How to use
- Type an angle in Value.
- Pick the From and To units, or tap a popular conversion.
- Read the answer. Degrees, minutes and seconds (DMS) are shown under it.
Formula
A full turn is 360°, which is 2π radians, so 180° = π rad:
radians = degrees × π ÷ 180
degrees = radians × 180 ÷ π
| Unit | Size |
|---|---|
| 1 radian | 180/π ≈ 57.2958° |
| 1 gradian (gon) | 0.9° (400 per turn) |
| 1 arcminute (′) | 1/60° |
| 1 arcsecond (″) | 1/3,600° |
| 1 mil (NATO) | 0.05625° (6,400 per turn) |
Examples
- 45° to radians: 45 × π ÷ 180 = π/4 ≈ 0.7854 rad
- 2.5 rad to degrees: 2.5 × 180 ÷ π = 143.24°
- 40.4461° as DMS: 0.4461 × 60 = 26.766′, then 0.766 × 60 ≈ 45.96″, so 40° 26′ 45.96″
Conversion charts
| Degrees | Radians | Radians (decimal) | Gradians |
|---|---|---|---|
| 0° | 0 | 0 | 0 |
| 30° | π/6 | 0.5236 | 33.33 |
| 45° | π/4 | 0.7854 | 50 |
| 60° | π/3 | 1.0472 | 66.67 |
| 90° | π/2 | 1.5708 | 100 |
| 120° | 2π/3 | 2.0944 | 133.33 |
| 180° | π | 3.1416 | 200 |
| 270° | 3π/2 | 4.7124 | 300 |
| 360° | 2π | 6.2832 | 400 |
| Mils (NATO) | Degrees |
|---|---|
| 1 | 0.05625° |
| 10 | 0.5625° |
| 100 | 5.625° |
| 1,600 | 90° |
| 3,200 | 180° |
| 6,400 | 360° |
More detail: DMS, mils and milliradians
- DMS to decimal: degrees + minutes ÷ 60 + seconds ÷ 3,600. So 40° 26′ 46″ is 40.4461°.
- Signs: for south latitudes or west longitudes, put the minus sign on the whole value: −0° 30′ is −0.5°, not +0.5°.
- Mils: this converter uses the NATO mil, 6,400 per turn. Some other armies have used different counts.
- Milliradians (mrad) are true thousandths of a radian, about 6,283 per turn. Rifle scopes often use them.
Measuring the sides of a shape too? Use the length converter.