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How to Calculate Torus

What is Torus?

A torus is the 3D shape of a donut or ring. It is formed by rotating a circle of radius r around an axis at distance R from the circle's centre. The inner hole appears when R > r.

Formula

Volume = 2π² × R × r²
R
radius of the tube itself — radius of the tube itself

Step-by-Step Guide

  1. 1R = distance from the centre of the tube to the centre of the torus
  2. 2r = radius of the tube itself
  3. 3Volume = 2π² × R × r²
  4. 4Surface area = 4π² × R × r

Worked Examples

Input
R=5, r=2 (donut shape)
Result
Volume = 394.8 units³ · SA = 394.8 units²
Coincidental equality for these values
Input
R=10, r=3 (thin ring)
Result
Volume = 1,776.5 units³
2π² × 10 × 9

Frequently Asked Questions

What is Torus Is The 3D Shape Of A Donut Or Ring?

A torus is the 3D shape of a donut or ring. It is formed by rotating a circle of radius r around an axis at distance R from the circle\

How accurate is the Torus Is The 3D Shape Of A Donut Or Ring calculator?

The calculator uses the standard published formula for torus is the 3d shape of a donut or ring. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Torus Is The 3D Shape Of A Donut Or Ring calculator use?

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Torus Is The 3D Shape Of A Donut Or Ring calculator use?

The core formula is: R = distance from the centre of the tube to the centre of the torus. Each step in the calculation is shown so you can verify the result manually.

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