step.
Formula and sources checked · How we check
Diameter 3 ft
14.137 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
3 / 21.5 ft- Volume
4 / 3 * pi * pow(1.5, 3)14.137 cu ft- Surface area
4 * pi * pow(1.5, 2)28.274 sq ft- Volume in cubic inches
14.137167 * 172824,429.024 cu in- Capacity in US gallons
14.137167 * 7.48052105.753 gal
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 3 ft sphere holds 14.137 cu ft — 106 US gallons — with 28.27 sq ft of surface. Doubling the diameter to 6 ft multiplies the volume by eight, because volume scales with the cube while surface scales with the square.
How to work it out yourself
- 1.Measure across the widest point for the diameter and halve it for the radius.
- 2.Cube the radius, multiply by π, then multiply by four thirds.
- 3.For the surface area, multiply four by π by the radius squared.
- 4.For gallons, multiply the cubic feet by 7.48052.
The formula
- Radius
3 / 2 - Volume
4 / 3 * pi * pow(1.5, 3) - Surface area
4 * pi * pow(1.5, 2) - Volume in cubic inches
14.137167 * 1728 - Capacity in US gallons
14.137167 * 7.48052
Source: Wolfram MathWorld — sphere, NIST Digital Library of Mathematical Functions
Questions people actually ask
- Why does volume grow so much faster than surface?
- Volume scales with the cube of the radius and surface with the square. Double the size and you get eight times the volume but only four times the surface — the reason large animals overheat and small ones lose heat.
- What is the surface-to-volume ratio?
- Three divided by the radius, in whatever units the radius is in. It falls as the sphere grows, which is the same fact stated as a ratio.
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