Radians to Compass Points (rad to point)
1 radian equals 5.092958179 compass points (rounded).
How to convert radians to compass points
To convert radians to compass points, multiply the number of radians by 5.092958179. The factor is rounded to 10 significant digits. To go the other way, multiply compass points by 0.1963495408 (rounded).
compass points = radians × 5.092958179
Example: 10 radians = 50.92958179 compass points.
About these units
Radian (rad)
The SI unit of angle: the angle at the center of a circle subtended by an arc equal in length to the radius. A full turn is 2π radians (about 6.2832).
The radian builds its unit out of the circle itself. Lay a length of string equal to the radius along the circumference, and the angle that arc makes at the center is one radian. The SI Brochure calls it the coherent unit of plane angle, and it also serves as the coherent unit of phase angle, which grows by 2π radians over one period of a repeating wave. The same document notes that you could write rad as m/m, but warns that this is not intrinsic and can mislead, since angle is not the same kind of quantity as an ordinary ratio of lengths. It also records an alternative definition: a right angle equals π/2 radian.
A circle's circumference is 2π times its radius, so a full turn is 2π radians, about 6.2832, which makes one radian roughly 57.3 degrees, or about 0.159 of a turn. The SI Brochure's table of derived units expresses angular velocity in radians per second.
1 radian = 0.1591549431 turns (approximately).
Sources: BIPM SI Brochure, 9th edition (2019); Wikipedia: Angle; NIST Guide to the SI, Appendix B.8 (angle conversion factors)
Compass Point (point)
One 32nd of a turn (11.25 degrees), the spacing of the 32 points of the traditional compass rose such as north-north-east.
Before sailors routinely steered by degrees, they steered by points. The traditional compass rose splits the horizon into 32 points spaced 11.25 degrees apart. The four cardinal and four intercardinal directions make eight principal winds 45 degrees apart, half-winds such as north-northeast bring the count to 16 at 22.5 degrees, and quarter-winds with names like northeast by east complete the 32. Later navigation extended the system to 128 directions using half and quarter points, though compass roses rarely labeled them.
Crews practiced boxing the compass, naming all the points in order, and used points for relative bearings, such as an obstacle two points off the starboard bow, which is 22.5 degrees. Medieval Mediterranean sailors gave the eight main winds Italianate names, among them Tramontana for north, Levante for east, and Ponente for west, and portolan charts color-coded the principal, half, and quarter winds. A right angle spans exactly 8 points.
1 compass point = 0.03125 turns (exactly).
Sources: Wikipedia: Points of the compass; Wikipedia: Right angle
Related conversions
- Compass points to radians (reverse)
- Radians to degrees
- Radians to gradians
- Radians to turns
- Radians to arcminutes
- Radians to arcseconds
- Radians to milliarcseconds
- Radians to milliradians
- Radians to right angles
- Radians to octants
- Radians to sextants
- Radians to hour angles
- Radians to mils (NATO)
- Degrees to compass points
See all angle units.