Knowledge (XXG)

Milliradian

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1957: 2300: 1550: mrad. The small adjustment value means these sights can be adjusted in very small increments. These fine adjustments are however not very well suited for dialing between varied distances such as in field shooting because of the high number of clicks that will be required to move the line of sight, making it easier to lose track of the number of clicks than in scopes with larger click adjustments. For instance to move the line of sight 0.4 mrad, a 0.1 mrad scope must be adjusted 4 clicks, while comparably a 0.05 mrad and 0.025 mrad scope must be adjusted 8 and 16 clicks respectively. 1337: 741: 4298: 784: 1624:
shot was off target. The number of milliradians to correct is then multiplied by ten if the scope has 0.1 mrad adjustments. If for instance the shot was 0.6 mrad to the right of the target, 6 clicks will be needed to adjust the sight. This way there is no need for math, conversions, knowledge of target size or distance. This is true for a first focal plane scope at all magnifications, but a variable second focal plane must be set to a given magnification (usually its maximum magnification) for any mrad scales to be correct.
2321:), converted back into milliradians, can be used to adjust the aiming point. Generally mrad-reticle scopes have both horizontal and vertical crosshairs marked; the horizontal and vertical marks are used for range estimation and the vertical marks for bullet drop compensation. Trained users, however, can also use the horizontal dots to compensate for bullet drift due to wind. Milliradian-reticle-equipped scopes are well suited for long shots under uncertain conditions, such as those encountered by military and law enforcement 1597: 4283: 3467: 2167: 2282: 4268: 4256: 732: 2949: 2158: 1620:. The most common scope adjustment increment in mrad based rifle scopes is 0.1 mrad, which are sometimes called "one centimeter clicks" since 0.1 mrad equals exactly 1 cm at 100 meters, 2 cm at 200 meters, etc. Similarly, an adjustment click on a scope with 0.2 mrad adjustment will move the point of bullet impact 2 cm at 100 m and 4 cm at 200 m, etc. 1973:
20 meters at 1000 meters (or 2 m at 100 m, 4 m at 200 m, 6 m at 300 m etc.). The horizontal and vertical adjustment ranges can be different for a particular sight, for instance a scope may have 20 mrad vertical and 10 mrad horizontal adjustment. Elevation differ between models, but about 10–11 mrad are common in hunting scopes, while scopes made for
652: 36: 2754: 3455: 2333: 158: 702:(4000 in a circle). The United Kingdom was also trialing them to replace degrees and minutes. They were adopted by France although decigrades also remained in use throughout World War I. Other nations also used decigrades. The United States, which copied many French artillery practices, adopted angular mils, later known as 1981:
100 meters the sight will thereafter always have to be adjusted upwards to compensate for bullet drop at longer ranges, and therefore the adjustment below zero will never be used. This means that when using a neutral mount only about half of the scope's total elevation will be usable for shooting at longer ranges:
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It is possible to purchase rifle scopes with a mrad reticle and minute-of-arc turrets, but it is general consensus that such mixing should be avoided. It is preferred to either have both a mrad reticle and mrad adjustment (mrad/mrad), or a minute-of-arc reticle and minute-of-arc adjustment to utilize
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is much simpler with decimal units, thereby requiring less mental calculation in the field. Using the range estimation formula with the units meters for range and millimeters for target size it is just a matter of moving decimals and do the division, without the need of multiplication with additional
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When using a scope with mrad adjustments, but without mrad markings in the reticle (i.e. a standard duplex cross-hair on a hunting or benchrest scope), sight correction for a known target subtension and known range can be calculated by the following formula, which utilizes the fact that an adjustment
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When using a scope with both mrad adjustment and a reticle with mrad markings (called a mrad/mrad scope), the shooter can spot his own bullet impact and easily correct the sight if needed. If the shot was a miss, the mrad reticle can simply be used as a "ruler" to count the number of milliradians the
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with an mrad reticle available), the reticle can be used to measure how many mrads to correct a shot even without knowing the shooting distance. For instance, assuming a precise shot fired by an experienced shooter missed the target by 0.8 mrad as seen through an optic, and the firearm sight has
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is the physical amount of space covered by an angle and varies with distance. Thus, the subtension corresponding to a mrad (either in an mrad reticle or in mrad adjustments) varies with range. Knowing subtensions at different ranges can be useful for sighting in a firearm if there is no optic with an
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If the firearm is attached in a fixed mount and aimed at a target, the shot grouping measures the firearm's mechanical precision and the uniformity of the ammunition. When the firearm also is held by a shooter, the shot grouping partly measures the precision of the firearm and ammunition, and partly
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Angle can be used for either calculating target size or range if one of them is known. Where the range is known the angle will give the size, where the size is known then the range is given. When out in the field angle can be measured approximately by using calibrated optics or roughly using one's
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In most regular sport and hunting rifles (except for in long range shooting), sights are usually mounted in neutral mounts. This is done because the optical quality of the scope is best in the middle of its adjustment range, and only being able to use half of the adjustment range to compensate for
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The horizontal and vertical adjustment range of a firearm sight is often advertised by the manufacturer using mrads. For instance a rifle scope may be advertised as having a vertical adjustment range of 20 mrad, which means that by turning the turret the bullet impact can be moved a total of
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While a radian is defined as an angle on the unit circle where the arc and radius have equal length, a milliradian is defined as the angle where the arc length is one thousandth of the radius. Therefore, when using milliradians for range estimation, the unit used for target distance needs to be
1980:
Sights can either be mounted in neutral or tilted mounts. In a neutral mount (also known as "flat base" or non-tilted mount) the sight will point reasonably parallel to the barrel, and be close to a zero at 100 meters (about 1 mrad low depending on rifle and caliber). After zeroing at
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Artillery spotters typically use their calibrated binoculars to move fired projectiles' impact onto a target. Here they know the approximate range to the target and so can read off the angle (+ quick calculation) to give the left/right corrections in meters. A mil is a meter at a range of one
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and the adoption of the metric system of measurement (e.g. artillery replaced "units of base" with meters) the Red Army expanded the 600 unit circle into a 6000 mil circle. Hence the Russian mil has a somewhat different origin than those derived from French artillery practices.
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Dapples: ... Charles-Marc (1837-1920), ingénieur, professeur à l'université de Lausanne, municipal à Lausanne, est l'inventeur de l'unité appelée "millième" pour mesurer les angles dans le tir d'artillerie. Une branche de la famille s'est fixée à Gênes à la fin du XVIIIe
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With a mrad reticle-equipped scope the distance to an object can be estimated with a fair degree of accuracy by a trained user by determining how many milliradians an object of known size subtends. Once the distance is known, the drop of the bullet at that range (see
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If using a mixed system scope that has a mrad reticle and arcminute adjustment, one way to make use of the reticle for shot corrections is to exploit that 14′ approximately equals 4 mrad, and thereby multiplying an observed corrections in mrad by a fraction of
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mrad reticle available, but involves mathematical calculations, and is therefore not used very much in practical applications. Subtensions always change with distance, but an mrad (as observed through an optic) is always an mrad regardless of distance. Therefore,
2783:) and about 10 m for a "big tank." From the front a Land Rover is about 1.5 m wide, most tanks around 3–3.5 m. So a SWB Land Rover from the side is one finger wide at about 100 m. A modern tank would have to be at a bit over 300 m. 2635: 2743: 2696: 1613:) increases with viewing distance to the target. For instance the same angle of 0.1 mrad will subtend 10 mm at 100 meters, 20 mm at 200 meters, etc., or similarly 0.39 inches at 100 m, 0.78 inches at 200 m, etc. 2017: 2847: 2398: 2910:
Where mag is scope magnification. However, a user should verify this with their individual scope since some are not calibrated at 10× . As above target distance and target size can be given in any two units of length with a ratio of 1000:1.
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For maps and artillery, three rounded definitions are used which are close to the real definition, but more easily can be divided into parts. The different map and artillery definitions are sometimes referred to as "angular mils", and are:
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Artillery uses angular measurement in gun laying, the azimuth between the gun and its target many kilometers away and the elevation angle of the barrel. This means that artillery uses mils to graduate indirect fire azimuth sights (called
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Premade table for range estimation showing target sizes, distances and corresponding angular measurements. Angular sizes are given in milliradians, ranges in meters, and target sizes are shown in both in centimeters, millimeters and
934: 985: 1014:, but unlike the radian where the same unit must be used for radius and arc length, the milliradian needs to have a ratio between the units where the subtension is a thousandth of the radius when using the simplified formula. 2030:
are common since it is very important to have enough vertical adjustment to compensate for the bullet drop at longer distances. For this purpose scope mounts are sold with varying degrees of tilt, but some common values are:
706:. Before 2007 the Swedish defence forces used "streck" (6300 in a circle, streck meaning lines or marks) (together with degrees for some navigation) which is closer to the milliradian but then changed to NATO mils. After the 4297: 2960:
In the table below conversions from mrad to metric values are exact (e.g. 0.1 mrad equals exactly 1 cm at 100 meters), while conversions of minutes of arc to both metric and imperial values are approximate.
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the shooter's consistency and skill. Often the shooters' skill is the most important element towards achieving a tight shot grouping, especially when competitors are using the same match grade firearms and ammunition.
