Torus Volume Calculator
A torus is a three-dimensional shape that resembles a donut or inner tube, created by rotating a circle around an axis that does not intersect the circle. The torus is defined by two radii: the major radius R, which is the distance from the center of the torus to the center of the tube, and the minor radius r, which is the radius of the tube itself. The volume of a torus is V = 2π² * R * r², and the surface area is A = 4π² * R * r. This calculator computes both the volume and surface area of a torus from the major and minor radii. Enter both values in the same unit of measurement.
Torus volume formulas
Volume = 2π² * R * r²
Surface Area = 4π² * R * r
Reference values
| Major Radius | Minor Radius | Volume | Surface Area |
|---|---|---|---|
| 3 cm | 1 cm | 29.61 cm³ | 118.44 cm² |
| 5 cm | 2 cm | 394.78 cm³ | 394.78 cm² |
| 10 cm | 3 cm | 2,960.94 cm³ | 1,185.45 cm² |
| 1 m | 0.5 m | 4.93 m³ | 19.74 m² |
Torus volume calculator: frequently asked questions
What is a torus?
A torus is a three-dimensional shape that looks like a donut or inner tube. It is formed by rotating a circle around an axis that does not intersect the circle.
What are major and minor radii?
The major radius R is the distance from the center of the torus to the center of the tube. The minor radius r is the radius of the tube itself.
What is the volume formula?
The volume of a torus is V = 2π² * R * r², where R is the major radius and r is the minor radius.
What is the surface area formula?
The surface area of a torus is A = 4π² * R * r.
Where are tori found?
Tori appear in nature and engineering as donuts, inner tubes, rings, and in various mathematical and physical applications.
Official sources
- Khan Academy: Volume and surface area of solids.
- NIST: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.