Torus Calculator
Compute volume and surface area of a torus from its major and minor radii.
Inputs
units
Distance from center of torus to center of tube
units
Radius of the tube
Volume
1,421.2230cu units
Surface Area
947.4820sq units
Step by step
Volume
V = 2π²Rr² = 2π² × 8 × 3²
= 1421.2230
Surface area
SA = 4π²Rr = 4π² × 8 × 3
= 947.4820
How it works
A torus is a donut-shaped surface of revolution. Major radius R is from the center of the torus to the center of the tube; minor radius r is the tube's radius. Volume = 2π²Rr², Surface area = 4π²Rr.
Formulas
Volume
V = 2π²Rr²
- R
- Major radius
- r
- Minor radius
Surface Area
SA = 4π²Rr
- R
- Major radius
- r
- Minor radius
Frequently Asked Questions
What happens when r > R?
The torus self-intersects (spindle torus). This calculator requires r ≤ R for a standard ring torus.
How is a torus generated?
By rotating a circle of radius r about an axis at distance R from its center.