One NATO mil is 0.05625 degrees, because a full circle is divided into 6,400 mils. The unit exists for one reason: at typical artillery ranges, one mil subtends approximately one metre at a thousand metres, which turns angle corrections into distance corrections with no arithmetic.
About the units
The milliradian would divide the circle into 2π × 1,000 = 6,283.19 parts, which is inconveniently irrational. Military systems round it to something divisible, and different armies chose differently: NATO uses 6,400, the former Warsaw Pact used 6,000, and Sweden historically used 6,300 — the streck. All are called mils, and all approximate the milliradian to within a few per cent. The NATO choice of 6,400 has the advantage of being divisible by 2 many times over, which suits a compass rose and simplifies mental division in the field.
The exact factor
One NATO mil is 360 ÷ 6,400 = 0.05625 degrees, or 0.98175 milliradians — about 1.8 per cent smaller than a true milliradian. The practical rule is the subtension: one mil covers approximately one metre at 1,000 metres, two metres at 2,000, and so on. That relationship is why fire correction orders are given in mils: an observer who sees a shell land 50 metres left at a range of 2,000 metres calls a correction of 25 mils right, without converting anything.
Where you meet this conversion
Artillery, mortars and military observation. Fire control computers, aiming circles and observation instruments are all graduated in mils. Rifle scopes use true milliradians rather than NATO mils, which is a distinction worth knowing since the two differ by nearly two per cent — a mil-dot reticle is milliradian-based and a artillery sight is not. Range estimation using known target sizes works through the same subtension relationship in both systems.