Distance Estimation - UNITAF Force Manual (FM)


Distance Estimation
This group is not in a published chapter and should not be relied upon.

FM/BG-520 - Milliradians: Definition

‘These are small. But the ones out there are far away.’

Give yourself a thumbs-up and hold it out at arm’s length. Congratulations! You’ve just measured two degrees of arc with the width of your thumb.

Now raise your hand and hold it out at arm’s length. Spread your fingers all the way. Brilliant! With the span between the tip of your thumb and pinky, you have measured 300 milliradians.


Degrees of arc, the kind you use routinely from your compass, are relatively imprecise compared to milliradians, mrad or mils. Remember, the width of your thumb is already one or two degrees. You can’t easily go smaller without chopping your body to bits for MOA, minutes of arc.

The width of a finger in mrad is closer to 20 to 30.

More specifically, where a circle is 360°, it is also 6400 mrad. This gives us a conversion factor of 17.77, or close enough 18. You can be 18 times more precise using mrad than degrees! This is why we use them for marksmanship and artillery.

Your real-world hands are great tools for remarkably reliable rule-of-thumb estimations. In Arma, much more accurate (and immediately usable) tools to measure mils include your compass, binoculars, rifle optics and spotting scopes.

US Army FM 6-30, Chapter 32

Above: US Army FM 6-30, Chapter 32

FM/BG-521 - Milliradians: Apparent Size

The apparent size of an object changes with distance, as we see daily. The width of your index finger may be a couple centimetres. Move it close to your eye and you can block your whole vision out of it. Move it further away and it occupies a small fraction of your field of view. All the while, the absolute width of your index finger has never changed.

Because our field of view is described by an angle, the area we can see increases with distance. As an object moves farther away, its real-world size doesn't change, but its apparent proportion of our field of view becomes smaller and smaller. This proportion of an angle is also an angle and we can describe it with milliradians.

A metre is always a metre, but we can measure its apparent size to us in milliradians, so we can tell what a metre is at any distance.

If you know how far an object is and measure the milliradians between it and another point, you know the distance between them.

Similarly, if you know the real size of an object, you can use its apparent size to calculate the distance to it. We can do this with surprising accuracy and very little effort using the mil-relation formula.

1 metre cube appearance at different ranges

Above: 1 metre cube appearance at different ranges

FM/BG-522 - Milliradians: Mil-Relation Formula

‘At 1000 metres, 1 mil is 1 metre.’

This relationship is the key to acquiring ranges quickly and accurately. Just like you know now how many milliradians are in different shapes of your hand, you can remember the real size of different objects, then use milliradians to get ranges from them.

Let’s go through that step by step.

Remember our finger (known size) appeared bigger (milliradians) the closer we held it to our eye, but always the same moved side to side. Therefore:

1 metre (known size) will always appear as 1 milliradian at a distance of 1000 metres.

That same metre will appear as 2 milliradians at a distance of 500 metres. Then again 4 mrad at 250, 5 mrad at 200, 10 mrad at 100 metres. Note how the distance halves for every further factor of 2 mrad. What would be the distance to that 1-metre object when measured 8 mrad?

So if you can remember different ‘metre sticks’ common to targets and terrain you encounter, you have a veritable arsenal of rangefinders using just your eyes and quick maths.

The specific formula is:

(object size in metres) * 1000 / mrad = (range in metres)

Note how this formula has one unknown for two known quantities: you know the size, because you pick the object, and can read off the mrad, therefore you can calculate the unknown range. 

With this knowledge, you are also not limited to using objects that are exactly 1 metre. You can plug in any number for the object size; 1 metre just makes it easier since you can divide 1000 by the number of mils you measured straight away, because 1 * 1000 is always 1000.

As a note, 1000 is a conversion factor. You could plug in the object size in millimetres without it and get the same effect. We just don't generally think in millimetres.

Therefore, it will serve you well to remember or collect a list of objects that are easy whole numbers either tall or wide. A standing person measures about one metre head to crotch, likewise head to toe when kneeling. You can approximate doors as 2 metres, which is a similarly nice round number for the formula.

A collection of common objects and their dimensions:

Person, standing1.8 mImage tbd
Person, head to crotch1 mImage tbd
Person, crouching1 mImage tbd
BTR-80, height2 m (2.5 m with turret)Image tbd
BTR-80, length7.7 m 
BMP-2, height2 m (2.5 m with turret)Image tbd
BMP-2, length6.3 m 
T-72, height2.2 mImage tbd
T-72, length7 m (9.5 m with barrel)Image tbd
Mi-8, height5 mImage tbd
Mi-8, length18 mImage tbd
Altis warehouse, wall5 mImage tbd
Altis warehouse, window1 mhttps://i.imgur.com/4cRv13M.png
Average door2.1 m (~2 m)Image tbd
Cobblestone wall, pillar2 mhttps://i.imgur.com/wRsYjzd.png
H-barrier, big2 mImage tbd
H-barrier, small1.4 mImage tbd
Sandbags1 mImage tbd
Bunker tower5 mImage tbd
Cargo watchtower, height6 m 
Cargo tower, height20 mImage tbd
Cargo HQ, height6 mImage tbd
FM/BG-523 - Milliradians: Mil-Dot Reticles

In your typical mil-dot scope, you will find a reticle with markings of dots or lines. These markings follow one prime rule: their centres are spaced 1 mrad apart.

