About the torus calculator
A torus is a circle of radius r swept around an axis at distance R. By Pappus’s theorems, its volume is the tube’s cross-section area (πr²) times the distance its center travels (2πR), and its surface area is the tube’s circumference times the same distance.
If you measured a physical ring, enter the outer and inner radius (or diameter ÷ 2), the calculator converts them to R and r.
Formulas
| Volume | V = 2π²Rr² |
| Surface area | S = 4π²Rr |
| Outer / inner radius | R ± r |
Frequently asked questions
What is the volume of a donut?
V = 2π²Rr², which is the tube’s cross-section πr² times the path length 2πR.