Right Angles to Radians (∟ to rad)

1 right angle equals 1.570796327 radians (rounded).

1 right angle = 1.570796327 radians

How to convert right angles to radians

To convert right angles to radians, multiply the number of right angles by 1.570796327. The factor is rounded to 10 significant digits. To go the other way, multiply radians by 0.6366197724 (rounded).

radians = right angles × 1.570796327

Example: 10 right angles = 15.70796327 radians.

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

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.