Right Angles to Degrees (∟ to °)

1 right angle equals 90 degrees exactly.

How to convert right angles to degrees

To convert right angles to degrees, multiply the number of right angles by 90. This factor is exact. To go the other way, multiply degrees by 0.01111111111 (rounded).

degrees = right angles × 90

Example: 10 right angles = 900 degrees.

About these units

Right Angle (∟)

General & non-SICurrent unit

A quarter turn, 90 degrees.

The right angle takes its name from the Latin rectus, meaning upright, the way a vertical line stands on a horizontal base. It is a quarter turn: 90 degrees, 100 gradians, π/2 radians, or exactly 8 points on a 32-point compass rose. The SI Brochure notes that a right angle equals π/2 radian.

Its role as a standard goes back to Euclid. Book 1 of the Elements defines right angles and perpendicular lines, and Postulate 4 states that all right angles are equal. That equality is what lets one right angle serve as a yardstick for measuring other angles. A right triangle contains one, and rectangles and squares have four. Diagrams usually mark it with a small square, and some European countries use an arc with a dot instead. A 3-4-5 triangle gives a quick check for one, and Thales' theorem says an angle inscribed in a semicircle is always a right angle.

1 right angle = 0.25 turns (exactly).

Sources: Wikipedia: Right angle; BIPM SI Brochure, 9th edition (2019); 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.