1743: mrad changes the impact as many centimeters as there are hundreds of meters. In other words, 1 cm at 100 meters, 2.25 cm at 225 meters, 0.5 cm at 50 meters, etc. See the table below 520:
to count the number of mrads a shot was off-target, which directly translates to the sight adjustment needed to hit the target with a follow-up shot. Optics with mrad markings in the reticle can also be used to make a
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So if the above-mentioned 6 m long BMP (6000 mm) is viewed at 6 mrad its distance is 1000 m, and if the angle of view is twice as large (12 mrad) the distance is half as much, 500 m.
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Subtension refers to the length between two points on a target, and is usually given in either centimeters, millimeters or inches. Since an mrad is an angular measurement, the subtension covered by a given angle
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that are marked in mrad. This can either be accomplished with lines or dots, and the latter is generally called mil-dots. The mrad reticle serves two purposes, range estimation and trajectory correction.
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adopted metric units of measurement for land and general use. NATO mils, meters, and kilograms became standard, although degrees remained in use for naval and air purposes, reflecting civil practices.
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A shot grouping is the spread of multiple shots on a target, taken in one shooting session. The group size on target in milliradians can be obtained by measuring the spread of the rounds on target in
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is mathematically defined as the angle formed when the length of a circular arc equals the radius of the circle, a milliradian, is the angle formed when the length of a circular arc equals
679:" (400 gradians in a circle) under various names having considerable popularity in much of northern Europe. However, Imperial Russia used a different approach, dividing a circle into 833: 2701:
If using the metric unit meters for distance and the imperial unit inches for target size, one has to multiply by a factor of 25.4, since one inch is defined as 25.4 millimeters.
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When used with some riflescopes of variable objective magnification and fixed reticle magnification (where the reticle is in the second focal plane), the formula can be modified to:
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thousand meters (for example, to move the impact of an artillery round 100 meters by a gun firing from 3 km away, it is necessary to shift the direction by 100/3 = 33.3 mils.)
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and other field shooters. These riflemen must be able to aim at varying targets at unknown (sometimes long) distances, so accurate compensation for bullet drop is required.
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and dividing by the shooting distance in meters. This way, using milliradians, one can easily compare shot groupings or target difficulties at different shooting distances.
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per turn instead of 360° or 2π radians, achieving higher resolution than a 360° compass while also being easier to divide into parts than if true milliradians were used.
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on target, and range. In such applications it is useful to use a unit for target size that is a thousandth of the unit for range, for instance by using the metric units
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and use simple ratios to determine size and distance with high accuracy for rifle and short distance artillery calculations by using the handy property of subtension:
4674: 2237: 1244:{\displaystyle \delta =100\%\times \left|{\frac {{\text{arcminutes}}_{\text{ trig}}-{\text{inches per hundred of yards}}}{{\text{arcminutes}}_{\text{trig}}}}\right|} 4597: 2348:
Milliradian reticles often have dots or marks with a spacing of 1 mrad in between, but graduations can also be finer and coarser (i.e. 0.8 or 1.2 mrad).
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at varied distances. The click values are fine enough to get dialed in for most target shooting and coarse enough to keep the number of clicks down when dialing.
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Reticles in some artillery sights are calibrated to the relevant artillery definition for that military, i.e. the Carl Zeiss OEM-2 artillery sight made in
950: 3482:) points to the north, instead of using NATO mils where direction is always relative to the target (0 or 6400 NATO mils is always towards target). 1956: 1727:
In firearm optics, where 0.1 mrad per click is the most common mrad based adjustment value, another common rule of thumb is that an adjustment of
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If, for instance a target known to be 1.5 m in height (1500 mm) is measured to 2.8 mrad in the reticle, the range can be estimated to:
4467:. However that Sweden has changed its map grid systems and angular measurement to those used by NATO, so the "streck" measurement unit is obsolete. 4561: 4525: 4743: 2345:
fingers and hands. With an outstretched arm one finger is approximately 30 mrad wide, a fist 150 mrad and a spread hand 300 mrad.
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load and firearm combination, the bullet may drop 13 mrad at 1000 meters (13 meters). To be able to reach out, one could either:
1317:{\displaystyle {\text{arcminutes}}_{\text{ trig}}=\arctan {\frac {\text{inches per hundred of yards}}{3600}}\times {\frac {180}{\pi }}\times 60} 528:
Milliradians are generally used for very small angles, which allows for very accurate mathematical approximations to more easily calculate with
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thousand times as large as the unit used for target size. Metric units are particularly useful in conjunction with a mrad reticle because the
4668: 756:(marked green, approximately 57.3°) corresponds to an angle where the length of the arc (blue) is equal to the radius of the circle (red). 631:, which are then often referred to as "mils", "lines", or similar. For instance there are artillery sights and compasses with 6,400  4255: 504:
sights by adjusting the angle of the sight compared to the barrel (up, down, left, or right). Milliradians are also used for comparing
1368:. New shooters are often explained the principle of subtensions in order to understand that a milliradian is an angular measurement. 4837: 4812: 667:
The milliradian (approximately 6,283.185 in a circle) was first used in the mid-19th century by Charles-Marc Dapples (1837–1920), a
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0.1 mrad adjustments, the shooter must then dial 8 clicks on the scope to hit the same target under the same conditions.
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the strength of each system. Then the shooter can know exactly how many clicks to correct based on what he sees in the reticle.
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of the angle of a radian. (The image on the right is exaggerated for illustration, as a milliradian is much smaller in reality).
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The adjustment range needed to shoot at a certain distance varies with firearm, caliber and load. For example, with a certain
185: 57: 2900:{\displaystyle {\text{distance in meters}}={\frac {\text{size in mm}}{\text{angle in mrad}}}\times {\frac {\text{mag}}{10}}} 1336: 1132:{\displaystyle \delta =100\%\times \left|{\frac {\theta _{\text{trig}}-\theta _{\text{rad}}}{\theta _{\text{trig}}}}\right|} 2084:{\displaystyle {\text{maximum elevation with tilted mount}}={\frac {\text{scope's total elevation}}{2}}+{\text{base tilt}}} 4902: 4651: 477: 100: 4486: 525:
of a known size target, or vice versa, to determine a target size if the distance is known, a practice called "milling".
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parts per billion) error for an angle of 0.1 mrad, for instance by assuming 0.1 mrad equals 1 cm at 100 m
619:, and rifle scope adjustments and reticles are calibrated to this definition. There are also other definitions used for 72: 53: 3510:
of the circumference of a circle, which is the definition used by telescopic rifle sight manufacturers in reticles for
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Also, in general the same unit can be used for subtension and range if multiplied with a factor of thousand, i.e.
740: 46: 3511: 2772: 2757: 796: 522: 171: 140: 806: 783: 4912: 2630:{\displaystyle {\text{distance in meters}}={\frac {\text{target in meters}}{\text{angle in mrad}}}\times 1,000} 133: 2738:{\displaystyle {\text{distance in meters}}={\frac {\text{target in inches}}{\text{angle in mrad}}}\times 25.4} 2691:{\displaystyle {\text{distance in yards}}={\frac {\text{target in inches}}{\text{angle in mrad}}}\times 27.78} 2121:
Use a scope with 14 mrad of adjustment and a 6 mrad tilted mount to achieve a maximum adjustment of
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Subtensions in mrad based optics are particularly useful together with target sizes and shooting distances in
3474:" ("Artilleriepromille") are used to indicate an absolute indication of direction by using the notation that 1587: mrad can be found in some short range sights, mostly with capped turrets, but are not very widely used. 1356:
Milliradian adjustment is commonly used as a unit for clicks in the mechanical adjustment knobs (turrets) of
86: 4907: 3685: 2842:{\displaystyle {\text{distance in meters}}={\frac {1500{\text{ mm}}}{2.8{\text{ mrad}}}}=535.7{\text{ m}}} 1011: 672: 660: 243: 4424: 4342: 3648: 2393:{\displaystyle {\text{distance in meters}}={\frac {\text{target in millimeters}}{\text{angle in mrad}}}} 1596: 1515: 675:. Degrees and minutes were the usual units of angular measurement but others were being proposed, with " 564:
of the radius. A common adjustment value in firearm sights is 1 cm at 100 meters which equals
167: 68: 2577:{\displaystyle {\text{distance in kilometers}}={\frac {\text{target in meters}}{\text{angle in mrad}}}} 170:
has markings with 1-mrad spacing, which can be used to compensate for wind drift, impact correction or
2012:{\displaystyle {\text{usable elevation in neutral mount}}={\frac {\text{scope's total elevation}}{2}}} 1511: 707: 680: 1502: mrad are used in speciality scope sights for extreme precision at fixed target ranges such as 548:
for range. This coincides with the definition of the milliradian where the arc length is defined as
2318: 2286: 1974: 1446: 1023: 493: 4447:, a unit of area, equal to the area of a square with sides of length of one thousandth of an inch. 1377:
and shot corrections are given in mrads, thereby avoiding the need for mathematical calculations.
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and similar abbreviations are often used by militaries in the English speaking part of the world.
2358: 1661:{\displaystyle {\text{adjustment in mrad}}={\frac {\text{subtension in mm}}{\text{range in m}}}.} 1507: 1503: 3466: 2262:{\displaystyle {\text{group size in mrad}}={\frac {\text{group size in mm}}{\text{range in m}}}} 2166: 2546:
The same holds true for calculating target distance in kilometers using target size in meters.
