Degrees to Milliradians (° to mrad)

1 degree equals 17.45329252 milliradians (rounded).

How to convert degrees to milliradians

To convert degrees to milliradians, multiply the number of degrees by 17.45329252. The factor is rounded to 10 significant digits. To go the other way, multiply milliradians by 0.05729577951 (rounded).

milliradians = degrees × 17.45329252

Example: 10 degrees = 174.5329252 milliradians.

About these units

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

Milliradian (mrad)

ScientificCurrent unit

One thousandth of a radian. Used in shooting and optics: 1 mrad subtends about 1 meter at a distance of 1 kilometer.

The milliradian cuts the radian into thousandths so that small angles turn into easy mental arithmetic. One mrad is about 0.0573 degree, or roughly 3.44 minutes of arc, and it covers about 1 meter at 1,000 meters, or 1 millimeter at 1 meter. That makes range estimation simple: the distance in meters is the target's size in millimeters divided by its angle in milliradians.

Swiss engineer Charles-Marc Dapples, a professor at the University of Lausanne, is credited with first using the unit in the mid-19th century. Today rifle scope reticles and many adjustment turrets are calibrated in it, and a 0.1 mrad click shifts the point of impact about 1 centimeter at 100 meters. A true milliradian gives 2000π, about 6,283.185, per turn, which is why military mils are rounded relatives rather than exact equivalents. Combining milliradian reticles with minute-of-arc turrets is generally discouraged.

1 milliradian = 0.0001591549431 turns (approximately).

Sources: Wikipedia: Milliradian; Wikipedia: Minute and second of arc; BIPM SI Brochure, 9th edition (2019)

Related conversions

See all angle units.