Torus Volume Calculator

About this calculator

A torus — the donut-like shape formed by revolving a circle around an axis outside itself — has a volume given by V = 2π² × R × r², where R is the distance from the center of the tube to the center of the torus, and r is the radius of the tube itself; its surface area follows a similar formula, A = 4π² × R × r.

Engineers use torus geometry to calculate material volume for O-rings, gaskets, and seals, to size donut-shaped storage tanks and pressure vessels, and in fields like plasma physics, where tokamak fusion reactors are built around a torus-shaped chamber. Mathematics students encounter the torus as a classic example in solid-of-revolution problems in calculus.

This calculator takes the two radii of a torus and returns its volume and surface area.