## Properties of Torus

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 =

## 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:

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