Torus Calculator
Compute volume and surface area of a torus from its major and minor radii.
About Torus Calculator
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
Worked example
With the default values below, Torus Calculator returns Volume of 1,421.2230. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Major Radius (R)minimum 0 units
- 8 units
- Minor Radius (r)minimum 0 units
- 3 units
Results
- Volume
- 1,421.2230 cu units
- Surface Area
- 947.4820 sq units
Step by step
- 1Volume= 1421.2230
- 2Surface area= 947.4820
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.