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Use a scope with 26 mrad of adjustment in a neutral mount, to get a usable adjustment of
1345: 529: 4441:, a unit of area, equal to the area of a circle with a diameter of one thousandth of an inch. 1146:
The approximation using mrad is more precise than using another common system where 1′ (
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1′ ≈ 0.291 mrad (or 2.91 cm at 100 m, approximately 3 cm at 100 m)
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by using the simplified linear formula will increase as the angle increases. For example, a
885: 877: 683:(60° per triangle, 6 triangles in a circle) and hence 600 units to a circle. 656: 533: 787:
For small observed angles (green) the arc length (blue) approaches the subtension (orange).
4374: 4345:), together with their manual plotting devices, firing tables and fire control computers. 3725: 3663: 2095: 1374: 1365: 1349: 1341: 792: 616: 509: 489: 190: 3655:, 32 "nautical lines" per circle) which sometimes use the same symbol. However, the 93: 3486:
Because of the definition of pi, in a circle with a diameter of one there are 2000 
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2.9% error for 300 mrad, i.e. assuming 300 mrad equals 300 m at 1 km
3730: 3659:(DIN 1301 part 3) is to use ¯ for artillery lines, and " for nautical lines.) 2641: 1381: 929:{\displaystyle \theta _{\text{trig}}=\arctan {\frac {\text{subtension}}{\text{range}}}} 608: 516:
with mrad markings (called an "mrad/mrad scope"), the shooter can use the reticle as a
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0.03% error for 30 mrad, i.e. assuming 30 mrad equals 30 m at 1 km
4896: 4764: 4382: 3735: 2976: 2953: 2326: 2147: 1617: 941: 505: 219: 4881: 4785: 4633: 2157: 980:{\displaystyle \theta _{\text{rad}}\simeq {\frac {\text{subtension}}{\text{range}}}} 731: 4699: 4660: 4438: 3598: 3560: 836: 668: 2644:
yards for distance and inches for target size, one has to multiply by a factor of
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7.36% error for 1000′, i.e. assuming 1000′ equals 1000 inches at 100 yd
1150:) is approximated as 1 inch at 100 yards, where comparably there is a: 4505: 4464: 4303: 3644: 2027: 1961: 1357: 687: 600: 338: 35: 2760:
using the hands on an extended arm as a reference for the angular size in mrad.
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9 mrad, which equals 9 m at 1000 m (or 0.9 m at 100 m)
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6 mrad, which equals 6 m at 1000 m (or 0.6 m at 100 m)
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3 mrad, which equals 3 m at 1000 m (or 0.3 m at 100 m)
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measures about 13 mm and was fired at about 45 meters, which equals
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One mrad approximately subtends one meter at a distance of one thousand meters
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4.72% error by assuming that an angle of 1′ equals 1 inch at 100 yd
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Conversion between true milliradian and derived units for maps and artillery
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Two shot groupings obtained with different firearms at different distances.
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which are rounded to more easily be divided into smaller parts for use with
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Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems
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of 1 mrad changes the impact as many millimeters as there are meters:
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at different distances. When using a scope with both mrad adjustment and a
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Various symbols have been used to represent angular mils for compass use:
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4.75% error for 100′, i.e. assuming 100′ equals 100 in at 100 yd
2228: 1723:= 0.05 mrad, or 1 click with a 0.05 mrad adjustment scope. 4856: 3494:) per full turn. In other words, one real milliradian covers just under 2201:
measures about 7 mm and was fired at about 90 meters, which equals
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With a tilted mount the maximum usable scope elevation can be found by:
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usually have an adjustment range of 20–30 mrad (70–100 moa).
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from 1969 to 1976 is calibrated for the eastern bloc 6000 mil circle.
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of the radius of the circle. Just like the radian, the milliradian is
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bullet drop is seldom a problem at short and medium range shooting.
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compass with scales both in 360 degrees and NATO 6400 mil
3567:(Finland phasing out the standard in favour of the NATO standard). 3465: 3453: 2947: 2780: 2331: 2298: 2280: 1955: 1595: 1335: 881: 782: 650: 545: 517: 226: 200: 163: 1380:
If a rifle scope has mrad markings in the reticle (or there is a
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Use of the milliradian is practical because it is concerned with
4750: 4732:. Light Test & Measurement Instruments. Vilnius, LT: Standa. 3538: 3031: 3024: 2776: 1600:
Illustration of sight adjustment with 0.1 milliradian increment.
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by using the definition of a radian and the simplified formula:
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These relations can easily be derived by looking at the units:
29: 1445:′ are used in general purpose sights for hunting, target and 869:{\displaystyle {\text{subtension}}\simeq {\text{arc length}}} 246:
with an arc length one thousandth of the radius, i.e. 1 
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load. Bullet drop and wind drift are shown both in mrad and
698:(6400 in a circle) for use with artillery sights instead of 500:(0.001 radian). Milliradians are used in adjustment of 4306:
wrist compass with two (opposite) scales, 360 degrees
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for the standard Warsaw Pact mil. Sometimes just marked as
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Photonics solutions for extending the frontiers of science
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divided into 1,000 mrad per radian, hence 2,000 
508:, or to compare the difficulty of hitting different sized 604: 4463:
Sweden (and Finland) have not been part of NATO nor the
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for describing small angles, i.e. measuring alignment,
