How do you convert radians to degrees?

Multiply the radian value by 180 divided by pi. So degrees = radians times (180 / pi). For example, pi radians = pi times (180/pi) = 180 degrees. And 1 radian = 180/pi = approximately 57.296 degrees.

What is 1 radian in degrees?

1 radian equals 180 divided by pi degrees, which is approximately 57.2958 degrees. This is the angle subtended at the centre of a circle by an arc equal in length to the radius.

How many radians are in a full circle?

A full circle (360 degrees) equals 2 times pi radians, which is approximately 6.2832 radians. A half circle (180 degrees) equals pi radians (approximately 3.1416). A quarter circle (90 degrees) equals pi over 2 radians (approximately 1.5708).

Radians to Degrees Calculator

This converter changes any angle from radians to degrees. Radians are the standard mathematical unit for angles and are what most programming languages and scientific calculators expect as inputs for trigonometric functions like sine, cosine, and tangent. Degrees are the everyday unit most people are more familiar with, dividing a circle into 360 equal parts. Converting between them is a matter of scaling: since a full circle is both 360 degrees and 2 pi radians, one radian equals 180 divided by pi, which is approximately 57.2958 degrees. The conversion formula is simply degrees = radians times (180 / pi). So if you have an angle of pi radians, multiplying by 180/pi gives exactly 180 degrees. If you have 1 radian, you get approximately 57.296 degrees. This calculator also converts to gradians (where a full circle is 400 gradians, a right angle is exactly 100 gradians) and turns (where one complete rotation equals 1 turn). Enter your radian value as a decimal number and all three outputs update instantly. The default value is pi, approximately 3.14159, which converts to 180 degrees. This tool is particularly useful for students working with trigonometry and calculus, programmers checking the output of math functions, surveyors moving between unit systems, and anyone who needs to interpret a radian value in more familiar degree terms. Results are for reference only.

Angle in radians

rad

180.00°

degrees

Gradians200.00 grad

Turns0.5000 turns

1 rad =57.296°

How it works

The conversion formula is: degrees = radians × (180 / π). Since 2π radians = 360°, one radian = 180/π ≈ 57.2958°. Gradians: multiply degrees by 10/9 (or multiply radians by 200/π). Turns: divide degrees by 360 (or divide radians by 2π). The calculator uses the full JavaScript Math.PI constant for maximum precision.

Worked example

π rad × (180/π) = 180.00°. Gradians: 180 × 10/9 = 200.00 grad. Turns: 180/360 = 0.5000. Other common values: 1 rad = 57.296°, π/2 rad = 90.00°, π/4 rad = 45.00°, π/3 rad = 60.00°, 2π rad = 360.00°.

Related calculators

Degrees to Radians Calculator: convert in the opposite direction from degrees to radians.
Triangle Calculator: solve any triangle using angles that may be input in degrees.
Percent Error Calculator: verify how closely a manual radian-to-degree conversion matches the exact result.

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