Convert between degrees, radians, gradians and more.
Converted instantly in your browser.
How do you convert degrees to radians and other angle units?
Each angle is converted to degrees, then to the target unit. One radian = 180/π degrees ≈ 57.2958°, and one full turn = 360°. For example, 180 degrees = π radians ≈ 3.1416 rad = 200 gradians = 0.5 turn. Radians are the natural unit for trigonometry and calculus, while degrees are common in everyday geometry.
Understanding your result
Radians are the natural unit for trigonometry and calculus; degrees are common in everyday geometry; gradians divide a right angle into 100.
Formula and method
Each angle is converted to degrees, then to the target unit. One radian = 180/π degrees ≈ 57.2958°, and one full turn = 360°.
Assumptions and limitations
Conversions are exact, using pi for the radian relationship (180 degrees = pi radians). The tool converts a plain angle value; it does not evaluate trigonometric functions or reduce angles into a standard 0–360 degree range, and displayed radian values are rounded, so pi appears as 3.14159 rather than a symbol.
Worked example
180 degrees = π radians ≈ 3.1416 rad = 200 gradians = 0.5 turn.
Common angle conversions
| Convert | Equals |
|---|---|
| 1 radian | 57.2958 degrees |
| 180 degrees | 3.14159 radians |
| 90 degrees | 1.5708 radians |
| 1 turn | 360 degrees |
| 1 degree | 60 arcminutes |
| 1 degree | 0.0174533 radians |
| 1 arcminute | 60 arcseconds |
| 1 gradian | 0.9 degrees |
How to use this tool
- Enter the angle.
- Choose the units to convert from and to.
- Read the result and the full unit table.
Common mistakes to avoid
- Using degrees where a formula expects radians (or vice versa).
About the Angle Converter
Convert an angle between degrees, radians, gradians and more. Enter a value and see every unit at once.
Who should use this tool
Students and engineers converting between degrees and radians for trigonometry and calculus, surveyors and navigators using arcminutes and arcseconds, and programmers or designers who need turns and gradians. It covers degrees, radians, gradians, arcminutes, arcseconds and full turns.
Benefits
- Covers both everyday (degrees) and mathematical (radians) units
- Includes surveying and navigation units — arcminutes and arcseconds
- Uses pi precisely for accurate radian conversion
- Private, offline and instant
Practical use cases
- Converting an angle from degrees to radians for a trig or calculus problem
- Reading bearings and coordinates that use arcminutes and arcseconds
- Setting rotation values in design or animation software that expects radians
- Checking that a programmed angle matches an expected degree value
Explore all Unit Converters tools
Frequently asked questions
How many radians is 180 degrees?
180 degrees equals π radians, about 3.1416.
What is a gradian?
A gradian (gon) divides a right angle into 100 parts, so a full turn is 400 gradians.
How do I convert degrees to radians?
Multiply degrees by pi/180 (about 0.0174533). So 180 degrees is pi radians (3.14159), and 90 degrees is pi/2 radians (1.5708). To go back, multiply radians by 180/pi.
How many degrees are in one radian?
One radian equals 57.2958 degrees (180 divided by pi). It is the angle where the arc length equals the circle's radius, which is why it appears throughout trigonometry and calculus.