The units used for the radius/distance dictate the value of the arc subtended by a Radian/milliRadian. Thus, MRAD are not specific to English or Metric units - a point of confusion for a lot of people.
However, if you want math...light math follows.
A circle is 2*Pi Radian of angle (aka: 360 degrees). If we use 3.1415 as our value for Pi, that's roughly 6.283 Radian. A milliRadian is 1/1000th of a Radian. If there are 6.283 Radian in a circle, there are 6283 milliRadian. That's not to be confused with the military's artillery "mil" scale which is based on 6400 for ease of use. Just some background/trivia.
What's that mean? The circumference of a circle is it's diameter (D) * Pi, or 2* radius (r) *Pi. When we range to a target, we range the radius in this context. You can see from this relationship that the radius (our distance to target) * angle subtended in radians = arc length (or the entire circumference in the case of 2*Pi radians). For example, if our range to target is 1000 yards and our target subtends exactly 1 MRAD, you get 1000 * .001 = 1 yd (1000 yds * 1/1000 Radian). 100 yards, 1 MRAD --> .1 yd. Easy, right? I suppose you could point out we're conflating the arc and the chord...however, the angle is so incredibly small (relatively speaking) that the error introduced is minimal (e.g. 1 MRAD subtends a 1 m arc @ 1000 m with a chord length of .999999958333334 m).
More trivia. Folks like the late Louis Awerbuck have advocated using 18 inches for the height of a human torso when estimating range. You can see an example of that here:
Link. You'll note that is 1/2 yd and lends itself pretty well to some fairly clean math, if you go that route.