4562:"Calculation of approximation error for 300 mrad" 4526:"Calculation of approximation error for 0.1 mrad" 4261:
A 360 degree and 6400 NATO mil compass rose.
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0.1 mrad equals exactly 1 cm at 100 m
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or approximately 6,283.185 milliradians in one
599:The true definition of a milliradian is based on a 436: 402: 368: 334: 303: 281: 239: 214: 206: 196: 184: 179: 150: 139:"Millirad" redirects here. Not to be confused with 60:. Unsourced material may be challenged and removed. 2899: 2841: 2737: 2690: 2629: 2576: 2392: 2261: 2083: 2011: 1660: 1316: 1243: 1131: 979: 928: 868: 827: 4870:"Mils / MOA & the range estimation equations" 4744:"The mirror alignment and control system for CT5" 4276:compass with 6400 ‰ ("artillery per milles") 2965:Conversion of various sight adjustment increment 2362:constants, thus producing fewer rounding errors. 3671:), a symbol used on some older French compasses. 3462:with the full circle divided into 6400 NATO mils 2767:are about 3 to 4 m long, "smaller tank" or 2654:≈ 27.78, since there are 36 inches in one yard. 1167:Calculation of percentage error for arcminutes 4828:Nebylov, Alexander V.; Watson, Joseph (2016). 4616:"Calculation of approximation error for 1000′" 4598:"Calculation of approximation error for 100′" 8: 4790:Encyclopedia of Laser Physics and Technology 4580:"Calculation of approximation error for 1′" 2308:Many telescopic sights used on rifles have 690:, France was experimenting with the use of 27:Angular measurement, thousandth of a radian 4487:"How to use milliradian-adjustable scopes" 4310:and 6000 Soviet mil counterclockwise. 1964:can be explained as the angle between the 1745: 828:{\displaystyle \sin \theta \simeq \theta } 156: 147: 2887: 2874: 2866: 2864: 2834: 2820: 2810: 2804: 2796: 2794: 2719: 2711: 2709: 2672: 2664: 2662: 2605: 2597: 2595: 2564: 2556: 2554: 2380: 2372: 2370: 2249: 2241: 2239: 2076: 2063: 2055: 2053: 1999: 1991: 1989: 1689:= 0.4 mrad, or 4 clicks with a 1645: 1637: 1635: 1298: 1285: 1270: 1265: 1262: 1229: 1224: 1217: 1208: 1203: 1199: 1178: 1117: 1106: 1093: 1086: 1065: 1054:Calculation of percentage error for mrad 967: 958: 952: 916: 901: 895: 861: 853: 851: 808: 799:shows that the angle approximates to the 120:Learn how and when to remove this message 3700: 2963: 2752: 4749:. The H.E.S.S. experiment. Geneva, CH: 4478: 4456: 4353:Other scientific and technological uses 4251: 2026:However, in long range shooting tilted 835:. This allows a user to dispense with 496:which is defined as a thousandth of a 2952:Comparison of milliradian (mrad) and 1506:. Some specialty iron sights used in 659:, one of the former buildings of the 7: 4507:Dictionnaire historique de la Suisse 4427:, an inch-based unit often called a 3458:Map measure M/70 of the NATO member 58:adding citations to reliable sources 3639:, called "artillery line" (German: 3470:In the Swiss Army, 6400 "artillery 2277:Range estimation with mrad reticles 2057:maximum elevation with tilted mount 4361:) is also used in other fields of 3450:Definitions for maps and artillery 2295:as seen at 25× magnification. 1592:Subtensions at different distances 1364:both in the military and civilian 1189: 1076: 25: 4329:), their associated instruments ( 1993:usable elevation in neutral mount 285: 4730:Opto-Mechanical Products Catalog 4706:from the original on 18 May 2019 4417:, today standardised as 10  4296: 4281: 4266: 4254: 3692:if superscript is not available. 3667:, called "thousandths" (French: 2406:Derivation of the range formula 2285:P4L mrad reticle as used in the 2165: 2156: 1518:come with adjustments in either 739: 730: 686:Around the time of the start of 232:meaning "one thousand") and the 34: 4680:from the original on 5 May 2016 3589:. The Swedish term for this is 2352:Units for target size and range 761:: A milliradian corresponds to 45:needs additional citations for 4726:"Optical Beam Alignment Meter" 4504:Renaud, Hugues (31 May 2002). 3697:Conversion table for compasses 2915:Mixing mrad and minutes of arc 1952:Adjustment range and base tilt 671:engineer and professor at the 1: 4405:, a unit of length common in 2944:Conversion table for firearms 795:, and when using radians the 536:observed in an optic, linear 532:, back and forth between the 484:, sometimes also abbreviated 4830:Aerospace Navigation Systems 2940:when adjusting the turrets. 1705: mrad adjustment scope. 4391:inertial navigation systems 4337:), their elevation sights ( 1288:inches per hundred of yards 1219:inches per hundred of yards 880:denoted by θ (Greek letter 4929: 4765:"Focusing and Collimating" 2145: 138: 131: 4886:The Online Compass Museum 4832:. John Wiley & Sons. 3647:(not to be confused with 3512:stadiametric rangefinding 2992: 2983: 2974: 2969: 1968:of a rifle and its scope. 1759: 1756: 1751: 1748: 876:, instead of finding the 797:small angle approximation 299: 155: 141:Millirad (radiation unit) 4803:Groves, Paul D. (2013). 3684:), a symbol used by the 3643:), a symbol used by the 3629:), a symbol used by the 3410:1 mrad ≈ 3.44′, so 2775:at about 6 m (e.g. 2336:Mildot chart as used by 1960:The concept of a tilted 846:More in detail, because 134:Minute and second of arc 132:Not to be confused with 4316:Use in artillery sights 3641:artilleristische Strich 3561:the former Soviet Union 2066:scope's total elevation 2002:scope's total elevation 1397:Gradations (clicks) of 940:one can instead make a 4661:Army Command (Finland) 4510:. Fonds, AV Laussane. 3686:Finnish Defence Forces 3483: 3463: 2957: 2901: 2843: 2761: 2739: 2692: 2631: 2578: 2558:distance in kilometers 2394: 2341: 2305: 2296: 2263: 2199:The group on the right 2085: 2013: 1969: 1662: 1601: 1394:General purpose scopes 1353: 1318: 1245: 1133: 981: 930: 870: 829: 803:of the angle, that is 788: 722:Mathematical principle 673:University of Lausanne 664: 661:University of Lausanne 4653:Taistelijan Opas 2013 4638:Online Compass Museum 4425:Thousandth of an inch 4357:The milliradian (and 3469: 3457: 2951: 2902: 2844: 2756: 2740: 2693: 2632: 2579: 2395: 2383:target in millimeters 2335: 2302: 2284: 2264: 2178:The group on the left 2086: 2014: 1959: 1663: 1599: 1339: 1319: 1246: 1134: 982: 931: 871: 830: 786: 752:: An angle of 1  681:equilateral triangles 654: 168:Dragunov sniper rifle 4903:Units of plane angle 4327:panoramic telescopes 3905:1 Warsaw Pact mil = 3621:, called "artillery 2863: 2793: 2708: 2661: 2594: 2553: 2369: 2287:Schmidt & Bender 2238: 2052: 1988: 1634: 1516:300 meter rifle 1261: 1177: 1064: 951: 894: 850: 807: 708:Bolshevik Revolution 544:for target size and 54:improve this article 4868:Simeone, Robert J. 4807:(Second ed.). 4700:"Suunnistus: Piiru" 3965:1 Swedish streck = 3705: 3593:, literally "line". 