# Perimeter of a deltoid

## Description

In geometry, a deltoid, also known as a tricuspoid or Steiner curve, is a hypocycloid of three cusps. In other words, it is the roulette created by a point on the circumference of a circle as it rolls without slipping along the inside of a circle with three times its radius. The perimeter (total arc length) of the deltoid is 16 times the radius of the rolling circle.

Related formulas## Variables

P | Perimeter of the deltoid (m) |

a | The radius of the rolling circle (m) |