Radians to Degrees Converter
Convert radians to degrees by multiplying by 180/π ≈ 57.29578. Includes a table of π fractions, worked examples, and when to use each unit in programming and maths.
Radians to degrees
Formula
Multiply by 180 and divide by π.
One radian is 57.29578° — an awkward number, which is exactly why degrees survive for everyday angles while radians rule in mathematics.
Worked example
Convert 2 radians:
When the input is already a fraction of π the work collapses. For 3π/4, the π cancels:
Conversion table
| Radians (rad) | Degrees (°) |
|---|---|
| 0.5 | 28.64789 |
| 1 | 57.29578 |
| 1.5708 | 90.00021 |
| 2 | 114.5916 |
| 3 | 171.8873 |
| 3.1416 | 180.0004 |
| 4 | 229.1831 |
| 5 | 286.4789 |
| 6 | 343.7747 |
| 6.2832 | 360.0008 |
| 10 | 572.9578 |
Fractions of π
Most radian values in practice arrive as a multiple of π. Cancel the π and you are left with simple arithmetic:
- π/6 = 30°
- π/4 = 45°
- π/3 = 60°
- π/2 = 90°
- 2π/3 = 120°
- 3π/4 = 135°
- π = 180°
- 3π/2 = 270°
- 2π = 360°
The rule: a value of radians is degrees.
Converting in code
Library trigonometric functions return radians, so results need converting before anyone reads them. Math.atan2(y, x) gives a bearing in radians between −π and π; multiply by 180 / Math.PI to get degrees between −180 and 180.
If you want a compass bearing from 0 to 360 instead, add 360 and take the remainder:
((Math.atan2(y, x) * 180 / Math.PI) + 360) % 360
FAQ
How many degrees is 1 radian? 57.29578°, or 57° 17′ 45″ in degrees, minutes and seconds.
How many radians is 1 degree? 0.01745329 rad.
What is π radians in degrees? 180° — half a turn.
What is 2 radians in degrees? 114.5916°.
Why is the conversion factor so untidy? Because 360 is a human choice, inherited from Babylonian astronomy, while the radian comes from the geometry of the circle itself. There is no reason the two should line up neatly.