What is MOA (minute of arc)? The basic measuring units in scopes are MIL and MOA. What are the miles?

You've probably heard of the acronym MOA - "minute of arc" (or more accurately minute of arc), but is it comparable to Milrad / MIL (milliradian)? In this video, Bryan Litz from Applied Ballitics explains what MOA (minute of arc) and MIL (milliradian) are. Brian reveals information about quantities and explains how they are used.
One minute of arc (1 MOA) is a unit of angle (1/60th of an angle) that corresponds to 1.047" inches at 100 yards.
One milliradian (1 MIL) is a unit of measurement of angle that corresponds to 1/10 m at 100 meters, which means that 0.1 MIL (standard division on the scope's handwheels) will equal 1 cm at 100 meters.
Is one system better than another? Not necessarily... Brian goes on to explain that scopes with Mildot crosshairs can be useful for determining distances, and MOA-based corrections work accurately at understandable distances. Since one minute of arc corresponds almost to 1" inch at 100 yards, such a system has become convenient for expressing the accuracy of a weapon. As a common expression, a rifle with semi-angular accuracy can produce groups of 1/2 inch (1.27 cm) or less at 100 yards.

Applied Ballitics MIL and MOA Angular Units Explained

What is an arc minute?
When talking about degrees of angle, a minute is simply 1/60. Therefore, an "Angular Minute" is simply 1/60 of one degree of the central angle, measured from the top or bottom (vertical) / right or left (horizontal). At 100 yards, 1 MOA equals 1.047" inches on target. This is most often rounded up for simplicity. Let's say for example you make an adjustment of 1 MOA (that's four clicks on the scope's 1/4 MOA dial). That's roughly 1 inch per 100 yards, or also 4 inches at 400 yards, since the target area is measured in angular value (approx. MOA) it increases with distance

MIL or MOA for weapons, precision shooting and ranging.
MIL or MOA - Which angle measurement system is better for determining distance and aiming? In a similar article on PrecisionRifleBlog.com, Cal Zant addressed this issue. Analyzing the pros and cons of each measurement system, Zant concluded that both systems work well as long as you use them according to what adjustments you have on your scope. Zant noted that 1/4 MOA is "a little more accurate" than 1/10 MIL, but that doesn't really matter: "Technically, 1/4 MOA clicks are slightly more accurate than 1/10 MIL. The difference is extremely small. .. it only equals 0.1" inch difference in adjustment at 100 yards or 1" inch at 1000 yards." Zant added that in practice, both input systems have graduations of 1/4 MOA and 1/10 MIL. in the click perform equally accurately in the field: "Most shooters will agree that 1/4MOA and 1/10MIL are both accurate systems."

The British metric system causes a lot of inconvenience for those who are accustomed to simple and understandable kilograms, meters and liters. How the mile in km is determined and why the ancient measure turned out to be so tenacious is discussed in this article.

Historical measures

From the distant past, inches and miles, pounds and yards, bushels and pints came to us. All these units of measurement were directly related to man. Without a standard system of weights and measures at hand, people used what was nearby. What could be closer? own hands and legs? This is how the first anthropometric measures related to the size of people’s body parts appeared. For example, an inch was the length of a phalanx index finger. A foot is the size of an adult man's foot, and so on. But what is 1 mile? How many kilometers is it?

What kind of miles are there?

This well-known measure of length came to us from ancient times. Due to its age, it has many interpretations. When answering the question “1 mile - how many kilometers?”, you should definitely clarify which unit of measurement the interlocutor has in mind. The Egyptian mile is 580 meters long, and the longest, the Norwegian mile, is almost 11 kilometers.

Until the mid-18th century, in Europe alone there were about 46 different miles, which measured completely different distances.

Why is that?

This discrepancy in interpretation of this standard measure of length is easily explained. The word "mile" has Latin roots. This standard measure of length was measured by one thousand steps of the ancient Roman legionnaires.

After the decline of the Roman Empire, a simple and convenient value began to be used throughout Europe. Yes, they just considered it differently. Many peoples agreed on the mile with their national measures of length. For example, the Russian mile was equal to seven versts, the French equated it to their Gallic leagues, and the British measured the mile in furlongs. The proud Scots also used this measure of length, but it differed significantly in its dimensions in different regions Highland and was slightly longer than the English one.