2966: 2319:external ballistics 2196:= 0.289 mrad. 1975:long range shooting 1447:long range shooting 1389:Common click values 1024:approximation error 1018:Approximation error 494:angular measurement 294:... is equal to ... 180:General information 4771:. Technical Note. 4359:other SI multiples 4170:1 minute of arc = 4028:1 Nautical line = 3701: 3627:Artilleriepromille 3484: 3478:(corresponding to 3464: 2964: 2958: 2897: 2868:distance in meters 2839: 2798:distance in meters 2762: 2749:Practical examples 2735: 2713:distance in meters 2688: 2627: 2599:distance in meters 2574: 2390: 2374:distance in meters 2342: 2306: 2297: 2259: 2243:group size in mrad 2217:= 0.078 mrad. 2137:+ 6 = 13 mrad 2081: 2009: 1970: 1658: 1639:adjustment in mrad 1602: 1504:benchrest shooting 1354: 1314: 1241: 1129: 977: 942:good approximation 926: 866: 825: 789: 665: 534:angular separation 530:direct proportions 446:    438:    412:    404:    378:    370:    344:    336:    313:    305:    4786:"beam divergence" 4670:978-951-25-2485-3 4403:Scandinavian mile 4250: 4249: 3653:Nautischer Strich 3404: 3403: 3150:0.0485 mrad 2895: 2891: 2882: 2881: 2878: 2869: 2837: 2826: 2823: 2813: 2799: 2727: 2726: 2723: 2714: 2680: 2679: 2676: 2667: 2666:distance in yards 2613: 2612: 2609: 2600: 2572: 2571: 2568: 2559: 2544: 2543: 2388: 2387: 2384: 2375: 2359:mental arithmetic 2257: 2256: 2253: 2244: 2079: 2071: 2067: 2058: 2007: 2003: 1994: 1949: 1948: 1653: 1652: 1649: 1640: 1452:Speciality scopes 1329: 1328: 1306: 1293: 1289: 1273: 1268: 1235: 1232: 1227: 1220: 1211: 1206: 1144: 1143: 1123: 1120: 1109: 1096: 975: 974: 971: 961: 924: 923: 920: 904: 864: 856: 603:with a radius of 470: 469: 282:Conversions 130: 129: 122: 104: 16:(Redirected from 4920: 4889: 4877: 4864: 4861:convertworld.com 4844: 4843: 4825: 4819: 4818: 4800: 4794: 4793: 4782: 4776: 4775: 4761: 4755: 4754: 4748: 4740: 4734: 4733: 4722: 4716: 4715: 4713: 4711: 4696: 4690: 4689: 4687: 4685: 4679: 4658: 4648: 4642: 4641: 4640:. Compassipedia. 4630: 4624: 4623: 4612: 4606: 4605: 4594: 4588: 4587: 4576: 4570: 4569: 4558: 4552: 4551: 4540: 4534: 4533: 4522: 4516: 4515: 4501: 4495: 4494: 4483: 4468: 4461: 4300: 4285: 4270: 4258: 4241: 4240: 4232: 4231: 4227: 4220: 4219: 4212: 4211: 4204: 4203: 4196: 4195: 4188: 4186: 4185: 4182: 4179: 4164: 4157: 4150: 4149: 4145: 4137: 4131: 4130: 4123: 4122: 4115: 4114: 4107: 4105: 4104: 4101: 4098: 4083: 4076: 4069: 4068: 4064: 4056: 4049: 4042: 4036: 4035: 4023: 4022: 4015: 4014: 4006: 4005: 4001: 3989: 3988: 3981: 3980: 3973: 3972: 3959: 3952: 3945: 3944: 3940: 3932: 3921: 3920: 3913: 3912: 3899: 3892: 3891: 3882: 3881: 3877: 3870: 3869: 3852: 3851: 3839: 3838: 3831: 3829: 3828: 3825: 3822: 3813: 3812: 3805: 3803: 3802: 3799: 3796: 3786: 3785: 3784: 3778: 3771: 3770: 3763: 3762: 3755: 3754: 3742:1 milliradian = 3719:Warsaw Pact Mil 3706: 3704: 3584: 3582: 3581: 3578: 3575: 3558: 3556: 3555: 3552: 3549: 3536: 3534: 3533: 3530: 3527: 3509: 3507: 3506: 3503: 3500: 3493: 3489: 3481: 3477: 3441: 3439: 3438: 3435: 3432: 3425: 3423: 3422: 3419: 3416: 3365:0.291 mrad 3335: 3334: 3330: 3303: 3302: 3298: 3278:0.145 mrad 3271: 3270: 3266: 3239: 3238: 3234: 3214:0.073 mrad 3207: 3206: 3202: 3175: 3174: 3170: 3143: 3142: 3138: 3118:0.036 mrad 3111: 3110: 3106: 3086:0.025 mrad 3079: 3078: 3074: 3054:0.024 mrad 3047: 3046: 3042: 3003: 2996: 2967: 2939: 2937: 2936: 2933: 2930: 2906: 2904: 2903: 2898: 2896: 2889: 2888: 2883: 2879: 2876: 2875: 2870: 2867: 2848: 2846: 2845: 2840: 2838: 2835: 2827: 2825: 2824: 2821: 2815: 2814: 2811: 2805: 2800: 2797: 2758:Estimating range 2744: 2742: 2741: 2736: 2728: 2724: 2722:target in inches 2721: 2720: 2715: 2712: 2697: 2695: 2694: 2689: 2681: 2677: 2675:target in inches 2674: 2673: 2668: 2665: 2653: 2652: 2648: 2636: 2634: 2633: 2628: 2614: 2610: 2608:target in meters 2607: 2606: 2601: 2598: 2583: 2581: 2580: 2575: 2573: 2569: 2567:target in meters 2566: 2565: 2560: 2557: 2537: 2535: 2534: 2529: 2526: 2517:= meter, (short 2516: 2514: 2513: 2508: 2505: 2495: 2493: 2492: 2489: 2486: 2471: 2469: 2468: 2463: 2460: 2450: 2448: 2447: 2442: 2439: 2429: 2427: 2426: 2423: 2420: 2403: 2399: 2397: 2396: 2391: 2389: 2385: 2382: 2381: 2376: 2373: 2291: 2290:5-25×56 PM II LP 2268: 2266: 2265: 2260: 2258: 2254: 2252:group size in mm 2251: 2250: 2245: 2242: 2216: 2214: 2213: 2210: 2207: 2195: 2193: 2192: 2189: 2186: 2169: 2160: 2136: 2134: 2133: 2130: 2127: 2117: 2115: 2114: 2111: 2108: 2090: 2088: 2087: 2082: 2080: 2077: 2072: 2065: 2064: 2059: 2056: 2018: 2016: 2015: 2010: 2008: 2001: 2000: 1995: 1992: 1774: 1772: 1771: 1768: 1765: 1746: 1742: 1740: 1739: 1736: 1733: 1722: 1720: 1719: 1716: 1713: 1704: 1702: 1701: 1698: 1695: 1688: 1686: 1685: 1682: 1679: 1667: 1665: 1664: 1659: 1654: 1650: 1648:subtension in mm 1647: 1646: 1641: 1638: 1611:angular diameter 1607:angular distance 1586: 1584: 1583: 1580: 1577: 1570: 1568: 1567: 1564: 1561: 1549: 1547: 1546: 1543: 1540: 1533: 1531: 1530: 1527: 1524: 1501: 1499: 1498: 1495: 1492: 1485: 1483: 1482: 1479: 1476: 1469: 1467: 1466: 1463: 1460: 1444: 1442: 1441: 1438: 1435: 1428: 1426: 1425: 1422: 1419: 1412: 1410: 1409: 1406: 1403: 1375:ballistic tables 1332:Sight adjustment 1323: 1321: 1320: 1315: 1307: 1299: 1294: 1287: 1286: 1275: 1274: 1271: 1269: 1266: 1250: 1248: 1247: 1242: 1240: 1236: 1234: 1233: 1230: 1228: 1225: 1222: 1221: 1218: 1213: 1212: 1209: 1207: 1204: 1200: 1164: 1138: 1136: 1135: 1130: 1128: 1124: 1122: 1121: 1118: 1112: 1111: 1110: 1107: 1098: 1097: 1094: 1087: 1051: 1040: 1036: 1034: 1009: 1007: 1006: 1003: 1000: 986: 984: 983: 978: 976: 972: 969: 968: 963: 962: 959: 935: 933: 932: 927: 925: 921: 918: 917: 906: 905: 902: 886:tangent function 878:angular distance 875: 873: 872: 867: 865: 862: 857: 854: 834: 832: 831: 826: 776: 774: 773: 770: 767: 743: 734: 657:Palais de Rumine 641:Swedish "streck" 637:Warsaw Pact mils 595: 593: 592: 589: 586: 579: 577: 576: 573: 570: 563: 561: 560: 557: 554: 523:range estimation 510:shooting targets 465: 463: 462: 461: 456: 453: 447: 439: 431: 429: 428: 427: 422: 419: 413: 405: 397: 395: 394: 393: 388: 385: 379: 371: 363: 361: 360: 359: 354: 351: 345: 337: 329: 327: 326: 323: 320: 314: 306: 277: 275: 274: 271: 268: 261: 259: 258: 255: 252: 172:range estimation 160: 148: 125: 118: 114: 111: 105: 103: 62: 38: 30: 21: 4928: 4927: 4923: 4922: 4921: 4919: 4918: 4917: 4913:Optical devices 4893: 4892: 4882:"Compassipedia" 4880: 4867: 4855: 4852: 4847: 4840: 4827: 4826: 4822: 4815: 4802: 4801: 4797: 4784: 4783: 4779: 4763: 4762: 4758: 4746: 4742: 4741: 4737: 4724: 4723: 4719: 4709: 4707: 4698: 4697: 4693: 4683: 4681: 4677: 4671: 4656: 4650: 4649: 4645: 4632: 4631: 4627: 4614: 4613: 4609: 4596: 4595: 4591: 4578: 4577: 4573: 4560: 4559: 4555: 4542: 4541: 4537: 4524: 4523: 4519: 4503: 4502: 4498: 4493:. 14 July 2011. 