Octants to Radians (oct to rad)

1 octant equals 0.7853981634 radians (rounded).

1 octant = 0.7853981634 radians

How to convert octants to radians

To convert octants to radians, multiply the number of octants by 0.7853981634. The factor is rounded to 10 significant digits. To go the other way, multiply radians by 1.273239545 (rounded).

radians = octants × 0.7853981634

Example: 10 octants = 7.853981634 radians.

About these units

Octant (oct)

General & non-SICurrent unit

One eighth of a full turn (45 degrees).

Octant is best known as the name of a navigation instrument. Its arc is an eighth of a circle, 45 degrees, but because mirrors double the measured angle it reads up to 90 degrees. Isaac Newton showed a reflecting quadrant to the Royal Society in 1699, though its description was not published until 1742. Around 1730 the English mathematician John Hadley and the Philadelphia glazier Thomas Godfrey developed the instrument independently, and Hadley's version published in 1731 took the familiar octant form. It let a navigator see the horizon and a star together, which made sightings easier.

Lunar distance measurements can exceed 90 degrees, so a larger instrument was needed, and the sextant followed. Octants stayed in use into the 19th century, especially on merchant and fishing vessels. As a plain angle, an octant is 1/8 of a turn: 45 degrees, π/4 radian, or 4 points on a 32-point compass rose, which is the spacing between neighboring principal winds such as north and northeast.

1 octant = 0.125 turns (exactly).

Sources: Wikipedia: Octant (instrument); Wikipedia: Points of the compass

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.