Link to geography

Later, with the advent of precise measuring instruments, they tried to standardize the wayward mile. Over the centuries, exploration of the surrounding world has given scientists accurate knowledge about the structure of our planet. It turned out to be very convenient to draw the surface of the Earth with parallels and meridians and tie the existing units of length to geographical dimensions. One of the first in this series was 1 mile. How many kilometers did it cover in geographical units? Everything depended on the name.

Such a different mile

Practical Germans were the first to fall in love with this conformity. From now on, the German mile (also known as the geographical mile) was equal to 1/15 of a degree of the equatorial parallel, which amounted to 7.420 km.

The French separated land and sea miles, but equated both values ​​to the share of the earth's meridian. One land league occupies the 25th part of one degree of the meridian. In the standard system of weights and measures, one French mile is 4.44 km. A nautical mile is slightly longer. The French equated it to 1/20 of a meridian degree. Accordingly, its length will be greater - a French nautical mile is 5.55 km.

The Swedes did it the easiest way. Before the spread of the metric system, they used their own mile, which was equal to 10.6 km. After approval international system The SI Swedes only slightly shortened their mile and recognized it as equal to 10.0 km.

British (American) mile

Undoubtedly, greatest distribution is the British mile, often called the American mile. By default, international business documents assume the British 1 mile. How many kilometers of air routes are converted into miles for British and American passengers is known only to employees of international airlines.

After all, according to tradition, the duration of air flights and bonuses for passengers are calculated in American miles. One such unit of length is 1.609 km and is a multiple of eight furlongs, 1760 yards and 5280 feet.

What is MOA (minute of arc)?

In some countries abroad, traditionally, the main measures of length do not correspond to the SI or GHS measurement systems and are measured in inches, yards, miles, nautical miles, etc.

MOA (Minute Of Angle) - minute of angle. This is a unit of measurement of angular quantities corresponding to the following:
1 degree is 60 minutes of arc (60 MOA);
A circle is 360 degrees, i.e. in a circle 360x60=21,600 arc minutes (21,600 MOA).

This angular value is used to assess the accuracy of hits, corrections when shooting, etc.
That is, an angle of 1 MOA at 100 meters gives a circle diameter of 2.9089 cm (roughly 3 cm at a distance of 100 meters)
(1 yard = 0.9144 meters) Therefore, 1 MOA at 100 meters in circumference will be slightly more than 1 MOA at 100 yards.

Westerners are accustomed to describing hit groups on targets in MOA because this angular width is almost exactly one inch at 100 yards, then widens out to become two inches at 200 yards, three inches at 300 yards, and so on down to 10 inches at 1000 yards.

A rifle with an accuracy of less than 1 MOA (that is, an accuracy of less than 3 cm at 100 meters) is considered a good weapon.

It should be remembered that in many imported scopes, adjustments are measured in MOA or can be proportional to this unit (1/2 MOA, 1/3 MOA, 1/4 MOA, 1/8 MOA), i.e. one click of such a sight shifts the STP by 3 cm at a distance of 100 meters (or in the corresponding proportion)

At the same time, the reticle of imported sights is often marked not in MOA but in milliradians (Mil-mils).
This is used so that using the sight you can quickly measure the distance to the target or make appropriate adjustments in shooting. The convenience is evident from the calculations below:

The relationship between MOA, mils and thousandths of distance.
1 thousandth of a distance at 100 meters is 10 cm.
1 MOA at 100 meters is 2.9089 cm
1 thousandth is greater than 1 MOA by 10/2.9089 = 3.4377 times. This is a linear relationship.

Angular ratio. If the circle of hits is 10 cm, then the angle will be equal to:
q = 2 * tan-1((10/2)/(100*100)) = 2 * 0.0005 = 0.001 radian or 1 milliradian
1 milliradian = 360*60/(2*3.14*1000) = 3.4377 MOA.

