Unit Circle Radians

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.

Common Angles (Degrees) Common Angles (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.

Common Angles (Degrees) Common Angles (Radians)

Good Links

Radians | Concept

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.

Unit Circle | Concept

The unit circle is a unifying idea in mathematics that connects many useful concepts together. This article goes over the basic properties of the circle using interactive examples and explains how they connect to the trigonometric functions and pythagorean theorem.

Unit Circle Chart | Concept

The unit circle chart shows the position of the points along the circle that are formed by dividing the circle into eight and twelve parts.