The unit circle uses the radians unit system which measures angles the radius of the circle. One radian is equal the arc-length required to travel the length of the radius of the circle. Click and drag the blue control point in the interactive above to see how a radian is defined.

A full rotation in radians is approximately equal to radians or . This number naturally occurs from dividing the length of a circle by the length its radius. Mathemeticians prefer radians since the concept of an angle and the concept of a circle are closely related together. So measuring angles using the proportional length of the radius leads to more succinct and elegant formulas throughout mathematics.

## Common Angles

Shown below are some common angles shown from dividing the circle into 8 equal angles. If you are using or are more familiar with the convention of using the constant the common angles around the unit circle can be calculating using fractions of a full rotation in radians.

## A Better Constant: (tau)

The constant (tau) is equal to a full rotation in radians, where . Adopting the convention of using this constant makes talking about, converting and using the radians system easier. For this reason, this website prefers the use of over . Shown below are another set of common angles this time from dividing the circle into 12 equal angles.