Radians are a unit that measure angle as the ratio of the angle’s arc-length over the radius of a circle. The (equivalent) symbol is used here in the definition to mean that radians are dimensionless by construction and are radius-invariant. In other words, the size of the circle used to measure the angle doesn’t change the value of the measured angle.

A full rotation in radians is equal to (tau) radians, where is the naturally occuring **circle constant** defined by any circle’s circumference divided by its radius. Shown below are the first ten digits of the circle constant.

- See the radian angle system for examples of angles measured in radians and the usage of the system in math.
- See radian vs. degrees for why radians are the preferred unit for measuring angles in math.

The circle constant τ (tau) is a geometric constant approximately equal to 6.283. The numeric value is defined as the length of any circle's circumference divided by the length of its radius.

Radians are a unit that measure angle using the radius of a circle. One radian is equal to the amount of rotation required to travel the length of one radius along the circumference of the circle.

This page compares and contrasts the two systems of measuring angles in math: radians and degrees, and explains why radians is the preferred unit of measure for angles.