Approximate conversion of Radians to NATO milliradians
Multiply by about 1,018.6. NATO splits a circle into 6,400 mils rather than the 2π × 1,000 ≈ 6,283 true milliradians, so each NATO mil is slightly smaller and you get a few more of them per radian.
The exact factor is 6,400 ÷ 2π, roughly 1,018.5916. So 2 radians is about 2,037.2 NATO mils, not the 2,000 you'd get by treating them as true milliradians.
Multiplying by 1,000 is under 2% out, which will do for a sketch on the back of a map but not on a gun line.
About Radians
The radian is the SI unit of angle. A full circle is 2π (about 6.28) radians, against 360 degrees.
The concept of radians is based on the relationship between the length of an arc and the radius of a circle. One radian is defined as the angle subtended by an arc that is equal in length to the radius of the circle. In other words, if we were to take a circle with a radius of 1 unit and measure an arc along its circumference that is also 1 unit long, the angle formed at the center of the circle would be 1 radian.
A radian is a ratio of two lengths, arc over radius, so it carries no units of its own and drops out of physics formulas – speed = radius × angular velocity works directly when the angle is in radians.
About NATO milliradians
NATO milliradians (NATO mils) are a unit of angular measurement commonly used in military and artillery applications. They are derived from the radian, which is the standard unit for measuring angles in the International System of Units (SI). A radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.
One NATO mil is 1/6,400th of a circle, or 0.05625°, so a degree is about 17.78 NATO mils.
A NATO mil is close enough to a true milliradian (6,283 of those make a circle) that gunners treat it as 1 meter of width at 1,000 meters of range. A circle of 6,400 also divides neatly into quarters, eighths and sixteenths.