The radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees.
| Definition | Relation to SI units |
|---|---|
The angle subtended at the center of a circle by an arc whose length is equal to the circle's radius. One full revolution encompasses 2π radians. |
| sextant | angular mil | sixth circle | revolution | quarter circle | eighth circle | arcminute | helf circle |
|---|---|---|---|---|---|---|---|
| 1 | 67,906.1102109 | 1 | 0.1666667 | 0.6666667 | 1.3333333 | 3 600 | 0.3333333 |
| 1.47262153125 × 10-5 | 1 | 1.47262153125 × 10-5 | 2.45436921875 × 10-6 | 9.817476875 × 10-6 | 1.963495375 × 10-5 | 0.0530144 | 4.9087384375 × 10-6 |
| 1 | 67,906.1102109 | 1 | 0.1666667 | 0.6666667 | 1.3333333 | 3 600 | 0.3333333 |
| 6 | 407,436.6612654 | 6 | 1 | 4 | 8 | 21 600 | 2 |
| 1.5 | 101,859.1653163 | 1.5 | 0.25 | 1 | 2 | 5 400 | 0.5 |
| 0.75 | 50,929.5826582 | 0.75 | 0.125 | 0.5 | 1 | 2 700 | 0.25 |
| 0.0002778 | 18.8628084 | 0.0002778 | 4.6296296296296 × 10-5 | 0.0001852 | 0.0003704 | 1 | 9.2592592592593 × 10-5 |
| 3 | 203,718.3306327 | 3 | 0.5 | 2 | 4 | 10 800 | 1 |
| Symbol | Definition |
|---|---|
| ≡ | exactly equal |
| ≈ | approximately equal to |
| = | equal to |
| digits | indicates that digits repeat infinitely (e.g. 8.294 369 corresponds to 8.294 369 369 369 369 …) |
| 1 radians | = 1 radians |
| 2 radians | = 2 radians |
| 3 radians | = 3 radians |
| 4 radians | = 4 radians |
| 5 radians | = 5 radians |