Volume of a torus calculator
Enter the dimensions of a torus and read off its volume and surface area. Volumes convert to litres and gallons with the unit selector.
Volume
222.0661m³
- Surface area
- 296.088 13
- Outer radius
- 6.5
- Inner radius
- 3.5
Show the working
- Major radius = 5
- Tube radius = 1.5
- Volume = 2 * pi^2 * 5 * 1.5^2 = 222.066
- Surface area = 4 * pi^2 * 5 * 1.5 = 296.088
- Outer radius = 5 + 1.5 = 6.5
- Inner radius = 5 - 1.5 = 3.5
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
- volume = 2 pi^2 R r^2
- surface area = 4 pi^2 R r
Both formulas follow from Pappus theorem: the volume is the tube cross-section swept round the major circle.
Switch the volume unit to litres or US gallons to read the capacity directly.