Radians to Degrees Converter

What is a radians to degrees converter?

A radians to degrees converter changes an angle measured in radians into its equivalent value in degrees. Radians describe an angle by the length of the arc it subtends on a unit circle, while degrees split a full turn into 360 equal parts. Because both units measure the same physical quantity, any angle can be expressed either way, and this tool moves between them in both directions.

Formula

The conversion relies on the fact that a half turn equals both $\pi$ radians and $180^\circ$:

$\text{Degrees} = \text{Radians} \times \frac{180}{\pi}$

Conversely, to go the other way:

$\text{Radians} = \text{Degrees} \times \frac{\pi}{180}$

How to convert radians to degrees

1. Take the angle value expressed in radians.
2. Multiply it by the base factor $\frac{180}{\pi} \approx 57.29578$.
3. The result is the same angle expressed in degrees.

So 1 radian equals approximately 57.29578 degrees. To reverse the process, multiply a degree value by $\frac{\pi}{180} \approx 0.0174533$.

Worked examples

Example 1: 1 radian to degrees

$1 \times \frac{180}{\pi} \approx 57.29578^\circ$

A single radian is just under 57.3 degrees.

Example 2: 90 degrees back to radians

$90 \times \frac{\pi}{180} \approx 1.570796 \text{ rad}$

A right angle of 90 degrees equals about 1.570796 radians, which is exactly $\frac{\pi}{2}$.

Example 3: 2 radians to degrees

$2 \times \frac{180}{\pi} \approx 114.59156^\circ$

FAQ

How many degrees is one radian?

One radian is approximately 57.29578 degrees, the value of $\frac{180}{\pi}$.

How do I convert back from degrees to radians?

Multiply the degree value by $\frac{\pi}{180}$. You can also use the degrees to radians converter or the arc length calculator for related work.