What are major and minor radius in a torus?

The major radius goes from the center of the torus to the center of the tube. The minor radius is the radius of the circular tube itself.

Can I enter tube diameter instead of tube radius?

Yes. Switch the tube input to diameter and the calculator will divide that value by two before calculating the torus.

Does this calculate mass?

No. To estimate mass, multiply the calculated volume by a material density in compatible units.

Torus Volume Calculator

Calculate torus volume, surface area, outer diameter, inner diameter, and centerline circumference from major and minor radii.

Major radius (cm)

Minor radius (cm)

Tube input

Unit

Enter the major radius and tube size in the same unit. The calculator returns volume, surface area, outer diameter, inner diameter, and centerline circumference.

Calculate torus volume from two radii

English search results consistently use major radius for the distance from the center of the ring to the center of the tube, and minor radius for the tube radius. This calculator keeps that terminology in the input labels and result summary.

V = 2 π^{2} R r^{2}

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

A = 4 π^{2} R r

Surface area uses the same two radii.

What the output means

Output	Meaning
Volume	Space inside the solid torus, in cubic units.
Surface area	Area of the torus surface, in square units.
Outer diameter	Overall diameter across the outside of the ring.
Inner diameter	Diameter of the hole.
Centerline circumference	Circumference traced by the tube center.

The standard ring torus model assumes the minor radius is smaller than the major radius. Equal or larger tube radii create degenerate or self-intersecting cases.

Frequently Asked Questions

Sources and References

Calculations are based on the listed reference sources. Links open in a new tab.

Updated: June 2, 2026

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