About the Torus Calculator
A torus is a doughnut or tyre shape, made by turning a circle round an axis that does not cross it. Two numbers describe it: the major radius, from the centre of the whole shape to the middle of the tube, and the minor radius, the radius of the tube itself. This calculator gives the volume, the surface area, the outer diameter and the diameter of the hole. Type the major radius and the minor radius and the torus volume appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Torus Calculator
- 1Enter the major radius and the minor radius.
- 2Pick the units or options from the menus if the torus volume tool offers them.
- 3Read the torus volume in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the torus volume
Designers use a torus for rings, bangles, inner tubes, rubber seals and O-rings. Engineers need the volume to find the mass of a part, and the surface area to estimate paint, coating or heat loss.
A useful cross-check: the volume equals the area of the tube's circle, π × r², times the distance its centre travels, 2π × R. The calculator uses the same idea, so the numbers always agree.
How the torus volume is worked out
Volume = 2π² × R × r². Surface area = 4π² × R × r, where R is the major radius and r the minor radius. A torus with R = 10 and r = 3 has a volume of 2π² × 10 × 9 = 1,776.53 and a surface area of 4π² × 10 × 3 = 1,184.35. Its outer diameter is 26 and the hole is 14 across.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Volume and surface area
- Outer diameter and hole size
- Checks that r is below R
Mistakes to avoid with torus volume
The minor radius must be smaller than the major radius, otherwise the tube would cut through itself and the shape is not a standard ring torus. Mix up the two radii and the answer changes a lot. The major radius is always to the centre of the tube, not to its outer edge.
On phone and computer
On a phone, type into the boxes one after another and read the torus volume underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the torus volume move. The torus calculator works the same on both. A torus is a doughnut shape, so use Annulus Calculator for the flat ring and Sphere Calculator and Cylinder Calculator for related solids. Surface Area Calculator covers more shapes.
Features
- Major radius to the tube centre
- Minor radius is the tube
- Volume = tube area × path length
- Clear messages when the torus volume inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate torus volume?
Volume = 2π² × R × r². Surface area = 4π² × R × r, where R is the major radius and r the minor radius. A torus with R = 10 and r = 3 has a volume of 2π² × 10 × 9 = 1,776.53 and a surface area of 4π² × 10 × 3 = 1,184.35. Its outer diameter is 26 and the hole is 14 across.
What is the formula for torus volume?
Volume = 2π² × R × r². Surface area = 4π² × R × r, where R is the major radius and r the minor radius. The torus calculator applies it exactly and rounds only the displayed answer to six significant figures.
What is the major radius?
The distance from the centre of the whole ring to the centre of the tube.
How do I measure it on a real ring?
Measure the outer diameter and the tube thickness. The minor radius is half the thickness, and the major radius is half the outer diameter minus the minor radius.
What happens when the radii are equal?
The hole closes to a point, a degenerate case called a horn torus. The calculator asks for a smaller minor radius.
Is this torus calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.