Multiples of Radian Units
Metric prefixes have limited use with radians, and none in mathematics.
There are 2π × 1000 milliradians (≈ 6283.185 mrad) in a circle. So a trigonometric milliradian is just under 1⁄6283 of a circle. This “real” trigonometric unit of angular measurement of a circle is in use by telescopic sight manufacturers using (stadiametric) rangefinding in reticles. The divergence of laser beams is also usually measured in milliradians.
An approximation of the trigonometric milliradian (0.001 rad), known as the (angular) mil, is used by NATO and other military organizations in gunnery and targeting. Each angular mil represents 1⁄6400 of a circle and is 1-⅞% smaller than the trigonometric milliradian. For the small angles typically found in targeting work, the convenience of using the number 6400 in calculation outweighs the small mathematical errors it introduces. In the past, other gunnery systems have used different approximations to 1⁄2000π; for example Sweden used the 1⁄6300 streck and the USSR used 1⁄6000. Being based on the milliradian, the NATO mil subtends roughly 1 m at a range of 1000 m (at such small angles, the curvature is negligible).
Smaller units like microradians (μrads) and nanoradians (nrads) are used in astronomy, and can also be used to measure the beam quality of lasers with ultra-low divergence. Similarly, the prefixes smaller than milli- are potentially useful in measuring extremely small angles.
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