milliradian

A milliradian is a unit of angular measurement equal to one thousandth of a radian. Because a radian is defined by the arc length equal to the radius, 1 milliradian equals 0.001 radians, which is about 0.0573 degrees or 3.4377 arcminutes.

In practical use, milliradians appear in fields such as ballistics, optics, and surveying. The term mil is widely used in military and shooting contexts to describe angular separations marked on reticles or used for range estimation. There are two common definitions in operation. The exact milliradian is 0.001 rad, while the NATO or artillery mil is 1/6400 of a circle, equal to about 0.00098175 rad (approximately 0.05625 degrees). The two definitions are close in scale, so they are often treated similarly in rough calculations, but precise work requires using the stated unit.

For small angles, the arc length approximation s ≈ rθ applies, where θ is in radians. At distance D, an angle of 1 milliradian subtends about D/1000 meters. For example, at 1000 meters, 1 mrad corresponds to roughly 1 meter of lateral displacement. With the NATO mil, 1 mil at 1000 meters is about 0.982 meters. This property makes mils useful in range estimation and targeting with reticles calibrated in mils, where the angular size of a target can be translated to a linear measurement on the ground.

See also: radian, angular measurement, ballistic mathematics.