Angle Conversion between Degrees and Radians

Instructions: Use this solver to convert angles from degrees to radians, or from radians to degrees. If you know the angle in degrees, type in the corresponding box. And if you know the angle in radians, type in the other box. Note that you can type Math expression like pi/3 (for \(\pi/3\)), or sqrt(2) for \(\sqrt{2}\), etc.

Angle in Degrees (if you know it) =

Angle in Radians (if you know it) =

More About Angle Conversions

Angles refer to a measure of the opening between to rays (or line segments), relative to the opening between segments in a circle, that start from the center of the circle. There are different systems, or conventions to measure that degree of opening. One system is the system of degrees, in which the opening is measured as 0o when the two segments overlap (so there is no opening at all), and 360o represents to the opening of the whole circle. Any other angle is measured in degrees proportionally to the amount of opening between 0o and 360o.

Another system used is radians, which uses a different approach. It measures an angle based on the “number of radiuses” the arc length of the segment in the circle determined by the angle represents. With that into consideration, the angle in radians corresponding to the full circle is \(2\pi\) radians, because the arc length of the full circle is \(2\pi r\), so it is \(2\pi\) times the radius \(r\).

How to Convert Degrees to Radians?

If you have an angle \(d\) in degrees, the angle in radians \(r\) is computed as follows:

\[r = \frac{2\pi d}{360} = \frac{\pi d}{180} \]

How to Convert Radians to Degrees?

If you have an angle \(r\) in radians, the angle in degrees \(d\) is computed as follows:

\[d = \frac{360 r}{2\pi} = \frac{180 r}{\pi} \]

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Angle Conversion between Degrees and Radians

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