Math

Torus Calculator

Volume and surface of a ring or donut.

By TheCalcTools Updated Formula checked and tested

Your numbers

Your results

Volume
Volume
—
Surface area
—
Outer diameter
—
Inner (hole) diameter
—

Torus Calculator by TheCalcTools

How the Torus Calculator works

Enter R, the distance from the centre of the hole to the centre of the tube.

Enter r, the radius of the tube itself.

The formulas follow from Pappus’s centroid theorems.

The formula

V = 2π² R r²A = 4π² R r

Worked example

Using the default values shown in the calculator:

Major radius R (centre to tube centre)5
Minor radius r (tube radius)1.5
  1. V = 2π² × 5 × 1.5² = 222.066.
  2. A = 4π² × 5 × 1.5 = 296.088; outer diameter 13.000, hole 7.000.

Result:

Volume222.066
Surface area296.088
Outer diameter13.000
Inner (hole) diameter7.000

Frequently asked questions

What if R is smaller than r?

The shape becomes a self-intersecting spindle torus, which this tool does not cover.

What are real examples?

Rings, O-rings, tyre inner tubes, bagels and donuts are torus-shaped.

Sources and further reading

Cylinder Volume CalculatorEnter the radius and height to find a cylinder's volume and surface area Sphere Volume and Surface Area CalculatorEnter the radius to find the volume and surface area of a sphere Circle CalculatorEnter the radius to get the diameter, circumference and area of a circle Triangle Calculator (Solve Any Triangle: SSS, SAS, ASA)Choose what you know and enter the values Triangle Area Calculator (Heron's Formula)Enter three side lengths to find the triangle's area, perimeter and angles Pythagorean Theorem CalculatorSolve for any side of a right triangle using a² + b² = c²

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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.