Torus Volume Calculator

Calculate the volume of a torus.

Major Radius (R)Minor Radius (r)

Enter radii above.

How to Use the Torus Volume Calculator

Enter the major radius and tube radius to calculate the volume of a torus.

Practical Example

With major radius 5 and tube radius 2, the torus volume is approximately 394.78 cubic units.

Factors That Affect the Result

The major radius is measured from the center of the torus to the center of the tube. Do not confuse it with the outside radius.

Frequently Asked Questions

What is a torus?

A ring-shaped 3D surface similar to a donut.

Which radius is the tube radius?

It is the radius of the circular cross-section.

What units are returned?

Cubic units.

Related Tools

Understanding Torus Volume

A torus is a ring-shaped solid. Using major radius R from the center of the hole to the center of the tube and minor radius r for the tube itself, volume is 2π²Rr².

Do not confuse major radius with the outer radius of the entire shape. Both measurements must use the same unit. The formula assumes a perfect circular tube and circular path, so real seals, rings or manufactured parts with flattened or irregular sections may have a different actual volume.

Understanding Torus Volume

A torus is formed by rotating a circle around an axis outside that circle. Its volume is commonly calculated with V = 2π²Rr², where R is the major radius from the center of the torus to the center of the tube and r is the minor radius of the tube itself.

Do not confuse the major radius with the outside radius of the whole shape. Keep both radii in the same unit; the result will be expressed in cubic units. For physical rings or tubing, wall thickness and manufacturing tolerances may change actual material volume.