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Torus Volume Calculator

Calculate the volume of a perfect mathematical donut.

V = 2 \pi^2 R r^2
R = ?
r = ?
Diagram updates instantly as you type.

What is a Torus?

A 3D shape that looks like a donut or inner tube.

A torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle, which does not touch the circle.

Key Information
Shape Focus
torus volume calculator

How to Find Torus Volume

You need the major radius and the minor radius.

1
Find the minor radius (radius of the tube itself).
2
Find the major radius (distance from the center of the hole to the center of the tube).
3
Apply the standard formula.

Torus Volume Formula

The equation for a torus.

V = 2 π^2 R r^2
V Volume
R Major Radius
r Minor Radius

Where 'R' is the major radius and 'r' is the minor radius.

Frequently Asked Questions

What is the major radius?

The major radius (R) is the distance from the center of the entire shape to the center of the 'tube' part.

What is the minor radius?

The minor radius (r) is the radius of the cross×section of the tube itself.

Is an inner tube a perfect torus?

An inflated inner tube or an O×ring are excellent real×world examples of a torus.

What if the hole in the middle disappears?

If the major radius becomes smaller than the minor radius, the shape intersects itself and is called a spindle torus or horn torus.