Octants to Degrees (oct to °)

1 octant equals 45 degrees exactly.

How to convert octants to degrees

To convert octants to degrees, multiply the number of octants by 45. This factor is exact. To go the other way, multiply degrees by 0.02222222222 (rounded).

degrees = octants × 45

Example: 10 octants = 450 degrees.

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

Degree (°)

General & non-SICurrent unit

One 360th of a full turn. The everyday unit of angle, inherited from the ancient Babylonians' base-60 counting.

Dividing the circle into 360 parts traces back to the astronomers of ancient Babylon, who counted in base 60. Why 360 in particular is still debated. One explanation points to Persian and Babylonian calendars, which used a year of about 360 days, so the Sun seemed to advance roughly one degree each day. Another says the Babylonians started from the angle of an equilateral triangle and split it into 60 pieces, and a third credits early chord-based trigonometry, where a chord equal to the radius made a natural base. Greek astronomers such as Aristarchus and Hipparchus were among the first to use Babylonian astronomical knowledge systematically.

The number also divides well. 360 has 24 divisors and splits evenly by every whole number from 1 to 10 except 7, which suits a world cut into 24 time zones of 15 degrees of longitude each. Each degree breaks into 60 arcminutes, and each of those into 60 arcseconds. The SI Brochure lists the degree among the widely used non-SI units, equal to π/180 radian, about 0.01745. For scale, the Moon and the Sun each look about half a degree wide, and a little finger held at arm's length covers roughly one degree of sky.

1 degree = 0.002777777778 turns (approximately).

Sources: BIPM SI Brochure, 9th edition (2019); Wikipedia: Degree (angle); Wikipedia: Angular diameter

Related conversions

See all angle units.