Torus Volume Calculator

A torus is the mathematical name for a donut: take a circle and sweep it in a loop around a central axis, and the solid ring you trace out is a torus. It is a shape that shows up far beyond the bakery, in O-rings and seals, inner tubes and tyres, rolled hoops, coils, architectural rings and countless engineering and manufacturing parts. This calculator gives you the two figures that matter most, the volume and the surface area, from just two measurements: the major radius, which runs from the centre of the hole out to the centre of the tube, and the minor radius, which is the radius of the tube itself. Enter both and the calculator returns the enclosed volume and the surface area in matching units, updating the moment you change a value. The volume tells you the capacity or the amount of material in the ring, useful for sizing a sealed tube, estimating the rubber in a tyre, or working out the contents of a ring-shaped vessel. The surface area is what you need for coating, plating, painting or working out heat transfer across the surface. The torus formulas come from a neat piece of geometry, Pappus's theorem, which says the volume equals the cross-sectional area of the tube multiplied by the distance its centre travels around the loop, and the surface area follows the same idea with the circumference. Doing it by hand means juggling pi squared and two different radii, which is easy to fumble, so this tool keeps it fast and correct. The formulas and a worked example are below.

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