Angles

Degrees is one way to measure angles but one will also often encounter radians which is the standard unit of angular measures in mathematics.

In order to convert your angle from either degrees to radians or vice versa, use the following formulas:

$$degrees=radians\: \cdot \frac{180^{\circ} }{\pi }$$

or

$$radians=\frac{\pi}{180^{\circ}}\cdot \: degrees$$

Example

Convert \(360^{\circ}\) to radians.

We now use the second formula and get:

$$radians=\frac{\pi}{180^{\circ}} \cdot 360^{\circ}=2\pi$$

Video lesson

Convert \(45^{\circ}\) to radians