How this conversion works
A full turn is 360 degrees, 2π radians or 400 gradians. The radian is the SI unit: the angle at which the arc length equals the radius.
Degrees subdivide into 60 arcminutes, and each arcminute into 60 arcseconds. The converter expresses your angle in degrees and divides by the size of the target unit.
Formula: radians = degrees × π / 180 · degrees = radians × 180 / π
Where this conversion is used
- Programming and spreadsheet trig functions, which use radians.
- Surveying and navigation in degrees, minutes and seconds.
- Firearm and optics adjustments in milliradians.
- Some European surveying equipment that uses gradians.
Worked example: 45° to radians
- Multiply by π/180.
- 45 × 3.14159265 ÷ 180 = 0.785398 rad.
- That is exactly π/4 radians.
Unit definitions
| Unit | In degrees | Note |
|---|---|---|
| Degree (°) | 1 | |
| Radian (rad) | 57.2957795131 | |
| Gradian (gon) | 0.9 | |
| Arcminute (′) | 0.0166666667 | |
| Arcsecond (″) | 0.0002777778 | |
| Milliradian (mrad) | 0.0572957795 | |
| Turn (revolution) (rev) | 360 |
Degrees to radians
| Degree (°) | Radian (rad) |
|---|---|
| 1 | 0.0175 |
| 15 | 0.2618 |
| 30 | 0.5236 |
| 45 | 0.7854 |
| 60 | 1.0472 |
| 90 | 1.5708 |
| 120 | 2.0944 |
| 180 | 3.1416 |
| 270 | 4.7124 |
| 360 | 6.2832 |
Precision and sources
Results are calculated from the definitions above and rounded to 12 significant digits; the converter shows up to eight decimal places and the tables four. Reference: SI Brochure, 9th edition, Table 4 (non-SI units accepted for use with the SI).
Frequently asked questions
How many degrees is one radian?
About 57.2958 degrees (180/π).
What is a gradian?
A gradian (gon) is 1/400 of a turn, so a right angle is 100 gradians. It is used in some surveying work.