Radian

In geometry and algebra, a radian is an angle measurement on a circle, though, instead of using degrees, the length of the circle's radius is used to measure angles.

One radian is approximately 60°.

Degrees to Radians
To convert from degrees to radians, multiply d degrees by π÷180.


 * $$r = \frac{\pi\,d}{180}\,$$

E.g.


 * $$\frac{60\pi\,}{180}\, = \frac{\pi\,}{3}\,$$

60° is equal to $$\frac{\pi\,}{3}\,$$ radians.

Radians to Degrees
To convert from radians to degrees, multiply r radians by 180÷π.


 * $$d = \frac{180r}{\pi\,}\,$$

E.g.


 * $$\frac{180\pi\,}{3\pi\,}\, = 60$$

How Many Radians is a Circle?
We know that a circle is 360°. Using our conversion methods to convert degrees into radians, we can figure this out.


 * $$r = \frac{\pi\,d}{180}\,$$


 * $$r = \frac{360\pi\,}{180}\,$$


 * $$r = 2\pi\,$$

Therefore, 360° is equal to 2π radians.