For all properly modelled mil-dot reticles, the rule is further:

  • from centre to centre of adjacent dots, there is 1 mrad,
  • from edge to the close edge of an adjacent dot, there are 0.8 mrad,
  • a mildot is 0.2 mrad wide.

They can also have other properties that extend their utility. Some have additional markings in between the main ones. Some have stadiametric tools to quickly get a range from a known object, or a combination of all of these features.

A commonly issued scope is the M8541A as illustrated, so it serves to manage expectations throughout. In its case, the dots are 1 mrad apart with 0.5 mrad dashes in between, making for accurate at-a-glance measurements.


First Focal Plane vs. Second Focal Plane

Telescopic sights come in two ‘zoom flavours’: FFP and SFP.

FFP, first focal plane, scopes show a constant subtension of markings. This means that the markings mean the same at any given zoom level, but it shrinks with lower magnifications and grows with larger magnifications. Their advantage is therefore that you can use the mil-relation formula as-is, without an intermediate conversion for the zoom factor. Their potential disadvantage is that lower magnifications make the reticle harder to read, which could hinder follow-up adjustments in close-quarters situations.

FFP scopes are the most commonly issued scopes.

SFP, second focal plane, scopes come with reticles that stay a constant size at every zoom level. This means that their angular measurements are only true at one specific power setting: usually the highest. If the space between two markings is 1 mrad at 12x magnification, it would cover 2 mrad at 6x magnification instead.

This can be useful for shooters who expect proportionally many close-range engagements, where fully zooming in with a high-power scope narrows the field of view too much, causing tunnel vision and loss of awareness. In such close-range situations, the scope can comfortably be kept at the lowest power setting but maintain a clear and visible reticle. Their disadvantage is that for accurate distance measurements at any magnification other than the true magnification, you have to convert. Good practice is to keep it at the 1:1 setting when ‘milling’ a range to avoid this.

M8541A sight picture with mil-dots and half-mil-dashes

Above: M8541A sight picture with mil-dots and half-mil-dashes

FM/BG-524 - Milliradians: Ranging

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FM/BG-525 - Milliradians: Ranging Example 1a

A person is 1.8 metres tall. He appears as 6 mrad in our scope, therefore following the mil-relation formula:

((person's height in metres) * 1000) / (mrad measured) = (range in metres)

(1.8 m * 1000) / 6 mrad = 1800 / 6

= 300 metres

A man standing relaxed, known to be 1.8 m tall

Above: A man standing relaxed, known to be 1.8 m tall

FM/BG-526 - Milliradians: Ranging Example 1b

From Example 1a we know the distance using the person's full height. However, you can’t always see a person’s whole body. For reliability and to avoid a decimal (we want it easy for expedience after all), consider the person’s height from the top of their head to the crotch: it’s one metre!

Head-to-crotch now appears as 3.2 mil. Round to 3 mil because we want it easy, so:

((head-to-crotch in metres) * 1000) / (mrad measured) = (range in metres)

(1 m * 1000) / 3 mil = 1000 / 3

≅ 330 metres

We’re off by 30 because we rounded. Try to be as precise as possible, but we preferred ease of use this time. Judging the balance of this is a skill, too.

A man standing relaxed, measured head to crotch as a known dimension of 1 metre

Above: A man standing relaxed, measured head to crotch as a known dimension of 1 metre

FM/BG-527 - Milliradians: Ranging Example 2

Sometimes personnel is hard to spot or track, making range estimation using body dimensions difficult. Especially at long ranges, smaller objects require a more accurate reading of mrads, which is error-prone. Other larger objects, including identifiable vehicles, lend themselves to the same purpose.

A BTR-80 is 2 metres from the base of its wheels to the top of the hull, appearing as 4 mrad in our scope:

((BTR wheel to roof) * 1000) / (mrad measured) = (range in metres)

(2 m * 1000) / 4 mrad = 2000 / 4

= 500 metres

A BTR-80, known to be 2 metres high when measured from the ground to the top of its hull

Above: A BTR-80, known to be 2 metres high when measured from the ground to the top of its hull

FM/BS-422 - Use a laser rangefinder to obtain a range to target

Look at the target and fire the laser rangefinder to obtain an exact range to the target.

FM/BS-423 - Use milliradians to calculate a range to target

Use milliradian tools to obtain a range to the target, by applying the core concept that at 1000 meters, 1 milliradian equals 1 meter.

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