Calculating your volume is straightforward once you know the Torus Volume formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Torus Volume Calculator.
What is Torus Volume?
The Torus Volume calculation tells you your volume from a few simple inputs. The figure you are solving for here is the volume.
The Torus Volume formula
The core formula is:
Volume = 2 × 9.869604401089358 × Major radius (R, centre to tube centre) × Minor radius (r, tube radius) ^ 2Here is what each input means:
- Major radius (R, centre to tube centre) — a value measured in units. Example: 10 units.
- Minor radius (r, tube radius) — a value measured in units. Example: 2 units.
How to calculate it step by step
- Write down the major radius (r, centre to tube centre) (for example, 10 units).
- Write down the minor radius (r, tube radius) (for example, 2 units).
- Apply the formula above to get your volume.
- Double-check the result with the Torus Volume Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Major radius (R, centre to tube centre) | 10 units |
| Minor radius (r, tube radius) | 2 units |
| Volume | 789.5684 |
| Surface area | 789.5684 |
With major radius (r, centre to tube centre) of 10 units and minor radius (r, tube radius) of 2 units, the volume works out to 789.5684.
Example 2
With major radius (r, centre to tube centre) of 20 units and minor radius (r, tube radius) of 2 units, the volume works out to 1,579.1367.
| Result | Value |
|---|---|
| Volume | 1,579.1367 |
| Surface area | 1,579.1367 |
Example 3
With major radius (r, centre to tube centre) of 5 units and minor radius (r, tube radius) of 2 units, the volume works out to 394.7842.
| Result | Value |
|---|---|
| Volume | 394.7842 |
| Surface area | 394.7842 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Torus Volume Calculator does it instantly, for free, with the formula and a worked example built in.
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