Minute of Angle
Encyclopedia
Minute of angle is the measurement (in fractions of degrees) of a ballistic round's deviation from its initial heading due to gravity and/or the effect of air resistance on velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

. Informally known as a "Bullet's Trajectory" or "the rainbow effect". Long range weapons must account for this effect because a fired round falls at a quadratic rate. Weapons such as large caliber rifles use scopes with adjustments for elevation
Elevation
The elevation of a geographic location is its height above a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface ....

and windage
Windage
Windage is a force created on an object by friction when there is relative movement between air and the object.There are two causes of windage:# the object is moving and being slowed by resistance from the air...

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The exact measure of MOA is 1.0471996" at 100 yards of distance. MOA is a linear measure so 1" of MOA at 100 yards would equate to .5235998" at 50 yards, 2.0943992" at 200 yards, 3.1415988" at 300 yards and so on. Most high-end rifle scopes used by military snipers, law enforcement snipers, and hunters are equipped with MOA adjustment knobs which provide the shooter with MOA adjustment. Depending on the scope, the adjustments are measured in "clicks" of the knob which equate to a manufacturer set adjustment. For example, one click may be 1/2 MOA for every click while another scope may have 1/4 MOA adjustments, which is considered to be a finer MOA adjustment.

Minute of Angle is a linear effect, not quadratic. That is: twice the distance will result in twice the deviation.
The value of 1 MOA @ 100 yds is 1.04719758 inches.
In linear progression, 1 MOA is equal to 0.52359879 inches @ 50 yds and to 2.09439516 inches @ 200 yds.
It is basically the measure of the opposite side of a right triangle with a 1 MOA (1/60th of 1 deg) "A" angle.