Angular mil
A milliradian, often called a mil or mrad (sometimes capitalized MRAD), is an SI derived unit for angular measurement which is defined as a thousandth of a radian (0.001 radian). Mils are widely used in adjustment of firearm sights, where an adjustment of 0.1 mil equals 1 cm at 100 meters.
Scopes with mil-dots or marks in the reticle can be used for range estimation if the target size is known (or vice versa to determine a target size if the distance is known). In such applications, the metric units millimeters for target size and meters for target distance is useful, because they coincide with the definition of the milliradian where arc length is defined as 1⁄1000 of the radius.
Just like a circle can be divided into 360 degrees or 2π radians, a circle can instead be divided into 2000π mil or approximately 6283 milliradians. One milliradian approximately equals ≈ 0.057296° or ≈ 3.4377′ (minutes of arc). While the definition of a mil as exactly a milliradian (circle/ 6283.185… mil) is used in scope adjustment knobs ("turrets") and optical reticles, there are other definitions used for land mapping and artillery, for instance a compass with 6400 NATO mils is used instead of a 360° compass, achieving higher resolution. The term angular mil is used in artillery. Other definitions of 6000 or 6300 mils per circle also exist depending on country, see below.
The milliradian (circle/6283.185…) was first used in the mid nineteenth Century by Charles-Marc Dapples (1837–1920), an engineer and professor at the University of Lausanne. Degrees and minutes were the usual units of angular measurement but others were being proposed, with “grads” (circle/400) under various names having considerable popularity in much of northern Europe. However, Imperial Russia used a different approach, dividing a circle into equilateral triangles (60°, circle/6) and hence 600 units to a circle.
Around the time of the start of World War I, France was experimenting with the use of milliemes (circle/6400) for use with artillery sights instead of decigrades (circle/4000). The United Kingdom was also trialing them to replace degrees and minutes. They were adopted by France although decigrades also remained in use throughout World War I. Other nations also used decigrades. The United States, which copied many French artillery practices, adopted mils (circle/6400). Before 2007 the Swedish defence forces used "streck" (circle/6300, streck meaning lines or marks) (together with degrees for some navigation) which is closer to the milliradian but then changed to NATO mils. After the Bolshevik Revolution and the adoption of the metric system of measurement (e.g. artillery replaced “units of base” with meters) the Red Army expanded the 600 unit circle into a 6000 mil one. Hence the Russian mil has nothing to do with milliradians as its origin.
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