Conclusion:
1 milliradian (mil) = 1 thousandth of distance = 3.4377 MOA = 10 cm at a distance of 100 meters.
Those. one reticle division of an imported sight (the so-called Mil-Dot sights) corresponds to 10 cm at a distance of 100 m (and, accordingly, 20 cm at 200 m, 30 cm at 300 m, etc.)

By the way, the root of the name Mil-Dot comes from Milliradian Dot (milliradian point). Hence the name of the unit of measurement - Mil, Mil, short for "milliradian".

General conclusion:
At a range of 100 meters, an accuracy of 1 MOA is equal to a diameter of 2.9089 cm, and 1 mil is equal to 10 linear centimeters.

the image of the target and the reticle is at the same distance from the eye, which allows you to see them clearly and reduces eye fatigue;

the optical sight increases the size of the target, which allows precise aiming of the weapon at distant and/or small targets;

The optical sight collects more light than the eye, allowing you to see objects clearly in low light. Some sights are additionally equipped with a reticle illumination device, which allows you to see it clearly against the background of a dark target;

• using the aiming reticle, you can determine the angular dimensions of the target, which allows you to calculate the distance to it;

  an optical sight, as a rule, allows you to configure it for a shooter with visual impairments (myopia or farsightedness), which allows you to shoot without glasses;

  the optical sight reduces the field of view, which may interfere with target search and aiming at a moving target;

  When shooting with a telescopic sight, the shooter often closes one eye, focusing on the sight of the target through the sight. This creates a danger for the shooter, because with one eye closed, he will not be able to notice the enemy if he appears from the side (say, when the enemy is patrolling the area), outside the field of view of the optical sight. Therefore, experienced shooters spend a lot of time camouflaging their position and aiming with both eyes open;

  at short distances (less than 20-30 m), the sight creates a blurry image and parallax appears (when the eye moves relative to the sight, the aiming reticle moves relative to the target image), which reduces aiming accuracy. Some scopes allow you to adjust them for short range shooting;

  when shooting, the eye must be at a certain distance from the sight (as a rule, this distance is within 5-10 cm), otherwise distortions occur, the field of view is reduced and there is a risk of injury to the eye due to the recoil of the weapon. If the scope is equipped with a rubber eyecup, then the eye must be placed close to it.

MOA (Minute Of Angle - minute of angle)

In the West, this angular value is widely used in ballistics to assess the accuracy of hits, corrections when shooting, etc. By the way, we instead use another, linear quantity - a thousandth of the distance.

A circle is 360 degrees;
1 degree is 60 arc minutes;
The circumference is 21,600 arc minutes.
In a circle - 2 * 3.14 radians

As you can see, the distance and diameter of the circle of hits form a triangle, solving which we will calculate the angle .

 = 2 tan-1((C/2)/d), where d is the distance in inches, C is the diameter of the circle in inches

In the West, target hit groups are described in MOA because this angular width is almost exactly one inch at 100 yards, then widens out to become two inches at 200 yards, three inches at 300 yards, and so on down to 10 inches at 1000 yards.

When you say that your rifle places bullets in a 1-inch circle at 100 yards, you can also say that your rifle's accuracy is about 1 MOA (minute of arc) and that would be a more accurate characteristic because it automatically means that the rifle gives a group of hits in a circle with a diameter of 2 inches at 200 yards, 4 inches at 400, and so on.

What if your rifle hits a two-inch group at 100 yards? Simply, the coefficients are the same. Only you start counting from a wider group of hits. This "two-inch" rifle should therefore produce a four-inch group at 200 yards (twice as wide, get it?), then a 10-inch group at 500 yards, since the range is 5 times greater and the group width is also 5 times greater than 2 inches at 100 yards.

By expressing hit groups and drop in MOA, you can understand how your rifle will perform at any range. And having understood, very accurately enter corrections into the sight.

In imported scopes, adjustments are measured in MOA.
For example:
Let's say your scope has one click = 1/4 MOA. You shoot at 300 yards and the bullet hits 15 inches below.
We calculate the correction: 15 (inches)/3 (hundreds of yards) = 5 MOA or 20 clicks on your scope.

Read more about the “price” of a sight click below.

To make the relationship between distance and MOA clear, look at the table.

By the way, in the West, a rifle with an accuracy of less than 1 MOA is considered a decent tool.

