Editing Radian (section)

=== Prefixes and variants ===
[[Metric prefix]]es for submultiples are used with radians. A [[milliradian]] (mrad) is a thousandth of a radian (0.001&nbsp;rad), i.e. {{nowrap|1=1 rad = 10<sup>3</sup> mrad}}. There are 2[[pi|{{pi}}]] × 1000 milliradians (≈ 6283.185&nbsp;mrad) in a circle. So a milliradian is just under {{sfrac|1|6283}} of the angle subtended by a full circle. This unit of angular measurement of a circle is in common use by [[telescopic sight]] manufacturers using [[Stadiametric rangefinding|(stadiametric) rangefinding]] in [[reticle]]s. The [[beam divergence|divergence]] of [[laser]] beams is also usually measured in milliradians.

The [[angular mil]] is an approximation of the milliradian used by [[NATO]] and other military organizations in [[gun]]nery and [[Sniper#Targeting, tactics and techniques|targeting]]. Each angular mil represents {{sfrac|1|6400}} of a circle and is {{sfrac|15|8}}% or 1.875% smaller than the 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 {{sfrac|1|2000{{pi}}}}; for example Sweden used the {{sfrac|1|6300}} ''streck'' and the USSR used {{sfrac|1|6000}}. Being based on the milliradian, the NATO mil subtends roughly 1&nbsp;m at a range of 1000&nbsp;m (at such small angles, the curvature is negligible).

Prefixes smaller than milli- are useful in measuring extremely small angles. Microradians (μrad, {{val|e=-6|u=rad}}) and nanoradians (nrad, {{val|e=-9|u=rad}}) are used in astronomy, and can also be used to measure the beam quality of lasers with ultra-low divergence. More common is the [[arc second]], which is {{sfrac|{{pi}}|648,000}}&nbsp;rad (around 4.8481&nbsp;microradians).

{{SI multiples
| unit=radian
| symbol=rad
| xm=[[milliradian]]
}}