Right Angle (∟)

A quarter turn, 90 degrees.

1 right angle = 0.25 turns (exactly).

About the right angle

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.

Sources: Wikipedia: Right angle; BIPM SI Brochure, 9th edition (2019); Wikipedia: Points of the compass

Right Angle conversion chart

1 right angle expressed in every other angle unit:

Unit	1 right angle
Degrees	90
Radians	1.570796327
Gradians	100
Turns	0.25
Arcminutes	5,400
Arcseconds	324,000
Milliarcseconds	324,000,000
Milliradians	1,570.796327
Octants	2
Sextants	1.5
Hour Angles	6
Mils (NATO)	1,600
Zodiac Signs	3
Compass Points	8
Mils (Soviet)	1,500
Streck	1,575
Binary Degrees	64

More General & non-SI units

All General & non-SI units

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