Plane Angle Converter
Degrees, radians, gradians, arcminutes and milliradians for code, maps and surveying
Degrees, radians, gradians, arcminutes and milliradians for code, maps and surveying. No data leaves your browser – every conversion happens locally.
Degrees, radians and the smaller units
The degree is the base unit here. A radian is 180/π degrees (about 57.3°), a gradian is 0.9° and arcminutes and arcseconds are sixtieths of a degree and of an arcminute.
The milliradian is popular with shooters. One mil subtends about 10 cm at 100 m, which makes scope adjustments easy to work out in metric. The tool treats it as 0.0573°.
One limitation: there's no degrees-minutes-seconds input. For a coordinate like 28° 36′ 50″, convert the minutes and seconds to degrees separately (36 ÷ 60 and 50 ÷ 3,600) and add them up.
Angle reference
| 90° | π/2 rad (1.5708) |
| 180° | π rad (3.1416) |
| 360° | 2π rad (6.2832) |
| 1 radian | 57.296° |
| 1° | 60 arcminutes |
| 1 arcminute | 60 arcseconds |
Worked examples
Code that needs radians
45° is 0.7854 rad. Pass that to Math.sin or Math.cos rather than 45, which JavaScript would read as 45 radians.
GPS precision
0.0001° of latitude is about 11 m on the ground, so four decimal places in a coordinate is roughly building-level accuracy.
Surveying
30° is 33.33 gradians. Some European total stations default to gradians, so readings need converting before use.
Common angles in radians, gradians and milliradians
Radians are degrees × π ÷ 180, gradians are degrees ÷ 0.9, and milliradians are radians × 1,000. These are the angles that come up most in code, geometry and surveying.
| Degrees | Radians | Gradians | Milliradians |
|---|---|---|---|
| 1° | 0.0175 | 1.11 | 17.5 |
| 15° | 0.2618 | 16.67 | 261.8 |
| 30° | 0.5236 | 33.33 | 523.6 |
| 45° | 0.7854 | 50 | 785.4 |
| 60° | 1.0472 | 66.67 | 1,047.2 |
| 90° | 1.5708 | 100 | 1,570.8 |
| 180° | 3.1416 | 200 | 3,141.6 |
| 270° | 4.7124 | 300 | 4,712.4 |
| 360° | 6.2832 | 400 | 6,283.2 |
Spreadsheet trig and the military mil
Spreadsheets trip people up the same way code does. Excel's and Google Sheets' SIN, COS and TAN all expect radians, so =SIN(30) returns about −0.988 rather than 0.5. Wrap the angle in RADIANS(), as in =SIN(RADIANS(30)).
Mils aren't all the same size. This tool uses the true milliradian, about 6,283 to a full circle. NATO artillery and many compasses use a rounded mil of 6,400 to the circle, so one NATO mil is 0.05625° against 0.0573° here. Check which one your scope or compass uses.
Changing units also doesn't change direction conventions. Maths measures angles anticlockwise from east, while compass bearings run clockwise from north. To turn a bearing into a maths angle, use 90 minus the bearing, then convert to radians if your code needs them.