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Torus Surface Area Calculator.

Calculate the surface area of a ring torus.

On-device calculationNo signup
01

Set your values

Results update as you type.

majorRadius: 5

majorRadius

0.000000
minorRadius: 2

minorRadius

0.000000
Surface area: 394.784176

Surface area

0.000000

Results update automatically as you type.

Use Cases

Engineering and Design

Determine the surface area of torus-shaped components, such as O-rings, gaskets, or donut-shaped parts, for material estimation or coating requirements.

Example: Calculate the surface area of an O-ring with R=10 cm and r=2 cm.

Mathematics and Education

Verify surface area calculations for torus problems in geometry or calculus, or use as a teaching aid to understand the formula.

Example: Check the surface area of a torus with R=5 and r=1.

Frequently Asked Questions

What is a torus and how is its surface area calculated?
A torus is a ring-shaped surface, like a donut. Its surface area is calculated using the formula A = 4π²Rr, where R is the major radius (distance from the center of the tube to the center of the torus) and r is the minor radius (radius of the tube).
What are the major radius (R) and minor radius (r) in the torus calculator?
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. Both are required inputs for the surface area calculation.
Can I use this calculator for any torus shape?
Yes, as long as you have the major and minor radii. The calculator works for any ring torus, including those with different proportions, as long as R > r. If R = r, the torus becomes a self-intersecting shape, and the formula may not apply.

Tips & Common Mistakes

Tips

  • Ensure both radii are in the same units (e.g., both in meters or both in inches) to get the surface area in square units.
  • Remember that the major radius R must be greater than the minor radius r for a standard ring torus.
  • Double-check your inputs: a small change in either radius significantly affects the surface area because it's proportional to the product R × r.
  • Use the calculator to explore how changing R or r affects the surface area, which can help in design optimization.

Common Mistakes to Avoid

  • Confusing major radius (R) with minor radius (r) – R is the distance to the tube's center, r is the tube's radius.
  • Using different units for R and r without converting, leading to incorrect surface area units.
  • Entering values where R ≤ r, which does not represent a valid ring torus and may produce misleading results.

Last updated: August 13, 2026