VolLab

Torus (Donut) Volume Calculator

The classic donut shape, from two radii.

Center-to-tube radius R

Tube radius r

Volume

1,421.223

Surface area: 947.482

What you entered

Center-to-tube radius R: 8Tube radius r: 3

1
Volume = 2π² × R × r²
2π² × 8 × 3²= 1421.223
2
Surface area = 4π² × R × r
4π² × 8 × 3= 947.482

Result

Volume: 1,421.223

A torus (donut shape) with center-to-tube radius 8 and tube radius 3 has a volume of 1,421.223 and a surface area of 947.482.

Torus volume and surface area

R is the distance from the centre of the hole to the centre of the tube; r is the tube's own radius. Volume is 2 pi squared R r squared.

Major radius R	Tube radius r	Volume	Surface area
5	2	394.78	394.78
6	2	473.74	473.74
8	3	1421.22	947.48
10	3	1776.53	1184.35
12	4	3789.93	1894.96
15	5	7402.20	2960.88

Volume and surface area coincide in the first two rows because both formulas share the 4 pi squared R r factor and differ only by r over 2 - so they are equal exactly when the tube radius is 2, whatever R is. Volume depends on the square of the tube radius but only linearly on R, so thickening the tube matters far more than widening the ring. Be careful which radius you have: some sources define R to the outer edge rather than to the tube centre, which gives a different answer.

Two radii, not one

A torus needs two measurements: R, the distance from the center hole to the middle of the tube, and r, the radius of the tube itself. Volume = 2π² × R × r².

Where torus volume matters

O-rings, inner tubes, bagels, and the donut-shaped vacuum chambers in fusion reactors (tokamaks) are all toruses — the same formula sizes all of them.

Frequently asked questions

How do I calculate the volume of a torus?

Volume = 2π² × R × r², where R is the distance from the center of the hole to the center of the tube, and r is the tube's radius. A donut with R=10 cm and r=3 cm: V = 2π² × 10 × 9 = 1,775.3 cm³.

What is the difference between R and r in a torus?

R (major radius) is the distance from the center of the torus to the center of the tube. r (minor radius) is the radius of the tube itself. The hole in the center has radius R−r, and the outer diameter is 2(R+r).

What is the surface area of a torus?

Surface area = 4π² × R × r. A torus with R=10 and r=3: SA = 4π² × 10 × 3 = 1,184 cm². The formula comes from revolving a circle (circumference 2πr) around a circular path (circumference 2πR).