If, say, a carbine hits a 6cm group at 100 meters, how does that compare to their accuracy standards? The following table will help solve this issue, converting MOA into centimeters of accuracy at meter distances.

How to Convert MOA to Thousands of Distances

As we found out above, an angle of 1 MOA at 100 meters gives a circle diameter of 2.9089 cm. And 1 thousandth of a distance at 100 meters is 10 cm. Accordingly, 1 etc. greater than 1 MOA is 10/2.9089 = 3.4377 times. This is a linear relationship.

Angular ratio. If the circle of hits is 10 cm, then the angle will be equal to:

= 2 * tan-1((10/2)/(100*100)) = 2 * 0.0005 = 0.001 radian or 1 milliradian

1 milliradian = 360*60/(2*3.14*1000) = 3.4377 MOA. It is this unit of measurement (milliradians) that is used in optical sights with a Mil Dot reticle.

Conclusion:
1 milliradian = 1 thousandth of distance = 3.4377 MOA,
accordingly: 1 MOA = 0.2909 thousandths of distance = 0.2909 milliradians

Price per click of a Mil-Dot sight

What is the "cost per click of a sight"? This, simply put, like any precision instrument (and a sight is one), is the price of dividing the scale marked on the vertical and horizontal correction drum. More precisely, this is the value of the angle by which the sight deviates when the drum is moved by one click or “click”. This angle is expressed in either MOA, thousandths of distance, or MILs.

How to find out the cost per click of a sight?
1. It is necessary to examine the instructions that came with the scope, as well as the scope itself, for any clear indications of the cost per click. Quite often there are such instructions, although often the cost per click is indicated in values ​​that are quite exotic for our country, such as “1/4 inch at a distance of 100 yards” (typical for scopes for the US market). But it’s even more mysterious when it’s written, for example, “1 click=1/4”/100yds.” The problem is that symbol inches and arcminutes are very similar - " And ". That is, it is clear that the cost of a click is one-fourth at a distance of 100 yards, but one-fourth of what (minutes or inches?) is easy to mistake. How much will it be in MOA? And in centimeters at a 100 meter distance? It's easy to get confused... (Answers: 0.2387 MOA and 0.7 centimeters can easily be obtained using a calculator). In any case, whether the cost per click is indicated or not, you cannot trust it until its value is confirmed by practice.

Practice
2. We print out a target on an A2 sheet of paper to check the sights. The targets are on our website in the section "Targets"

3 . We check the zeroing of the rifle on the central circle of this target.

4 . Let’s say the estimated (or manufacturer’s stated) cost per click is 0.25 MOA.
On the vertical correction drum, make 32 clicks (32x0.25 = 8 MOA) in the direction where the arrow with the inscription points UP or the symbol " IN" (or U.P. for imported sights. Or just one character U). The barrel will move upward relative to the sight.

We aim for the lower right circle.

If the cost per click is close to that stated by the manufacturer, the hits should be in the upper right circle.

We measure the distance from the aiming point to the point of impact vertically in cells. The target is lined with a reticle with a side length corresponding to 1 MOA at a distance of 100 meters. We divide this distance, in cells (that is, in MOA!) by the number of clicks. We get the cost of a vertical click in MOA.

5. Then, without returning the vertical correction to 0, click the horizontal correction drum 32 clicks in the direction reverse where the arrow with the inscription points RIGHT or the symbol " P" (or RIGHT for imported sights. Sometimes just one character R). The barrel will move to the left relative to the sight.

We aim at the same lower right circle.
If the cost per click is close to that stated by the manufacturer, the hits should be in the upper left circle.

Measuring the distance horizontally from the aiming point to the impact point in the cells. We divide this distance, in cells (that is, in MOA!) by the number of clicks. We get the cost of a horizontal click in MOA.

6. We return the vertical correction drum to 0. We shoot, aiming at the same lower right circle. The hits should be in the lower left circle. This item controls the ability of the sight mechanism to return the aiming point to exactly the same place vertically. Let's call this property "sight repeatability".

7. Well, finally, we return the horizontal correction drum to 0. We shoot, aiming at the same lower right circle. The hits must land exactly where we are aiming. This item controls the ability of the sight mechanism to return the aiming point to exactly the same place horizontally.

