Case 1
- Major radius R
- 5
- Minor radius r
- 2
394.784176
Open with these valuesTorus Surface Area Calculator
394.784176units²
Result: 394.784176 units²4π²Rr: the tube's circumference 2πr carried once round the path 2πR. Both radii enter only once here, unlike the volume where r is squared — so doubling the tube doubles the skin but quadruples the contents.
The numbers at a glance
Held fixed: Major radius R 5.000.
| Minor radius r | Result |
|---|---|
| 0.500 | 98.696044 |
| 1.000 | 197.392088 |
| 1.500 | 296.088132 |
| 2.000Your value | 394.784176 |
| 2.500 | 493.480220 |
| 3.000 | 592.176264 |
| 3.500 | 690.872308 |
| 4.000 | 789.568352 |
Worked examples
Case 2
- Major radius R
- 3
- Minor radius r
- 1
118.435253
Open with these valuesCase 3
- Major radius R
- 10
- Minor radius r
- 3
1,184.352528
Open with these valuesHow it's calculated
A = 4 × π² × R × r
- StepMeasure from the centre of the hole to the middle of the tube — that is R.
- StepMeasure the radius of the tube itself — that is r.
- ResultRead the area in the square of the unit you entered.
Reference table
| R, r | Exact | Surface area |
|---|---|---|
| 1, 0.5 | 2π² | 19.739209 |
| 3, 1 | 12π² | 118.435253 |
| 4, 1.5 | 24π² | 236.870506 |
| 5, 2 | 40π² | 394.784176 |
| 10, 3 | 120π² | 1184.352528 |
Questions
How do you find the surface area of a torus?
4π² times both radii. R of 5 and r of 2 give 40π², about 394.78 square units.
How does it relate to the volume?
The volume is 2π²Rr², so the area is the volume divided by r ÷ 2. At r = 2 the two happen to be equal, which is why the same number appears twice in that case.
Is a torus the same as a doughnut?
Geometrically yes, provided the hole is open. A doughnut with a filled centre is a different solid and this formula does not describe it.
Sources and last check
Information, not professional advice.