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Concept# Milliradian

Summary

A milliradian (SI-symbol mrad, sometimes also abbreviated mil) is an SI derived unit for angular measurement which is defined as a thousandth of a radian (0.001 radian). Milliradians are used in adjustment of firearm sights by adjusting the angle of the sight compared to the barrel (up, down, left, or right). Milliradians are also used for comparing shot groupings, or to compare the difficulty of hitting different sized shooting targets at different distances. When using a scope with both mrad adjustment and a reticle with mrad markings (called an "mrad/mrad scope"), the shooter can use the reticle as a ruler to count the number of mrads a shot was off-target, which directly translates to the sight adjustment needed to hit the target with a follow-up shot. Optics with mrad markings in the reticle can also be used to make a range estimation of a known size target, or vice versa, to determine a target size if the distance is known, a practice called "milling".
Milliradians are generally used for very small angles, which allows for very accurate mathematical approximations to more easily calculate with direct proportions, back and forth between the angular separation observed in an optic, linear subtension on target, and range. In such applications it is useful to use a unit for target size that is a thousandth of the unit for range, for instance by using the metric units millimeters for target size and meters for range. This coincides with the definition of the milliradian where the arc length is defined as 1/1,000 of the radius. A common adjustment value in firearm sights is 1 cm at 100 meters which equals 10 mm/100 m = 1/10 mrad.
The true definition of a milliradian is based on a unit circle with a radius of one and an arc divided into 1,000 mrad per radian, hence 2,000 π or approximately 6,283.185 milliradians in one turn, and rifle scope adjustments and reticles are calibrated to this definition. There are also other definitions used for land mapping and artillery which are rounded to more easily be divided into smaller parts for use with compasses, which are then often referred to as "mils", "lines", or similar.

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