How Angle Conversion Works
Angle conversion is based on the relationship between a full rotation and the unit being used. Degrees are the most common, radians are standard in mathematics, gradians divide a circle into 400 parts, and turns represent whole rotations.
Quick note: The conversion is linear, so the angle can be positive or negative. The converter preserves the sign and only changes the unit.
Formula Summary
Degrees -> Radians = degrees x pi / 180
Degrees -> Gradians = degrees x 10 / 9
Degrees -> Turns = degrees / 360
Degrees -> Arcminutes = degrees x 60
Quick Reference Table
| Degrees | Radians | Gradians | Turns |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 30 | 0.5236 | 33.3333 | 0.0833 |
| 45 | 0.7854 | 50 | 0.125 |
| 60 | 1.0472 | 66.6667 | 0.1667 |
| 90 | 1.5708 | 100 | 0.25 |
| 180 | 3.1416 | 200 | 0.5 |
| 270 | 4.7124 | 300 | 0.75 |
| 360 | 6.2832 | 400 | 1 |
| 15 | 0.2618 | 16.6667 | 0.0417 |
| 22.5 | 0.3927 | 25 | 0.0625 |
| 1 | 0.0175 | 1.1111 | 0.0028 |
| 2.5 | 0.0436 | 2.7778 | 0.0069 |
| 5 | 0.0873 | 5.5556 | 0.0139 |
| 10 | 0.1745 | 11.1111 | 0.0278 |
| 75 | 1.3090 | 83.3333 | 0.2083 |
| 120 | 2.0944 | 133.3333 | 0.3333 |
| 135 | 2.3562 | 150 | 0.375 |
| 150 | 2.6180 | 166.6667 | 0.4167 |
| 210 | 3.6652 | 233.3333 | 0.5833 |
| 225 | 3.9270 | 250 | 0.625 |
| 240 | 4.1888 | 266.6667 | 0.6667 |
| 300 | 5.2360 | 333.3333 | 0.8333 |
| 330 | 5.7596 | 366.6667 | 0.9167 |
| -30 | -0.5236 | -33.3333 | -0.0833 |
| -90 | -1.5708 | -100 | -0.25 |
| 540 | 9.4248 | 600 | 1.5 |
| 720 | 12.5664 | 800 | 2 |
| 0.5 | 0.0087 | 0.5556 | 0.0014 |
What Is an Angle Converter?
An angle converter changes the same rotation or slope measurement into another unit. This is helpful when one formula expects radians and another uses degrees or gradians.
FAQ
Why are radians important?
Radians are the standard unit in calculus and many physics formulas because they simplify trigonometry.
What is a turn?
A turn is one complete rotation, equal to 360 degrees, 2 pi radians, or 400 gradians.
Can I convert arcminutes and arcseconds?
Yes. They are included for fine angle measurements such as astronomy, surveying, and precision engineering.