Torus Volume and Surface Area Calculator

A torus is a donut shape, a tube bent into a circle. It is defined by a major radius from the center to the tube and a minor radius for the tube itself.

The volume equals two times pi squared times the major radius times the minor radius squared. This comes from sweeping the tube cross section around the central ring.

The surface area equals four times pi squared times the major radius times the minor radius. It is the tube circumference multiplied by the path it travels.

The major radius is the distance from the center of the hole to the center of the tube. The minor radius is the radius of the tube cross section.

A standard ring torus keeps the major radius at least as large as the minor radius. This calculator accepts any positive values, but small major radii give a self intersecting shape.