Hour Angles to Radians (h to rad)

1 hour angle equals 0.2617993878 radians (rounded).

1 hour angle = 0.2617993878 radians

How to convert hour angles to radians

To convert hour angles to radians, multiply the number of hour angles by 0.2617993878. The factor is rounded to 10 significant digits. To go the other way, multiply radians by 3.819718634 (rounded).

radians = hour angles × 0.2617993878

Example: 10 hour angles = 2.617993878 radians.

About these units

Hour Angle (h)

AstronomicalCurrent unit

One twenty-fourth of a turn (15 degrees), the angle the Earth rotates in one hour. Right ascension is measured in hours.

Hour angle measures how far an object has moved west of the local meridian, expressed in time instead of degrees. A full circle is exactly 24 hours, so one hour equals 15 degrees, one minute of time equals 15 arcminutes, and one second of time equals 15 arcseconds. Astronomers use the same scheme for right ascension, the sky's equivalent of longitude, which is measured eastward from the March equinox in hours, minutes, and seconds.

Local hour angle equals local sidereal time minus an object's right ascension. Zero means it is crossing the meridian, a negative value means it is still approaching, and a positive value means it has passed. The Sun's hour angle advances about one hour per clock hour, but a fixed star's advances roughly 1.0027 hours per clock hour, so an hour of hour angle takes about 59 minutes 50 seconds for stars. The same 15 degrees per hour underlies the division of the globe into 24 time zones.

1 hour angle = 0.04166666667 turns (approximately).

Sources: Wikipedia: Hour angle; Wikipedia: Right ascension

Radian (rad)

Metric (SI)Current unit

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)

Related conversions

See all angle units.