Tori appear in inner tubes, O-rings, doughnuts and some reactor designs.
How to use the Torus Calculator
- Major radius (R)
- Minor radius (r)
Results update as you type, and every field accepts the units shown in its menu.
How it works
The volume equals the tube’s cross-sectional area times the distance travelled by its centre around the ring.
Inputs explained
| Field | What to enter |
|---|---|
| Major radius (R) | Units: m, cm, mm, km, in, ft … |
| Minor radius (r) | Units: m, cm, mm, km, in, ft … |
What each result means
- Volume = 2×pi^2×[Major radius (R)]×[Minor radius (r)]^2
- Surface area = 4×pi^2×[Major radius (R)]×[Minor radius (r)]
Example values
How the main result changes when Major radius changes and everything else stays at the example values above:
| Major radius (R) (m) | Volume (m³) |
|---|---|
| 5 | 888.26 |
| 7.5 | 1,332.4 |
| 10 | 1,776.53 |
| 12.5 | 2,220.66 |
| 15 | 2,664.79 |
| 20 | 3,553.06 |
Formula
V = 2π² R r²Surface area = 4π² R rWorked example
Inputs — Major radius (R): 10 m; Minor radius (r): 3 m.
Results — Volume = 1,776.53 m³; Surface area = 1,184.35 m².
Frequently asked questions
What if r is larger than R?
The torus self-intersects (a spindle torus); the formulas then overestimate.
How do I measure R?
From the centre of the hole to the centre of the tube.
What formula does the Torus Calculator use?
V = 2π² R r².