Binary Degrees to Degrees (brad to °)

1 binary degree equals 1.40625 degrees exactly.

How to convert binary degrees to degrees

To convert binary degrees to degrees, multiply the number of binary degrees by 1.40625. This factor is exact. To go the other way, multiply degrees by 0.7111111111 (rounded).

degrees = binary degrees × 1.40625

Example: 10 binary degrees = 14.0625 degrees.

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

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.