Radians are a unit that measures 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 occurring **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.