4485: 4484: 4480: 4476: 4471: 4462: 4458: 4454: 4399: 4375:beam divergence 4355: 4318: 4311: 4301: 4292: 4286: 4277: 4271: 4262: 4259: 4238: 4236: 4229: 4225: 4224: 4217: 4215: 4209: 4207: 4201: 4199: 4193: 4191: 4183: 4180: 4177: 4176: 4174: 4162: 4155: 4147: 4143: 4142: 4135: 4128: 4126: 4120: 4118: 4112: 4110: 4102: 4099: 4096: 4095: 4093: 4081: 4074: 4066: 4062: 4061: 4054: 4047: 4040: 4033: 4031: 4020: 4018: 4012: 4010: 4003: 3999: 3998: 3986: 3984: 3978: 3976: 3970: 3968: 3957: 3950: 3942: 3938: 3937: 3930: 3918: 3916: 3910: 3908: 3897: 3889: 3887: 3879: 3875: 3874: 3867: 3865: 3849: 3847: 3836: 3834: 3826: 3823: 3820: 3819: 3817: 3810: 3808: 3800: 3797: 3794: 3793: 3791: 3782: 3780: 3776: 3775: 3768: 3766: 3760: 3758: 3752: 3750: 3722:Swedish streck 3702: 3699: 3585:of a circle in 3579: 3576: 3573: 3572: 3570: 3559:of a circle in 3553: 3550: 3547: 3546: 3544: 3537:of a circle in 3531: 3528: 3525: 3524: 3522: 3504: 3501: 3498: 3497: 3495: 3492:≈ 6283.185 mrad 3491: 3487: 3479: 3475: 3452: 3436: 3433: 3430: 3429: 3427: 3420: 3417: 3414: 3413: 3411: 3332: 3328: 3327: 3310:0.15 mrad 3300: 3296: 3295: 3268: 3264: 3263: 3236: 3232: 3231: 3204: 3200: 3199: 3182:0.05 mrad 3172: 3168: 3167: 3140: 3136: 3135: 3108: 3104: 3103: 3095:0.0985 in 3076: 3072: 3071: 3063:0.0958 in 3044: 3040: 3039: 3001: 2994: 2987: 2978: 2971: 2946: 2934: 2931: 2928: 2927: 2925: 2917: 2861: 2860: 2816: 2806: 2791: 2790: 2751: 2706: 2705: 2659: 2658: 2650: 2646: 2645: 2592: 2591: 2551: 2550: 2530: 2527: 2521: 2520: 2518: 2509: 2506: 2500: 2499: 2497: 2490: 2487: 2484: 2483: 2481: 2476:and vice versa 2464: 2461: 2455: 2454: 2452: 2451:= mrad, (short 2443: 2440: 2434: 2433: 2431: 2424: 2421: 2418: 2417: 2415: 2367: 2366: 2354: 2327:varmint hunters 2289: 2279: 2236: 2235: 2221: 2220: 2219: 2218: 2211: 2208: 2205: 2204: 2202: 2197: 2190: 2187: 2184: 2183: 2181: 2176: 2172: 2171: 2170: 2162: 2161: 2150: 2144: 2131: 2128: 2125: 2124: 2122: 2112: 2109: 2106: 2105: 2103: 2050: 2049: 1986: 1985: 1954: 1769: 1766: 1763: 1762: 1760: 1737: 1734: 1731: 1730: 1728: 1717: 1714: 1711: 1710: 1708: 1699: 1696: 1693: 1692: 1690: 1683: 1680: 1677: 1676: 1674: 1632: 1631: 1594: 1581: 1578: 1575: 1574: 1572: 1571: mrad and 1565: 1562: 1559: 1558: 1556: 1544: 1541: 1538: 1537: 1535: 1528: 1525: 1522: 1521: 1519: 1496: 1493: 1490: 1489: 1487: 1480: 1477: 1474: 1473: 1471: 1464: 1461: 1458: 1457: 1455: 1439: 1436: 1433: 1432: 1430: 1429: mrad and 1423: 1420: 1417: 1416: 1414: 1407: 1404: 1401: 1400: 1398: 1391: 1366:shooting sports 1342:ballistic table 1334: 1264: 1259: 1258: 1223: 1202: 1201: 1195: 1175: 1174: 1113: 1102: 1089: 1088: 1082: 1062: 1061: 1038: 1032: 1030: 1020: 1004: 1001: 998: 997: 995: 954: 949: 948: 897: 892: 891: 884:) by using the 848: 847: 805: 804: 781: 780: 779: 778: 771: 768: 765: 764: 762: 757: 746: 745: 744: 736: 735: 724: 649: 590: 587: 584: 583: 581: 574: 571: 568: 567: 565: 558: 555: 552: 551: 549: 490:SI derived unit 459: 457: 454: 451: 450: 448: 445: 437: 425: 423: 420: 417: 416: 414: 411: 403: 391: 389: 386: 383: 382: 380: 377: 369: 357: 355: 352: 349: 348: 346: 343: 335: 324: 321: 318: 317: 315: 312: 304: 272: 269: 266: 265: 263: 256: 253: 250: 249: 247: 210:mrad, mil 191:SI derived unit 175: 144: 137: 126: 115: 109: 106: 63: 61: 51: 39: 28: 23: 22: 15: 12: 11: 5: 4926: 4924: 4916: 4915: 4910: 4908:Decimalisation 4905: 4895: 4894: 4891: 4890: 4878: 4865: 4851: 4850:External links 4848: 4846: 4845: 4838: 4820: 4813: 4795: 4777: 4756: 4735: 4717: 4702:(in Finnish). 4691: 4669: 4659:(in Finnish). 4643: 4634:"Divisions GB" 4625: 4607: 4589: 4571: 4553: 4535: 4517: 4496: 4477: 4475: 4472: 4470: 4469: 4455: 4453: 4450: 4449: 4448: 4442: 4436: 4422: 4398: 4395: 4383:accelerometers 4354: 4351: 4335:aiming circles 4317: 4314: 4313: 4312: 4302: 4295: 4293: 4287: 4280: 4278: 4272: 4265: 4263: 4260: 4253: 4248: 4247: 4242: 4234: 4221: 4213: 4205: 4197: 4171: 4167: 4166: 4159: 4152: 4139: 4132: 4124: 4116: 4090: 4086: 4085: 4078: 4071: 4058: 4051: 4044: 4037: 4029: 4025: 4024: 4016: 4008: 3995: 3990: 3982: 3974: 3966: 3962: 3961: 3954: 3947: 3934: 3927: 3922: 3914: 3906: 3902: 3901: 3894: 3884: 3871: 3863: 3858: 3853: 3845: 3841: 3840: 3814: 3788: 3772: 3764: 3756: 3748: 3743: 3739: 3738: 3733: 3728: 3723: 3720: 3717: 3714: 3709: 3698: 3695: 3694: 3693: 3672: 3660: 3634: 3616: 3595: 3594: 3568: 3542: 3490:milliradians ( 3451: 3448: 3447: 3446: 3443: 3408: 3402: 3401: 3398: 3395: 3392: 3389: 3386: 3383: 3379: 3378: 3377:1.047 in 3375: 3372: 3369: 3366: 3363: 3360: 3356: 3355: 3352: 3349: 3346: 3343: 3342:0.2 mrad 3340: 3337: 3324: 3323: 3320: 3317: 3314: 3311: 3308: 3305: 3292: 3291: 3288: 3285: 3282: 3281:14.54 mm 3279: 3276: 3273: 3260: 3259: 3256: 3253: 3250: 3247: 3246:0.1 mrad 3244: 3241: 3228: 3227: 3224: 3221: 3218: 3215: 3212: 3209: 3196: 3195: 3192: 3191:0.197 in 3189: 3186: 3183: 3180: 3177: 3164: 3163: 3162:0.175 in 3160: 3159:0.192 in 3157: 3156:0.485 cm 3154: 3151: 3148: 3145: 3132: 3131: 3130:0.131 in 3128: 3127:0.144 in 3125: 3122: 3119: 3116: 3113: 3100: 3099: 3096: 3093: 3090: 3087: 3084: 3081: 3068: 3067: 3066:0.087 in 3064: 3061: 3060:0.242 cm 3058: 3055: 3052: 3049: 3036: 3035: 3028: 3021: 3014: 3006: 3005: 2998: 2991: 2982: 2973: 2945: 2942: 2916: 2913: 2908: 2907: 2894: 2886: 2873: 2850: 2849: 2833: 2830: 2819: 2809: 2803: 2750: 2747: 2746: 2745: 2734: 2731: 2718: 2699: 2698: 2687: 2684: 2671: 2642:imperial units 2638: 2637: 2626: 2623: 2620: 2617: 2604: 2585: 2584: 2563: 2542: 2541: 2540: 2539: 2474: 2473: 2408: 2407: 2401: 2400: 2379: 2353: 2350: 2278: 2275: 2270: 2269: 2248: 2174: 2173: 2164: 2163: 2155: 2154: 2153: 2152: 2151: 2146:Main article: 2143: 2142:Shot groupings 2140: 2139: 2138: 2119: 2118:= 13 mrad 2092: 2091: 2075: 2070: 2062: 2043: 2042: 2039: 2036: 2020: 2019: 2006: 1998: 1953: 1950: 1947: 1946: 1943: 1940: 1937: 1934: 1930: 1929: 1926: 1923: 1920: 1917: 1913: 1912: 1909: 1906: 1903: 1900: 1896: 1895: 1892: 1889: 1886: 1883: 1879: 1878: 1875: 1872: 1869: 1866: 1862: 1861: 1858: 1855: 1852: 1849: 1845: 1844: 1841: 1838: 1835: 1832: 1828: 1827: 1824: 1821: 1818: 1815: 1811: 1810: 1807: 1804: 1801: 1798: 1794: 1793: 1790: 1787: 1784: 1781: 1777: 1776: 1758: 1754: 1753: 1750: 1725: 1724: 1706: 1670:For instance: 1657: 1644: 1593: 1590: 1589: 1588: 1554: 1551: 1534: mrad or 1508:ISSF 10 m 1453: 1450: 1395: 1390: 1387: 1382:spotting scope 1346:7.62×51mm NATO 1333: 1330: 1327: 1326: 1325: 1324: 1313: 1310: 1305: 1302: 1297: 1292: 1284: 1281: 1278: 1252: 1251: 1239: 1216: 1198: 1194: 1191: 1188: 1185: 1182: 1169: 1168: 1162: 1161: 1158: 1155: 1142: 1141: 1140: 1139: 1127: 1116: 1105: 1101: 1092: 1085: 1081: 1078: 1075: 1072: 1069: 1056: 1055: 1049: 1048: 1045: 1042: 1019: 1016: 988: 987: 966: 957: 938: 937: 915: 912: 909: 900: 860: 824: 821: 818: 815: 812: 748: 747: 738: 737: 729: 728: 727: 726: 725: 723: 720: 714:In the 1950s, 648: 645: 639:or 6,300  506:shot groupings 468: 467: 443: 434: 433: 409: 400: 399: 375: 366: 365: 341: 332: 331: 310: 301: 300: 297: 296: 291: 284: 283: 279: 278: 