Milliradian

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Milliradian
The PSO-1 reticle in a Dragunov sniper rifle has markings with 1-mrad spacing, which can be used to compensate for wind drift, impact correction or range estimation.
General information
Unit system	SI derived unit
Unit of	Angle
Symbol	mrad, mil
Named after	The metric prefix milli- (from Latin mille meaning "one thousand") and the radian
In units	Dimensionless with an arc length one thousandth of the radius, i.e. 1 ⁠mm/m⁠ or 1 ⁠m/km⁠
Conversions
1 mrad in ...	... is equal to ...
radians	⁠1/1000⁠ rad
turns	⁠1/2000π⁠ turn
gons	⁠1/5π⁠ ≈ 0.063662g
degrees	⁠9/50π⁠ ≈ 0.057296°
arcminutes	⁠54/5π⁠ ≈ 3.4377′

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.^[1] 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. For instance there are artillery sights and compasses with 6,400 NATO mils, 6,000 Warsaw Pact mils or 6,300 Swedish "streck" per turn instead of 360° or 2π radians, achieving higher resolution than a 360° compass while also being easier to divide into parts than if true milliradians were used.