Torus Volume Calculator

What Is a Torus?

A torus is a 3D donut shape formed by revolving a circle around an axis. It has two radii: the minor radius $r$ (tube thickness) and the major radius $R$ (distance from the center of the torus to the center of the tube). You can also describe it using inner radius $a$ and outer radius $b$, where $r = (b-a)/2$ and $R = (a+b)/2$.

For other 3D shapes, try our Cylinder Calculator and Sphere Equation Calculator.

Torus Volume and Surface Area

Volume:

$$V = 2\pi^2 r^2 R$$

Surface area:

$$S = 4\pi^2 r R$$

Using inner and outer radii: $V = \frac{\pi^2}{4}(b-a)^2(b+a)$.

Worked Example

A torus has inner radius 60 mm and outer radius 140 mm. Then $r = 40$ mm, $R = 100$ mm, and $V = 2\pi^2 \times 40^2 \times 100 \approx 3{,}158{,}273$ mm³.