Sextants to Radians (sext to rad)

1 sextant equals 1.047197551 radians (rounded).

1 sextant = 1.047197551 radians

How to convert sextants to radians

To convert sextants to radians, multiply the number of sextants by 1.047197551. The factor is rounded to 10 significant digits. To go the other way, multiply radians by 0.9549296586 (rounded).

radians = sextants × 1.047197551

Example: 10 sextants = 10.47197551 radians.

About these units

Sextant (sext)

General & non-SICurrent unit

One sixth of a full turn (60 degrees), named after the navigation instrument whose arc spans a sixth of a circle.

The name sextant comes from the Latin for one sixth, and the instrument's frame is a sector of roughly 60 degrees, a sixth of a circle. Double reflection lets its scale read up to 120 degrees, enough for lunar distance measurements, which can exceed 90 degrees. John Hadley and Thomas Godfrey implemented the principle around 1731, and Isaac Newton's unpublished writings contain it as well. Navigators mainly use the sextant to measure the height of the Sun or a star above the horizon, from which latitude can be estimated.

It needs no electricity or satellite signal, so it still serves as a backup. The best accuracy possible in celestial navigation is about 0.1 nautical mile, and a highly skilled navigator can reach roughly 0.25. Buzz Aldrin used one on Gemini XII in 1966, and Carlos Viegas Gago Coutinho adapted it for aviation in 1922. As a unit of angle, a sextant is simply 60 degrees: 1/6 of a turn, or π/3 radian.

1 sextant = 0.1666666667 turns (approximately).

Sources: Wikipedia: Sextant; Wikipedia: Octant (instrument)

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.