Degrees and Radians

There are two commonly used units of measurement for angles. The more familiar unit of measurement is that of degrees and the other one is radians.

In this lesson, we will learn

• how to measure angles in degrees, minutes and seconds
• how to convert an angle measured in degrees, minutes and seconds to decimal notation and vice versa.
• how to add and subtract angles measured in degrees, minutes and seconds
• how to measure angles in radians
• how to convert between degree and radian measurement

The following diagrams show how to define radian in terms of the arc length and the radius and how to convert between radians and degrees. Scroll down the page for examples and solutions.

Angles in radians

We can define radian in terms of the arc length and the radius:

The size of an angle in radian is given by the ratio of the arc length to the length of the radius.

An angle with 1 radian will have an arc length that is equal to the length of the radius.
An angle with 2 radians will have an arc length that is twice the length of the radius.