Math

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Torus Volume Calculator.

Calculate the volume 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
Volume: 394.784176

Volume

0.000000

Results update automatically as you type.

Use Cases

Engineering and Design

Determine the volume of torus-shaped components, such as O-rings, gaskets, or magnetic cores, to estimate material requirements or weight.

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

Mathematics and Education

Verify manual calculations or explore the relationship between torus dimensions and volume in geometry or calculus studies.

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

Frequently Asked Questions

What is a torus and how is its volume calculated?
A torus is a ring-shaped surface, like a donut. Its volume is calculated using the formula V = 2π²Rr², 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 and minor radii of a torus?
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. For a donut, R is the distance from the hole's center to the middle of the dough, and r is the thickness of the dough.
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 a hole (R > r) and those that are self-intersecting (R < r). However, for a standard donut shape, R should be greater than r.

Tips & Common Mistakes

Tips

  • Ensure both radii are in the same unit before calculating to get the volume in cubic units of that unit.
  • For a standard donut shape, the major radius (R) must be greater than the minor radius (r). If R is less than r, the torus self-intersects.
  • Double-check your inputs: the major radius is the distance from the center of the hole to the center of the tube, not the outer radius.
  • Use the calculator to quickly compare volumes for different torus sizes in design iterations.

Common Mistakes to Avoid

  • Confusing the major radius with the outer radius. The outer radius is R + r, not R.
  • Using inconsistent units for R and r, leading to incorrect volume units.
  • Entering the diameter instead of the radius for either R or r, which will give a volume that is off by a factor of 4 or 8.

Last updated: August 13, 2026