Binary Degrees to Radians (brad to rad)

1 binary degree equals 0.02454369261 radians (rounded).

1 binary degree = 0.02454369261 radians

How to convert binary degrees to radians

To convert binary degrees to radians, multiply the number of binary degrees by 0.02454369261. The factor is rounded to 10 significant digits. To go the other way, multiply radians by 40.74366543 (rounded).

radians = binary degrees × 0.02454369261

Example: 10 binary degrees = 0.2454369261 radians.

About these units

Binary Degree (brad)

ComputingTraditional unit (still used in some regions)

One 256th of a turn (1.40625 degrees). A power-of-two angle used in computer graphics and old game engines so that wrapping is free.

Binary angular measurement stores an angle as an unsigned integer in which a full turn is 2ⁿ steps. In the 8-bit version a turn is 256 steps, so each step is 1.40625 degrees, and the values 0, 64, 128, and 192 mark 0, 90, 180, and 270 degrees. Wiktionary glosses the name brad, used for such units, as a binary radian.

The appeal is wraparound. Integer addition and subtraction overflow modulo 2ⁿ, so angles that differ by whole turns are automatically equivalent and no code is needed to reduce them to a standard range. With signed two's-complement values, the same bits cover −180 to +180 degrees. Real systems use longer words. The 16-bit furman, named for Alan T. Furman, who adapted the CORDIC method to 16-bit fixed-point arithmetic, is 1/65,536 of a turn, slightly less than 20 arcseconds, and GPS satellite ephemerides encode four orbital angles as 32-bit binary angles. Computer games are another common home for binary angles.

1 binary degree = 0.00390625 turns (exactly).

Sources: Wikipedia: Binary angular measurement; Wiktionary: brad

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.