241: 237: 236: 216: 212: 211: 208: 204: 203: 198: 194: 193: 188: 182: 181: 177: 176: 161: 153: 152: 128: 127: 42: 40: 33: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 4925: 4914: 4911: 4909: 4906: 4904: 4901: 4900: 4898: 4887: 4883: 4879: 4875: 4871: 4866: 4862: 4858: 4854: 4853: 4849: 4841: 4839:9781119163060 4835: 4831: 4824: 4821: 4816: 4814:9781608070053 4810: 4806: 4799: 4796: 4791: 4787: 4781: 4778: 4774: 4770: 4766: 4760: 4757: 4752: 4745: 4739: 4736: 4731: 4727: 4721: 4718: 4705: 4701: 4695: 4692: 4676: 4672: 4666: 4662: 4655: 4654: 4647: 4644: 4639: 4635: 4629: 4626: 4621: 4620:Wolfram Alpha 4617: 4611: 4608: 4603: 4602:Wolfram Alpha 4599: 4593: 4590: 4585: 4584:Wolfram Alpha 4581: 4575: 4572: 4567: 4566:Wolfram Alpha 4563: 4557: 4554: 4549: 4548:Wolfram Alpha 4545: 4539: 4536: 4531: 4530:Wolfram Alpha 4527: 4521: 4518: 4514: 4509: 4508: 4500: 4497: 4492: 4488: 4482: 4479: 4473: 4466: 4460: 4457: 4451: 4446: 4443: 4440: 4437: 4434: 4430: 4426: 4423: 4420: 4416: 4412: 4408: 4404: 4401: 4400: 4396: 4394: 4392: 4388: 4384: 4380: 4376: 4372: 4368: 4364: 4360: 4352: 4350: 4346: 4344: 4340: 4336: 4332: 4328: 4324: 4315: 4309: 4305: 4299: 4294: 4290: 4284: 4279: 4275: 4269: 4264: 4257: 4252: 4246: 4243: 4235: 4233: 4222: 4214: 4206: 4198: 4189: 4172: 4169: 4168: 4165: 4160: 4158: 4153: 4151: 4140: 4138: 4133: 4125: 4117: 4108: 4091: 4088: 4087: 4084: 4079: 4077: 4072: 4070: 4059: 4057: 4052: 4050: 4045: 4043: 4038: 4030: 4027: 4026: 4017: 4009: 4007: 3996: 3994: 3991: 3983: 3975: 3967: 3964: 3963: 3960: 3955: 3953: 3948: 3946: 3935: 3933: 3928: 3926: 3923: 3915: 3907: 3904: 3903: 3900: 3895: 3893: 3885: 3883: 3872: 3864: 3862: 3859: 3857: 3854: 3846: 3844:1 NATO mil = 3843: 3842: 3832: 3815: 3806: 3789: 3787: 3773: 3765: 3757: 3749: 3747: 3744: 3741: 3740: 3737: 3736:Minute of arc 3734: 3732: 3729: 3727: 3724: 3721: 3718: 3715: 3713: 3710: 3708: 3707: 3696: 3691: 3687: 3683: 3679: 3675: 3673: 3670: 3666: 3665: 3661: 3658: 3654: 3650: 3649:Compass Point 3646: 3642: 3638: 3635: 3632: 3628: 3624: 3620: 3617: 3614: 3610: 3607: 3606: 3605: 3602: 3600: 3592: 3588: 3569: 3566: 3562: 3543: 3540: 3521: 3520: 3519: 3515: 3513: 3473: 3468: 3461: 3456: 3449: 3444: 3426: mrad ≈ 3409: 3406: 3405: 3399: 3396: 3393: 3390: 3387: 3384: 3381: 3380: 3376: 3374:1.15 in 3373: 3371:2.91 cm 3370: 3368:29.1 mm 3367: 3364: 3361: 3358: 3357: 3354:0.72 in 3353: 3351:0.79 in 3350: 3347: 3344: 3341: 3338: 3326: 3325: 3322:0.54 in 3321: 3319:0.59 in 3318: 3315: 3312: 3309: 3306: 3294: 3293: 3290:0.52 in 3289: 3287:0.57 in 3286: 3284:1.45 cm 3283: 3280: 3277: 3274: 3262: 3261: 3258:0.36 in 3257: 3255:0.39 in 3254: 3251: 3248: 3245: 3242: 3230: 3229: 3226:0.26 in 3225: 3223:0.29 in 3222: 3220:0.73 cm 3219: 3217:7.27 mm 3216: 3213: 3210: 3198: 3197: 3194:0.18 in 3193: 3190: 3187: 3184: 3181: 3178: 3166: 3165: 3161: 3158: 3155: 3153:4.85 mm 3152: 3149: 3146: 3134: 3133: 3129: 3126: 3124:0.36 cm 3123: 3121:3.64 mm 3120: 3117: 3114: 3102: 3101: 3098:0.09 in 3097: 3094: 3092:0.25 cm 3091: 3088: 3085: 3082: 3070: 3069: 3065: 3062: 3059: 3057:2.42 mm 3056: 3053: 3050: 3038: 3037: 3033: 3029: 3026: 3022: 3019: 3015: 3012: 3008: 3007: 2999: 2989: 2980: 2968: 2962: 2955: 2954:minute of arc 2950: 2943: 2941: 2921: 2914: 2912: 2892: 2884: 2880:angle in mrad 2871: 2859: 2858: 2857: 2854: 2831: 2828: 2817: 2807: 2801: 2789: 2788: 2787: 2784: 2782: 2778: 2774: 2770: 2766: 2759: 2755: 2748: 2732: 2729: 2725:angle in mrad 2716: 2704: 2703: 2702: 2685: 2682: 2678:angle in mrad 2669: 2657: 2656: 2655: 2643: 2640:If using the 2624: 2621: 2618: 2615: 2611:angle in mrad 2602: 2590: 2589: 2588: 2570:angle in mrad 2561: 2549: 2548: 2547: 2533: 2524: 2512: 2503: 2479: 2478: 2477: 2467: 2459: 2446: 2438: 2413: 2412: 2410: 2409: 2405: 2404: 2386:angle in mrad 2377: 2365: 2364: 2363: 2360: 2351: 2349: 2346: 2339: 2334: 2330: 2328: 2324: 2320: 2314: 2311: 2301: 2294: 2288: 2283: 2276: 2274: 2246: 2234: 2233: 2232: 2230: 2226: 2200: 2179: 2168: 2159: 2149: 2148:Shot grouping 2141: 2120: 2101: 2100: 2099: 2097: 2073: 2068: 2060: 2048: 2047: 2046: 2040: 2037: 2034: 2033: 2032: 2029: 2024: 2004: 1996: 1984: 1983: 1982: 1978: 1976: 1967: 1963: 1958: 1951: 1944: 1941: 1938: 1936:1000 mm 1935: 1932: 1931: 1927: 1924: 1921: 1918: 1915: 1914: 1910: 1907: 1904: 1901: 1898: 1897: 1893: 1890: 1887: 1884: 1881: 1880: 1876: 1873: 1870: 1867: 1864: 1863: 1859: 1856: 1853: 1850: 1847: 1846: 1842: 1839: 1836: 1833: 1830: 1829: 1825: 1822: 1819: 1816: 1813: 1812: 1808: 1805: 1802: 1799: 1796: 1795: 1791: 1788: 1785: 1782: 1779: 1778: 1755: 1747: 1744: 1707: 1673: 1672: 1671: 1668: 1655: 1642: 1629: 1625: 1621: 1619: 1614: 1612: 1608: 1598: 1591: 1555: 1552: 1517: 1513: 1509: 1505: 1454: 1451: 1448: 1396: 1393: 1392: 1388: 1386: 1383: 1378: 1376: 1371: 1367: 1363: 1359: 1351: 1347: 1343: 1338: 1331: 1311: 1308: 1303: 1300: 1295: 1290: 1282: 1279: 1276: 1257: 1256: 1255: 1237: 1214: 1196: 1192: 1186: 1183: 1180: 1173: 1172: 1171: 1170: 1166: 1165: 1159: 1156: 1153: 1152: 1151: 1149: 1148:minute of arc 1125: 1114: 1103: 1099: 1090: 1083: 1079: 1073: 1070: 1067: 1060: 1059: 1058: 1057: 1053: 1052: 1046: 1043: 1029: 1028: 1027: 1025: 1017: 1015: 1013: 1012:dimensionless 993: 964: 955: 947: 946: 945: 943: 913: 910: 907: 898: 890: 889: 888: 887: 883: 879: 858: 844: 842: 838: 822: 819: 816: 813: 810: 802: 798: 794: 785: 760: 755: 751: 742: 733: 721: 719: 717: 712: 709: 705: 701: 697: 693: 689: 684: 682: 678: 674: 670: 662: 658: 653: 646: 644: 642: 638: 635:, 6,000  634: 630: 626: 622: 618: 614: 610: 606: 602: 597: 547: 543: 539: 535: 531: 526: 524: 519: 515: 511: 507: 503: 499: 495: 491: 487: 483: 479: 475: 444: 442: 435: 410: 408: 401: 376: 374: 367: 342: 340: 333: 311: 309: 302: 298: 295: 292: 290: 286: 280: 245: 244:Dimensionless 242: 238: 235: 231: 228: 224: 221: 220:metric prefix 217: 213: 209: 205: 202: 199: 195: 192: 189: 187: 183: 178: 173: 169: 166:reticle in a 165: 159: 154: 149: 146: 142: 135: 124: 121: 113: 102: 99: 95: 92: 88: 85: 81: 78: 74: 71: –  70: 69:"Milliradian" 66: 65:Find sources: 59: 55: 49: 48: 43:This article 41: 37: 32: 31: 19: 4885: 4873: 4860: 4829: 4823: 4804: 4798: 4789: 4780: 4772: 4768: 4759: 4738: 4729: 4720: 4708:. Retrieved 4694: 4682:. Retrieved 4652: 4646: 4637: 4628: 4619: 4610: 4601: 4592: 4583: 4574: 4565: 4556: 4547: 4538: 4529: 4520: 4511: 4506: 4499: 4490: 4481: 4459: 4439:Circular mil 4432: 4428: 4356: 4347: 4334: 4330: 4326: 4322: 4319: 4244: 4223: 4173: 4161: 4154: 4141: 4134: 4092: 4080: 4073: 4060: 4053: 4046: 4039: 3997: 3992: 3956: 3949: 3936: 3929: 3924: 3896: 3886: 3873: 3860: 3855: 3816: 3790: 3774: 3745: 3711: 3689: 3681: 3677: 3674: 3668: 3662: 3657:DIN standard 3652: 3640: 3636: 3626: 3618: 3612: 3608: 3603: 3599:East Germany 3596: 3590: 3516: 3485: 3400:3.6 in 3397:3.9 in 3391:100 mm 3388:1 mrad 3382:1 mrad 3316:1.5 cm 3188:0.5 cm 3089:2.5 mm 