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A torus — the mathematical name for a donut or ring shape — has volume and surface area formulas that depend on two separate radii rather than just one, which makes it easy to mix up by hand. This calculator finds both the volume and surface area of a torus from its major and minor radii, with a full step-by-step solution.
How it works
Enter the major radius (the distance from the center of the hole to the center of the tube) and the minor radius (the radius of the tube itself). The calculator applies the standard torus volume and surface area formulas.
- Enter major radius (R).
- Enter minor radius (r).
- Click Calculate to see your results.
Examples
A torus with major radius 10 and minor radius 3
With a major radius of 10 and a minor radius of 3, the torus has a volume of about 1,776.53 cubic units and a surface area of about 1,184.35 square units.
Who should use it
- Calculating the volume of a torus-shaped object like an O-ring or gasket for engineering purposes.
- Solving geometry homework or exam problems involving torus volume and surface area.
Industry applications
- Mechanical engineering and manufacturing (O-rings, gaskets, seals)
- Mathematics and geometry education
Advantages
- Calculates both volume and surface area in a single step from the same two measurements.
- Uses the exact standard torus formulas, not an approximation.
Limitations
- Assumes a perfect, standard ring torus — irregular or self-intersecting donut shapes aren't supported.
Common mistakes to avoid
- Mixing up the major and minor radii, which changes both results significantly.
- Forgetting that both formulas use π² (pi squared), not just π.
Best practices
- Measure the major radius from the very center of the whole shape, not from the inner edge of the hole, to match the standard formula.
Tips
- If you only know the tube's diameter and the whole shape's outer diameter, first convert both to radii (divide by 2), then find the major radius by subtracting the minor radius from the outer radius.