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.

1 milliradian = 0.0001591549431 turns (approximately).

About the milliradian

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.

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

Milliradian conversion chart

1 milliradian expressed in every other angle unit:

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