In 1 radians there are 57.29578 degrees. Meanwhile in 1 degrees there are 0.017453 radians. Keep reading to learn more about each unit of measure and how they are calculated. Or just use the Degrees to Radians calculator above to convert any number.
* Values rounded to 6 decimal places for readability
To convert radians to degrees, use the radians-to-degrees formula:
This works because π radians = 180 degrees.
Steps: take your radian value, multiply by 180, then divide by π.
Common reference values:
Radians and degrees are two ways to measure angles. Degrees split a full turn into 360 equal parts. Radians measure angles by using the radius of a circle. One full turn equals (2\pi) radians.
Use this formula: [ \text{degrees}=\text{radians}\times\frac{180}{\pi} ] Multiply the radian value by 180, then divide by (\pi).
A half-turn is 180 degrees. That same half-turn is (\pi) radians. Since (180^\circ=\pi) radians, the conversion factor becomes (180/\pi).
1 radian equals: [ 1\times\frac{180}{\pi}\approx57.2958^\circ ] So 1 radian is about (57.3^\circ).
Here are some quick conversions many people use:
Use known (\pi) fractions when you can. If the value is a multiple of (\pi), convert by matching it to common angles (like (\pi/2 = 90^\circ)). For other values, you can estimate by using ( \pi \approx 3.14 ) and then apply: [ \text{degrees}\approx\text{radians}\times57.3 ]
Convert the same way: [ \text{degrees}=\text{radians}\times\frac{180}{\pi} ] A negative angle in radians becomes a negative angle in degrees. Example: [ -\pi/3 \text{ rad} = -60^\circ ]
If the angle is written with (\pi), multiply the fraction by 180. Example: [ \frac{3\pi}{4}\text{ rad}=\frac{3}{4}\times180^\circ=135^\circ ] The (\pi) cancels out when you multiply by (180/\pi).
Yes. Degrees are common in basic geometry and many real-world angle measures. Radians are common in trigonometry, calculus, and physics because many formulas work best in radians.
It depends on the setting and the formula. Many math formulas (especially in calculus) assume radians. Some tools and classes use degrees by default. Check your mode or settings before you calculate.
Multiply by (57.3) for a fast estimate: [ \text{degrees}\approx\text{radians}\times57.3 ] This works well for quick checks and rough answers.
(2\pi) radians equals one full turn: [ 2\pi\times\frac{180}{\pi}=360^\circ ] So (2\pi) radians is (360^\circ).
The Calculate Box tool to convert radians to degrees uses the open source script Convert.js to convert units of measurement. To use this tool, simply type a radians value in the box and have it instantly converted to degrees.