How to convert angles
A full circle is 360 degrees = 2π radians = 400 gradians = 1 turn. So:
- Degrees to radians: multiply by π/180 (90° = π/2 ≈ 1.5708 rad).
- Radians to degrees: multiply by 180/π ≈ 57.2958.
- Degrees, minutes, seconds: 1° = 60′ (arcminutes) = 3,600″ (arcseconds), so 12° 30′ = 12.5°.
Military and surveying use mils: NATO divides a circle into 6,400 mils, close to a milliradian (6,283.2 per circle).
Common angle conversion factors
| Unit | Equals | Reverse |
|---|---|---|
| 1 degree | 0.0174532925 rad | 1 radian = 57.29577951 ° |
| 1 degree | 1.111111111 grad | 1 gradian = 0.9 ° |
| 1 arcminute | 0.0166666667 ° | 1 degree = 60 ′ |
| 1 degree | 3,600 ″ | 1 arcsecond = 0.0002777778 ° |
| 1 turn (revolution) | 360 ° | 1 degree = 0.0027777778 rev |
| 1 degree | 17.77777778 mil | 1 NATO mil = 0.05625 ° |
| 1 milliradian | 0.0572957795 ° | 1 degree = 17.45329252 mrad |
Angle conversions
Each of these has its own page with the formula, worked examples and a full conversion table:
All angle units on this converter
| Unit | Symbol | 1 unit equals | System |
|---|---|---|---|
| Degree | ° | 0.0174532925 rad | |
| Radian | rad | 1 rad | |
| Gradian | grad | 0.0157079633 rad | |
| Arcminute | ′ | 0.0002908882 rad | |
| Arcsecond | ″ | 0.0000048481 rad | |
| Turn (revolution) | rev | 6.283185307 rad | |
| Milliradian | mrad | 0.001 rad | |
| NATO mil | mil | 0.0009817477 rad | |
| Quadrant (right angle) | quad | 1.570796327 rad |
Frequently asked questions
How many degrees is 1 radian?
1 radian = 180/π ≈ 57.2958 degrees.
How do I convert degrees to radians?
Multiply by π and divide by 180. For example 45° × π / 180 = π/4 ≈ 0.7854 rad.
What is a gradian?
A gradian (gon) is 1/400 of a circle, so a right angle is 100 grad. It is used in some surveying instruments.