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 180.0000 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.
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.