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Mils Versus Mils Versus Mils

By Joe Huffman
Copyright 2000

'Mil' in the context of long distance shooting is short for milli-radian.  This is, literally, one-thousandth of a radian. More on what a radian is later.  For now think of it as a unit of angle, like degrees, as in a 180 degree turn, that sort of thing.  Mil-dot reticules in optics are used for various things.  They can be used for range finding and they can be used for windage and elevation offset when shooting.  They are found in rifle scopes and in binoculars. I won't go into the details of using these here.  There are numerous references available that go into great detail on them.  What I do want to explain is the differences between the versions of what is commonly called a 'mil'.

A radian is commonly used in mathematics as a unit of measure for angles instead of the more common known degree because of some very convenient properties that result in calculus and other advanced math usage.  One of those convenient properties, at the low level math usage, is also of great use to us in the shooting world.  Something that measures one milli-radian is 1/1000th as long as the distance to it.  Or put another way -- if something 1 yard long measures 1 milli-radian then it is 1000 yards away from us. 

Now for the confusing stuff.  In a complete circle, 360 degrees, there are 2 pi radians.  This is about 6.283 radians per circle.  Since there are 1000 milli-radians in one radian, there are about 6283 milli-radians in a circle.  This is where the confusion starts.  The US military found the concept of a milli-radian very useful and adapted it for use with maps, artillery spotting and numerous other things.  However, the US military made things 'simpler' by standardizing on 6400 mils in a circle.  To make things even more interesting the Russians, and perhaps others in Europe, use 6000 mils in a circle.  The errors from the mathematical definition are not that great for most uses.  Suppose you are ranging an object that is about 2 yards long you don't know for certain but that is your best guess.  If you come up with exactly 4 mils then:

Object True Size

Range Using True Mils Range using US military Mils Russian Mils
 Exactly 2 yards 500 yards 509 yards 477 yards
2 yards + 2 inches 514 yards 523 yards 491 yards

In other words, if you are off just two inches in your estimate of the size of an object that is six feet long then your total error from that one source is greater than the error from using the US military version of mils and over half of the error if you are using a Russian mil optic device.  Another way of looking at it is that a true mil is 102% of a US military mil and 95.5% of a Russian mil.  When estimating the size of object 500 yards away and with the errors in measuring the number of mils in most optics, the errors in estimation and number of mils are almost for certain greater than the errors introduced by the approximations used by the US and Russian military.

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I did some tests with two Leupold scopes and a pair of Russian binoculars with mil reticules.  I put a series of markers at 99 (+/- 1) yards away.  I then measured the distance for an integral number of mils.  The results are below:

Optics. Object size (inches). Apparent mils. Actual mils. "mils"/circle. Error.
Russian Binoculars 76.75  20  21.5 5850 7.0%
Leupold 10 X scope 29.5  8.28 6070 3.4%
Leupold 4.5 -> 14 scope (at 14) 28.75 8.07 6223 0.87%

My measurement were probably accurate to about 1%.

My conclusions are:

1) One should test their optics before relying on them for critical measurements -- even if you know what the manufacture intends them to be.
2) My 14-power Leupold optics can be assumed to use the mathematical definition of a milli-radian.
3) My 10-power Leupold optics may be using the European definition but are probably close enough to the mathematical definition for most purposes.
3) The Russian and probably Europe in general use a different definition of mils and one needs to take this into account.

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From our 'resident' military expert:

From: Eugene Econ 
Sent: Friday, May 12, 2000 8:46 AM
To: Joe Huffman

Subject: Re: Mil-dots.

Joe:

[...off topic stuff deleted...]

Soviet mils are 6000 to a circle. US are 6400. These are Artillery mils used for artillery work and apply to how the Russian and US artillery estimate range and give corrections for Artillery fire.

If you do some math with these numbers you find that the US Artillery mil (6400) equates to one degree equaling 17.777 mils. Thus one mil equals 3.375 minutes. Therefore one mil equals just under one yard at a thousand yards and one meter at a thousand meters.

The Russian mil (6000) equates to one degree equaling 16.666 mils. One mil equals 3.6 minutes. And so one mil equals very, very slightly over one yard at 1000 yards.

Either way -- artillery considers hits if the round lands within fifty meters of a target so use of 6400 or 6000 mils is more a matter of convenience in fire direction control than precision in terms of exactly equaling one yard or one meter. Both are close enough.

BTW -- the PSO-1 scope for the SVD bases its ranging reticle on a 5'7" man and we use a six foot tall man. The PSO-1 scope does not use mil dots. Instead it uses a scale where you fit the average 5'7" man into the scale and where he fits you read the range. Then you index the range on the elevation dial that is a BDC in hundreds of meters.

Unlike the US optics, the windage of the Russian optics are graduated in Russian mils with two clicks between each mil on the knob. Each click then corresponds to about one minute of angle for windage.

Hope this helps you out.

Gene

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From: Shapiro Gregor
Sent: Friday, March 17, 2006 1:34 AM
To: joeh@boomershoot.org
Subject: mils

Swedish mills (used by the Swedish military) are 6300 mils (called ‘streck’ in Swedish and symbolized with an apostrophe [‘]) to a circle the French are a little more mathematically stringent with 6280 mils to a circle.
/GS

From: Shapiro Gregor
Sent: Monday, March 27, 2006 12:49 AM
To: Joe Huffman
Subject: RE: mils

Yes you may use my name. I probably should make you aware that presently the Swedish military is in the process of internationalization and will adopt the NATO standards of measurements and methods of ordering indirect fire, other artillery orders as well as generally adopting international ‘standards’ (read US forces) across the board. So the 6300 to a circle ‘Swedish mils’ is on it’s way out. I have no time scale for this transition but the simulators that my company has delivered and is in the process of developing have multiple units of measurement including both 6300 and 6400.
/Gregor

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See also Mil-dots and Minutes-of-angle, From a Technical Perspective.

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Email: Joe Huffman
Last updated: February 10, 2008