Converting Between Radians and Degrees

Radians and Degrees are two ways of measuring angles. Radians are defined as numbers and do not have an attached unit, while degrees are defined with the ° symbol. Here are a few examples of angles defined using either radians or degrees.





There is a simple conversion factor which can be used to convert between the two: pi radians = 180°. When it is set up as a conversion factor, it can be easily used to convert between the two different ways of measuring angles. 

Who invented degrees?

Degrees were originally a concept of the Egyptians who used a base-60 number system. They found that 6 equilateral triangles fit inside of a circle, and therefore determined it to have 360 degrees (6*60). The Egyptians also invented the degrees symbol. (°

Who invented radians?

James Thomson defined and named the radian in 1873. Thomson was a professor of mathematics at Queen's College, Belfast, Northern Ireland, and the brother of the famous physicist William Thomson, Lord Kelvin, who developed the Kelvin measure of temperature. A radian is approximately 57.3°.


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