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Properties of Torus

- By Dr. Minas E. Lemonis, PhD - Updated: March 3, 2019

This tool calculates the basic geometric properties of a ring torus. Enter the shape dimensions Rout and Rin below. The calculated results will have the same units as your input. Please use consistent units for any input.

Rout =
Rin =
Volume =
Surface area =
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Definitions

Geometry

The torus is a 3-dimensional object, that can be created through rotation a circular disc around a circle. The volume of a torus is given by the formula:

\[ V = \frac{\pi^2}{4}\left(R_{\textrm{out}}+R_{\textrm{in}}\right)\left(R_{\textrm{out}}-R_{\textrm{in}}\right)^2 \]

where \(R_{\textrm{out}}\) the outer radius of the torus and \(R_{\textrm{in}}\) its inner radius.

The surface area of the torus is given by the next formula:

\[ A= \pi^2\left(R_{\textrm{out}}+R_{\textrm{in}}\right)\left(R_{\textrm{out}}-R_{\textrm{in}}\right) \]

See also
Sphere properties
Ellipsoid properties
Cone properties
Cylinder properties
Pyramid properties
All solids
All Geometric Shapes tools