The angle units
- Degree (°): a full turn is 360°, a right angle 90°.
- Radian (rad): a full turn is 2π radians, so 1 rad is 180/π, about 57.2958°.
- Milliradian (mrad): a thousandth of a radian, about 0.0573°.
- Gradian or gon: a full turn is 400 gon, so a right angle is exactly 100 gon.
- Minute (′) and second (″) of arc: 1° = 60′ and 1′ = 60″.
- Turn: one full revolution, 360°.
The formulas
radians = degrees × π ÷ 180 and degrees = radians × 180 ÷ π. Negative angles work too: −90° is −π/2. For sines, cosines and other trig functions of an angle, use the scientific calculator.
Common angle conversions
| From | Equals |
|---|---|
| 1 degree | 0.01745329252 radians |
| 1 radian | 57.29577951 degrees |
| 1 degree | 1.111111111 gradians |
| 1 degree | 60 minutes of arc |
| 1 turn | 6.283185307 radians |
| 1 milliradian | 0.05729577951 degrees |
Degrees to radians
| Degrees (°) | Radians (rad) |
|---|---|
| 1 | 0.0174533 |
| 15 | 0.261799 |
| 30 | 0.523599 |
| 45 | 0.785398 |
| 60 | 1.0472 |
| 90 | 1.5708 |
| 120 | 2.0944 |
| 135 | 2.35619 |
| 150 | 2.61799 |
| 180 | 3.14159 |
| 270 | 4.71239 |
| 360 | 6.28319 |
How to use it
- 1Pick the unit you have on the left and the one you want on the right. Degrees to radians is set up when the page opens.
- 2Type the angle. Either side accepts input, and swap turns the conversion around.
- 3Read the result and see the same angle in every other unit in the list. Copy the number or a link.
Frequently asked questions
How do I convert degrees to radians?
Multiply the degrees by π and divide by 180. 90° is π/2, about 1.5708 radians.
How many degrees is 1 radian?
180 ÷ π, about 57.2958 degrees.
What is a gradian?
A gradian, or gon, divides a right angle into 100 parts, so a full turn has 400 gradians and one gradian is 0.9 degrees.
How many minutes of arc are in a degree?
Sixty. Each minute of arc has 60 seconds of arc, so a degree has 3,600 seconds.