Torus (Donut) Volume
It equals the cross-section area times the circumference of the centre circle — a cylinder bent into a loop.
Your numbers
Volume
1,776.53cm³
Surface area
1,184.35cm²
Formula
Volume = 2π² × Radius × Inner radius²
The centre radius runs from the middle of the hole to the centre of the tube, not to its outer edge.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Radius (cm)Centre to edge — half the diameter. | 10 | 0 and up |
| Inner radius (cm)The smaller of two radii when the ends differ. | 3 | 0 and up |
Step by step
Quick reference table
Results when only Radius (cm) changes and everything else stays put.
| Radius (cm) | Volume (cm³) | Surface area (cm²) |
|---|---|---|
| 5 | 888.26 | 592.18 |
| 7.5 | 1,332.4 | 888.26 |
| 10 | 1,776.53 | 1,184.35 |
| 15 | 2,664.79 | 1,776.53 |
| 20 | 3,553.06 | 2,368.71 |
What each result means
| Result | At default values |
|---|---|
| Volume (cm³)The space a solid holds — length cubed. | 1,776.53 |
| Surface area (cm²)The total area of a solid’s outer skin. | 1,184.35 |
Common mistakes
The centre radius runs from the middle of the hole to the centre of the tube, not to its outer edge.
Glossary
- Radius
- Centre to edge — half the diameter.
- Inner radius
- The smaller of two radii when the ends differ.
- Volume
- The space a solid holds — length cubed.
- Surface area
- The total area of a solid’s outer skin.
Frequently asked questions
Q. How is Torus (Donut) Volume calculated?
Volume = 2π² × Radius × Inner radius² — It equals the cross-section area times the circumference of the centre circle — a cylinder bent into a loop.
Q. Can you walk through an example?
With Radius 10cm, Inner radius 3cm, the answer is Volume 1,776.53cm³.
Q. What do I need to enter?
Enter Radius, Inner radius. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Radius (cm) moves the answer to Radius (cm) 5 → Volume (cm³) 888.26 and Radius (cm) 20 → Volume (cm³) 3,553.06. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
The centre radius runs from the middle of the hole to the centre of the tube, not to its outer edge.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.