Surface area to volume ratio calculator
Surface area grows as the square of size and volume as the cube, so small things have proportionally far more surface. It is why mice eat constantly and elephants overheat.
Sphere ratio
3per metre
- Cube ratio Using the size as the side.
- 6 per metre
- Cube ratio at half the size
- 12 per metre
- Sphere volume
- 4.188 790 2
- Sphere surface area
- 12.566 371
- Cube volume
- 1
- Cube surface area
- 6
Show the working
- Characteristic size = 1
- Sphere ratio = 1 > 0 ? 3/1 : 0 = 3
- Cube ratio = 1 > 0 ? 6/1 : 0 = 6
- Sphere volume = 4/3*pi*1^3 = 4.188 79
- Sphere surface area = 4*pi*1^2 = 12.5664
- Cube volume = 1^3 = 1
- Cube surface area = 6*1^2 = 6
- Cube ratio at half the size = 1 > 0 ? 6/(1/2) : 0 = 12
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- sphere: SA/V = 3/r
- cube: SA/V = 6/s
- Halving the size doubles the ratio.