2985: 2959: 2922: 2918: 2909: 2855: 2851: 2785: 2763: 2700: 2639: 2586: 2545: 2531: 2522: 2510: 2501: 2475: 2465: 2457: 2444: 2436: 2355: 2347: 2343: 2315: 2307: 2271: 2222: 2198: 2177: 2093: 2044: 2028:scope mounts 2025: 2021: 1979: 1971: 1942:100 mm 1939:100 cm 1933:1000 m 1919:900 mm 1902:800 mm 1885:700 mm 1868:600 mm 1851:500 mm 1834:400 mm 1817:300 mm 1800:200 mm 1783:100 mm 1726: 1669: 1630: 1626: 1622: 1618:metric units 1615: 1603: 1470: mrad, 1379: 1369: 1362:scope sights 1355: 1344:for a given 1253: 1145: 1021: 989: 939: 845: 840: 837:trigonometry 793:small angles 790: 758: 749: 713: 703: 696:angular mils 695: 691: 685: 666: 640: 636: 632: 621:land mapping 598: 596: mrad. 527: 485: 481: 473: 471: 293: 288: 287:1 mrad 229: 222: 197:Unit of 145: 116: 107: 97: 90: 83: 76: 64: 52:Please help 47:verification 44: 4491:Outdoor Hub 4465:Warsaw Pact 4371:collimation 4339:clinometers 4323:dial sights 4304:Soviet Army 4089:1 degree = 3712:Milliradian 3680:, Swedish: 3645:German Army 3625:" (German: 3394:10 cm 3345:20 mm 3336: mrad 3313:15 mm 3304: mrad 3249:10 mm 3240: mrad 3176: mrad 3080: mrad 2970:Increment, 2765:Land Rovers 2293:scope sight 2225:millimeters 1962:scope mount 1945:10 cm 1925:90 mm 1922:90 cm 1916:900 m 1908:80 mm 1905:80 cm 1899:800 m 1891:70 mm 1888:70 cm 1882:700 m 1874:60 mm 1871:60 cm 1865:600 m 1857:50 mm 1854:50 cm 1848:500 m 1840:40 mm 1837:40 cm 1831:400 m 1823:30 mm 1820:30 cm 1814:300 m 1806:20 mm 1803:20 cm 1797:200 m 1789:10 mm 1786:10 cm 1780:100 m 1775: mrad 1752:Subtension 1718:1000 m 688:World War I 601:unit circle 542:millimeters 474:milliradian 432:≈ 0.057296° 215:Named after 186:Unit system 151:Milliradian 18:Angular mil 4897:Categories 4874:scribd.com 4474:References 4445:Square mil 4419:kilometers 4413:, but not 4387:gyroscopes 4367:technology 4274:Swiss Army 3676:(Finnish: 3631:Swiss Army 3623:per milles 3541:countries. 3472:per milles 3348:2 cm 3252:1 cm 3185:5 mm 2877:size in mm 2822: mrad 2485:millimeter 2419:millimeter 2255:range in m 1928:9 cm 1911:8 cm 1894:7 cm 1877:6 cm 1860:5 cm 1843:4 cm 1826:3 cm 1809:2 cm 1792:1 cm 1712:50 mm 1678:20 mm 1651:range in m 1370:Subtension 1272: trig 1267:arcminutes 1226:arcminutes 1210: trig 1205:arcminutes 970:subtension 919:subtension 863:arc length 855:subtension 700:decigrades 538:subtension 441:arcminutes 398:≈ 0.063662 364: turn 262:or 1  110:April 2021 80:newspapers 4452:Footnotes 4343:quadrants 4331:directors 4308:clockwise 3716:NATO mil 3682:delstreck 3669:millièmes 3651:(German: 2972:or click 2885:× 2730:× 2683:× 2616:× 2078:base tilt 1966:bore-axis 1684:50 m 1512:50 m 1309:× 1304:π 1296:× 1283:⁡ 1215:− 1193:× 1190:% 1181:δ 1115:θ 1104:θ 1100:− 1091:θ 1080:× 1077:% 1068:δ 965:≃ 956:θ 914:⁡ 899:θ 859:≃ 823:θ 820:≃ 817:θ 814:⁡ 704:NATO mils 692:millièmes 633:NATO mils 629:compasses 625:artillery 466:≈ 3.4377′ 330: rad 4857:"angles" 4704:Archived 4675:Archived 4397:See also 3480:6400 A ‰ 2812: mm 2480:meter = 2310:reticles 1340:Example 990:Since a 488:) is an 480:-symbol 240:In units 4769:Newport 4415:Denmark 4363:science 4289:US Army 4228:⁄ 4187:⁠ 4175:⁠ 4146:⁄ 4106:⁠ 4094:⁠ 4065:⁄ 4055:196.875 4032:196.349 4002:⁄ 3941:⁄ 3878:⁄ 3830:⁠ 3818:⁠ 3804:⁠ 3792:⁠ 3779:⁄ 3731:Degrees 3583:⁠ 3571:⁠ 3565:Finland 3557:⁠ 3545:⁠ 3535:⁠ 3523:⁠ 3508:⁠ 3496:⁠ 3460:Denmark 3440:⁠ 3428:⁠ 3424:⁠ 3412:⁠ 3385:3.438′ 3339:0.688′ 3331:⁄ 3307:0.516′ 3299:⁄ 3267:⁄ 3243:0.344′ 3235:⁄ 3203:⁄ 3179:0.172′ 3171:⁄ 3147:0.167′ 3139:⁄ 3115:0.125′ 3107:⁄ 3083:0.086′ 3075:⁄ 3051:0.083′ 3043:⁄ 2988:radians 2938:⁠ 2926:⁠ 2836: m 2649:⁄ 2536:⁠ 2519:⁠ 2515:⁠ 2498:⁠ 2494:⁠ 2482:⁠ 2472:= mrad) 2470:⁠ 2453:⁠ 2449:⁠ 2432:⁠ 2428:⁠ 2416:⁠ 2414:mrad = 2338:snipers 2323:snipers 2304:inches. 2229:caliper 2227:with a 2215:⁠ 2203:⁠ 2194:⁠ 2182:⁠ 2135:⁠ 2126:14 mrad 2123:⁠ 2116:⁠ 2107:26 mrad 2104:⁠ 1773:⁠ 1761:⁠ 1757:1 mrad 1741:⁠ 1729:⁠ 1721:⁠ 1709:⁠ 1703:⁠ 1691:⁠ 1687:⁠ 1675:⁠ 1585:⁠ 1573:⁠ 1569:⁠ 1557:⁠ 1548:⁠ 1536:⁠ 1532:⁠ 1520:⁠ 1500:⁠ 1488:⁠ 1484:⁠ 1472:⁠ 1468:⁠ 1456:⁠ 1443:⁠ 1431:⁠ 1427:⁠ 1415:⁠ 1411:⁠ 1399:⁠ 1008:⁠ 996:⁠ 775:⁠ 763:⁠ 647:History 607:and an 594:⁠ 582:⁠ 578:⁠ 566:⁠ 562:⁠ 550:⁠ 514:reticle 502:firearm 464:⁠ 449:⁠ 430:⁠ 415:⁠ 407:degrees 396:⁠ 381:⁠ 362:⁠ 347:⁠ 328:⁠ 316:⁠ 308:radians 276:⁠ 264:⁠ 260:⁠ 248:⁠ 94:scholar 4836:  4811:  4710:18 May 4684:18 May 4667:  4411:Sweden 4407:Norway 4381:, and 4379:optics 4373:, and 4127:16.666 4119:17.777 4111:17.452 3861:0.9375 3591:streck 3587:Sweden 3211:0.25′ 3002:  3000:At 100 2995:  2993:At 100 2986:milli- 2979:of arc 2956:(moa). 2504:-meter 2435:milli- 1749:Range 1553:Others 1486:′ and 1280:arctan 1254:where 1037:% (or 992:radian 911:arctan 754:radian 546:meters 498:radian 289:in ... 234:radian 225:(from 223:milli- 207:Symbol 96:  89:  82:  75:  67:  4747:(PDF) 4678:(PDF) 4657:(PDF) 4431:or a 4237:0.016 4230:21600 4216:0.291 4208:0.277 4200:0.296 4192:0.290 4075:11.25 4048:187.5 4019:3.428 4011:0.057 3985:0.952 3977:1.015 3969:0.997 3917:1.066 3909:1.047 3898:3.375 3888:0.056 3866:0.984 3848:0.981 3835:3.437 3809:0.057 3767:1.002 3759:0.954 3751:1.018 3678:piiru 3476:0 A ‰ 3362:1.0′ 3275:0.5′ 2977:mins 2832:535.7 2686:27.78 2538:= m). 2502:milli 2445:meter 2437:meter 2425:meter 2185:13 mm 973:range 922:range 882:theta 759:Right 677:grads 669:Swiss 575:100 m 569:10 mm 559:1,000 518:ruler 339:turns 230:mille 227:Latin 201:Angle 164:PSO-1 101:JSTOR 87:books 4834:ISBN 4809:ISBN 4751:CERN 4712:2019 4686:2019 4665:ISBN 4429:thou 4409:and 4385:and 4365:and 4136:17.5 4004:6300 3951:0.06 3943:6000 3931:1.05 3880:6400 3781:2000 3726:Turn 3580:6300 3563:and 3554:6000 3539:NATO 3532:6400 3505:6283 3073:0.25 2808:1500 2777:T-34 2773:MICV 2733:25.4 2647:1000 2532:mrad 2511:mrad 2491:mrad 2212:90 m 2206:7 mm 2191:45 m 2096:.308 1539:0.25 1514:and 1459:0.25 1360:and 1358:iron 1291:3600 1231:trig 1119:trig 1095:trig 1022:The 1005:1000 903:trig 801:sine 772:1000 750:Left 716:NATO 655:The 623:and 617:turn 492:for 482:mrad 373:gons 356:2000 325:1000 218:The 162:The 73:news 4433:mil 4389:in 4377:in 4341:or 4333:or 4325:or 4239:667 4218:667 4210:778 4202:297 4194:880 4148:360 4129:667 4121:778 4113:778 4097:50π 4082:675 4041:200 4034:541 4021:572 4013:143 3987:381 3979:873 3971:302 3958:3.6 3919:667 3911:167 3868:375 3850:719 3837:747 3811:296 3801:50π 3769:677 3761:930 3753:592 3613:MIL 3609:mil 3359:1′ 3297:1.5 3169:0.5 3004:yd 2890:mag 2818:2.8 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358:π 353:/ 350:1 322:/ 319:1 270:/ 267:m 257:m 254:/ 174:. 143:. 136:. 123:) 117:( 112:) 108:( 98:· 91:· 84:· 77:· 50:. 20:)

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Minute and second of arc
Millirad (radiation unit)

PSO-1
Dragunov sniper rifle
range estimation
Unit system
SI derived unit
Angle
metric prefix
Latin
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Dimensionless
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