The term "minute-of-angle" (MOA) is
used regularly by target shooters at the range,
but is probably understood, thoroughly, by few
(the same goes for mil-dots). Defined loosely,
one MOA = 1" @ 100 yards; so, if you shot
your rifle 5 times into a 100-yard target and
every shot went into a one-inch circle you had
drawn on the paper, then your rifle could be said
to shoot 1 MOA. Likewise, if every shot goes into
a two-inch circle at 200 yards, then you're shooting
1 MOA. A 10-inch group at 500 yards would be 2
Now for the fun part. There are 360 degrees in
a circle. Each degree can be broken down further
into minutes. There are 60 minutes in a degree.
Likewise, there are 60 seconds in a minute. Now,
to figure out the distance subtended by 1 minute
at any particular distance, we need merely to
plug those two values into a simple trigonometric
equation. The tangent function fits the bill nicely.
Here's the equation:
tan(angle) = distance subtended/distance to the
target (units must be consistent--e.g., 1/36 of
a yard [1"] divided by 100 yards)
Now, we know the angle (1 minute or 1/60 of a
degree) and we know the distance to the target
(100 yards), but we need to figure out the actual
distance subtended at the target (i.e., is 1 MOA
actually 1" @ 100 yards?). What we need to
do is solve for "distance subtended."
Here's our final equation:
tan(angle)*distance to the target = distance subtended
Make sure your calculator is in "degree"
mode (as opposed to "radian" or "gradian")
and type in 1/60 (for degrees) and hit the "tangent"
button. Then multiply that by 100 yards. This
should give you the distance (in yards) subtended
at 100 yards. Multiply this by 36 to get inches.
The answer should be:
This is just a hair over the commonly quoted
"one inch." At 1000 yards, this would
be almost 10 1/2 inches. Apparently, it is just
a coincidence that 1 MOA happens to be REALLY
close to 1" @ 100 yards. It is, however,
The "Mil" in "Mil-Dot" does
not stand for "Military"; it stands
for "milliradian." The radian is a unitless
measure which is equivalent, in use, to degrees.
It tells you how far around a circle you have
gone. 2 PI radians = 360 degrees. Using 3.14 as
the value of PI, 6.28 radians take you all the
way around a circle. Using a cartesian coordinate
system, you can use "x"- and "y"-values
to define any point on the plane. Radians are
used in a coordinate system called "polar
coordinates." A point on the plane is defined,
in the polar coordinate system, using the radian
and the radius. The radian defines the amount
of rotation and the radius gives the distance
from the origin (in a negative or positive direction).
ANYWAY, the radian is another measurement of
rotation (the degree/minute/second-system being
the first). This is the system used in the mil-dot
reticle. We use the same equation that we used
before, but, instead of your calculator being
in "degree" mode, switch it to "radian"
mode. One milliradian = 1/1000 (.001) radians.
So, type .001 into your calculator and hit the
"tangent" button. Then multiply this
by "distance to the target." Finally,
multiply this by 36 to get inches subtended at
the given distance. With the calculator in "radian"
tangent(.001)*100*36 = 3.6000012"
So, one milliradian is just over 3.6 inches at
100 yards. If we extrapolate, two milliradians
equal about 6 feet at one-thousand yards. You'll
see the importance of this, shortly.
The Mil-Dot Reticle
The mil-dot reticle was designed around the measurement
unit of the milliradian. The dots, themselves,
were designed with this in mind and the spacing
of the dots was also based upon the milliradian.
This allows the shooter to calculate the distance
to an object of known height or width. Height
of the target in yards divided by the height of
the target in milliradians multiplied by 1000
equals the distance to the target in yards. For
example, take a 6-foot-tall man (2 yards). Let's
say that the top of his head lines up with one
dot and his feet line up four dots down. So: (2/4)*1000
= 500 yards away. This same tecnique can be used
to estimate lead on a moving target or to compensate
for deflection on a windy day.
The distance from the center of one dot to the
center of the next dot is 1 milliradian. We are
told (by the folks at Leupold) that the length
of a dot is 1/4 milliradian or 3/4 MOA (Given
this much information, one can determine that
the distance between dots is 3/4 milliradian.).*
I use the term "length" because the
mil-dot is not round. It is oblong. The "dots"
on the verticle crosshair run oblong in the vertical
direction. The dots on the horizontal crosshair
run oblong in the horizontal direction (i.e.,
they are lying on their sides). The width of each
dot is an arbitrary distance and is not used for
any practical purpose. Like a duplex reticle,
the mil-dot reticle is thicker towards the edges
and uses thin lines in the middle where the dots
are located and the crosshairs cross. The distance
between the opposite thick portions is 10 milliradians.
*NOTE: 1/4 milliradian = .9" and 3/4 MOA
= .785", so, obviously, a mil-dot cannot
be both 1/4 milliradian and 3/4 MOA. I called
Premier Reticles (they make Leupold's mil-dot
reticles) and got an explanation: the dots on
their mil-dot reticles are 1/4 mil. They are not
3/4 MOA. Apparently, they (Leupold?) just figured
that more shooters understand MOA than milliradians,
so they just gave a figure (in MOA) that was close,
but not super precise.
1 Mil Increment
100 yds - 3.6"
200 yds - 7.2"
300 yds -12"
400 yds - 14.4"
500 yds - 18"
here are some easy places to look: