Find the volume and surface area of a torus from its major and minor radii, with its ring, horn or spindle type.
Torus volume
How to use this tool
Centre of the donut to the centre of the tube.
The tube radius itself.
Both are shown in the units implied by your radii.
Ring, horn or spindle, from the ratio of the radii.
Formula & worked example
A torus with major radius 10 and tube radius 3 has volume 1,776.53 and surface area 1,184.35.
Limitations — read this before you rely on it
Exact for a perfect circular torus. Real donuts, tyres and rings deviate slightly from a perfect tube.
Frequently asked questions
A donut shape: a circle swept around an axis. R is the distance from the centre to the tube centre; r is the tube radius.
Ring (r < R) has a hole; horn (r = R) just touches at the centre; spindle (r > R) overlaps itself. Everyday donuts are ring tori.
Volume equals the cross-section area times the distance its centre travels: πr² × 2πR.
Use the same unit for both radii; volume is in cubic units and area in square units.
Halve each diameter first: the formulas need radii.