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Metrology

The science of measurement, embracing both experimental and theoretical determinations at any level of uncertainty in any field of science and technology.


MIL vs. MRAD vs. NATO-MIL

In mathematics and all natural sciences, the angular distance (angular separation, apparent distance, or apparent separation) between two points, as observed from a location different from either of these points, is the size of the angle between the two directions originating from the observer and pointing towards these two points.

This angular distance, or size, is measured in degrees or units specified as fractions of a degree, like the MIL.

Clarification of terms

MIL usually denotes MRAD, MILliradians; thousandths of a radian. Militaries around the world have historically used rounded versions of the MRAD, the NATO-MIL and the German army's 'Artilleristischer Strich' divide the full circle (or turn) by 6400 -- instead of the MRAD's more accurate but also harder to subdivide 6283.x -- while the Warsaw Pact established 6000 mils in a turn and the Swedish divide it into 6300 "streck".

Definitions

  • 1 MRAD is 1000/rad (0.001 radian) hence there are 1000 mils per radian, hence 2000π or approximately 6283.185 milliradians in 360° or approximately 0.057296° for 1 MRAD.
  • 1 NATO-MIL is 360°/6400 or exactly 0.05625°.
0.05625 / 0.057296 = 0.98174392627    
0.057296 / 0.05625 = 1.01859555556    
Difference = 1.8595%

Conversions[1]

  • 1 MRAD = 1.02 NATO-MIL ≅ 0.057296°
  • 1 NATO-MIL = 0.98 MRAD = 0.05625°

Summary

  • A full circle is made up of 360°.
  • A full circle is 2π radians, hence each radian measuring 57.3°.
  • Each radian (180/π ≅ 57.3°) is made up of 1000 milliradians (MRAD).
  • A full circle is approximately 6283 MRAD.
  • To simplify, NATO rounds these to 6400 NATO-MIL in a circle.

Calculators, and the instruments:

References:

  1. Note that the difference of MRAD vs. NATO-MIL is, with 1.86%, smaller than the typical uncertainty of measurement and below the accuracy of most measuring techniques. Still, be aware of which unit is used, and make sure that it doesn't add to the overall measurement uncertainty.