Talk about the principles of operation, parallax and other wisdom optical sights I won't, because... There are special resources for this on the Internet. I'll just tell you about the notation. For example, the AkhB sight. A - magnification, B - diameter of the entrance pupil (lens) in mm. Those. 8x56 - eight-fold constant magnification sight with an entrance pupil of 56 mm. 2-10x52 - sight with variable magnification from 2x to 10x with an entrance pupil of 52mm. It is necessary to pay attention to sights with an entrance pupil of at least 40mm, because they have good aperture.

There is an important task of choosing a sight for powerful pneumatics. Choosing a scope for pneumatic guns, especially powerful ones, is really a problem. It's all about poor double recoil on spring-piston pneumatics. First back, when the massive piston moves away, and then sharply forward, when the piston crashes into the front wall of the cylinder. Double recoil is especially strong on pneumatics with a powerful spring (Diana, Gamo, etc.). This is a test that a LOT of scopes cannot do. In the case of the MP-512, everything is a little simpler, but the low power of the reinforced MP512 does not guarantee that the sight will not fly apart.

Sights with variable magnification are especially susceptible to “expansion”. They have more mechanics and more to loosen up. I lost one sight (I don’t remember the office, otherwise I would have definitely “advertised”) 3-9x39 on an enhanced MP512 after ~300 shots. I can imagine what would happen if I put it on Diana. He would probably EXPLODE from the tension!

Therefore, if a salesperson in a store shows you a 4x20 “pneumatic” sight (you’ll recognize it right away - it’s a finger-thick tube that you can’t see anything) with a bad mount, then know that these sights are for Daizy plastic pneumatic toys. It TOTALLY sucks. NEVER take this bucket. You can read about sights that handle the double recoil of powerful rifles on our website

One MP512 rifle is used by me to carry out " special operations"at home. A competent "muzzle" is installed on the rifle, allowing grandmothers sitting on a bench under the window to be pleasantly surprised by the crows "for no reason" flopping from the trees onto the asphalt. Accordingly, from the conditions of use it follows that shooting is carried out at stationary targets. Hence the conclusion - It’s better to install a scope with a higher magnification. From 6x to 12x. I have a BelOMO 3-9x40 with a standard “T” shaped reticle. The magnification is 6x (I’ll tell you why below).


The second MP512 is used by me “when going out” into nature. Workhorse. I carry it everywhere. I use it on stationary, slow-moving, moving targets. Accordingly, the sight must provide the ability to observe a moving target. This range is from 3x to 6x. I have a VOMZ 2-10x52 with a standard “T” shaped mesh. The multiplicity is 6x (I’ll tell you why below).


I use Diana 52 to make long-range shots at stationary and very slow-moving targets. When shooting long-range at small targets, it is necessary to have a thin reticle with rangefinder marks to make aiming easier. And the sight magnification should be greater. From 6x to 12x. I have an exclusive BelOMO 6x40 scope with a Mil-Dot reticle. Excellent scope and reticle, but the magnification is clearly not enough. 8x-10x would be ideal.

Now about 6x. I have vision (-5) diopters and the common hunting 4x is not enough for me. Moreover, having used many rifles and sights in different situations I came to the conclusion that 6x-8x is the ideal hunting magnification (IMHO). One more thing. Variable power scopes (at least mine) have one ugly feature. Increasing mesh sizes with increasing magnification. At maximum magnification in my scopes, the reticle bars become the size of a log. It's terribly annoying and hard to shoot. Therefore, I chose the best option for myself. Regarding the sight reticle. There are many grids invented in the world, but the main ones are those in the pictures.

Having selected a scope, you need to select a mount for it. This is also a very responsible node. From my own experience, I will say that I prefer mounts with a single base. Inseparable. This opinion was formed based on extensive experience in removing and installing sights on rifles. The sight is removed along with the mount (naturally). If, after installing the sight back, the MTP (average point of impact) has not changed, the mount is excellent. So, monolithic fastenings provide this requirement.

If it turns out that the cost of a scope with a mount will be equal to or more than the cost of a rifle, know that this is how it should be.