Torus Surface Area Calculator

What Is Torus Surface Area?

A torus is a donut-shaped 3D solid formed by revolving a circle around an axis. Its surface area measures the total outer skin of the shape, useful for material estimates on rings, tubes, and tires. The torus has a minor radius $r$ (tube thickness) and a major radius $R$ (center-to-tube distance), or equivalently inner radius $a$ and outer radius $b$.

For volume calculations, see our Torus Volume Calculator and Surface Area of Cylinder Calculator.

Torus Surface Area Formula

Using minor and major radii:

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

Using inner and outer radii:

$$S = \pi^2 (b - a)(b + a)$$

where $r = (b-a)/2$ and $R = (a+b)/2$.

Worked Example

A ring-type torus has inner radius 50 mm and outer radius 120 mm. Then $r = 35$ mm, $R = 85$ mm, and $S = 4\pi^2 \times 35 \times 85 \approx 117{,}437$ mm².