Understanding angle units
A complete turn is 360 degrees or 2π radians. An arcminute is 1/60 degree and an arcsecond 1/3600 degree. Negative angles remain signed; the converter does not wrap them into a single turn.
Conversion method
For linear units, multiply the input by its factor to the base unit, then divide by the target factor. The table lists definitions where exact and approximate constants where applicable.
| Unit | 1 unit in base units | Definition |
|---|---|---|
| Radian (rad) | 1 | Exact definition; display may be rounded |
| Degree (°) | 0.0174532925 | Exact definition; display may be rounded |
| Gradian (gon) | 0.0157079633 | Exact definition; display may be rounded |
| Arcminute (′) | 0.0002908882 | Exact definition; display may be rounded |
| Arcsecond (″) | 0.0000048481 | Exact definition; display may be rounded |
| Turn (tr) | 6.2831853072 | Exact definition; display may be rounded |
| Milliradian (mrad) | 0.001 | Exact definition; display may be rounded |
Worked example and common conversions
10 ° = 0.1745329252 rad. Keep full precision during conversion, then round the final result to the precision of your measurement.
| From | To |
|---|---|
| 10 ° | 0.1745329252 rad |
| 10 rad | 572.9577951308 ° |
| 10 tr | 3,600 ° |
| 10 gon | 9 ° |