Volume of Torus Calculator
Volume = 2π²Rr² (R = tube center distance / major radius, r = tube minor radius)
The Donut Shape, Measured
A torus is what you get by sweeping a small circle around a larger circular path — the geometry of a donut, an inner tube, or an O-ring seal. Two radii define it completely: the major radius, from the center of the whole shape out to the center of the tube, and the minor radius, the tube's own thickness.
The Formula
Volume = 2π²Rr²
where R is the major radius and r is the minor (tube) radius. The minor radius can never exceed the major radius — if it did, the tube would overlap itself at the center and the shape would no longer be a simple torus.
Worked Example
For a torus with major radius 5 and minor radius 2:
| Step | Calculation | Result |
|---|---|---|
| r² | 2² | 4 |
| Volume | 2 × π² × 5 × 4 | 394.7842 |
Where This Matters
- O-ring and gasket design — the rubber cross-section volume of a sealing ring follows this formula.
- Tokamak and pipe engineering — toroidal chambers and bent piping sections are modeled with major/minor radius geometry.
- Product design — inner tubes, stress balls, and donut-shaped components size their material from this volume.
How to Use This Calculator
- Enter the Major Radius (R, center to tube center).
- Enter the Minor Radius (r, tube radius).
- Select Calculate to get the volume.
Related Calculations
For the simpler sphere this shape is related to, see the Sphere Volume Calculator.