The difference of whether the angular measurement of a scope is in MRAD or MOA doesn’t impact the quality of the scope. It does, however, impact the ease with which a sportsman can use it. The difference is similar to having “miles per hour” and “kilometers per hour” marked on the speedometer in a car. Neither makes the car go any faster than the other. But using one or the other makes sense depending on how comfortable the driver is with each measurement. There are also external factors that impact which measurement is better, similar to whether the road signs showing the speed limit are printed in miles or kilometers. In the same way, MRAD and MOA each fit some circumstances better than others, even though they measure the same thing. Here, we’ll take a look at the MRAD vs MOA question in detail.
MRAD vs MOA: The Math
How do MOA measurements Work?
Since most sportsmen in North America and Europe are more familiar with MOA, we’ll look at it first. Minutes of angle (MOA) is based on the 360-degree circle model. Every circle can be divided into 360 equal degrees. Also, each degree of that circle can be further divided into 60 minutes, just like an hour of time. That means a full circle has 21,600 minutes of angle. For precision shooting, a sportsman obviously doesn’t need to worry about 99% or more of those minutes.
Milliradians are a more difficult measure to understand, initially, than degrees, but make for a much easier scale to use. Just as the circumference of every circle can be divided into 360 degrees, it can also be divided into radians. The radian is equal to the measurement of the radius of the circle, the distance from the center out to any point along the edge.
So How Does Milliradians Work?
The circumference of a circle always follows the same ratio. This is twice the measure of the radius multiplied by the mathematical constant, pi. For simplicity, I’ll use the simplified value of pi, 3.14. Because the ratio is the same, there are always the same number of radians in a circle. This is true no matter how large the circle is.
For example, a circle with a radius of one meter would have a circumference of 6.28 meters (1 meter x 2 x 3.14). The radius of 1 meter would go into the circumference 6.28 times. A circle with a radius of two meters would have a circumference of 12.56 meters (2 meters x 2 x 3.14). The radius of 2 meters would still go into the circumference 6.28 times.
A milliradian is 1/1000th of a radian. Since there are always 6.28 (or so) radians in a circle, there are 6,280 milliradians in any circle. Like minutes of angle, most of those milliradians aren’t useful for shooting purposes.
MRAD vs MOA in Turrets
Comparing MOA to MRAD, then, there are roughly 3.44 minutes of angle in each milliradian. That difference would seem to make MOA the clear choice for better precision in scopes. That’s absolutely true for closer-range shooting (within 100 meters), which is why most hunting optics in the United States and Europe are in MOA. The opposite is true for longer-range shooting when additional scope adjustments are factored in. I’ll discuss this further in the upcoming paragraphs.
Accuracy Over Distance
First, a note about accuracy over distance. For closer-range shooting, the ability to make scope adjustments more precise than one minute of angle doesn’t really factor in much. For true precision shooting at a distance, though, using just milliradians or minutes of angle without adjustments will give poor accuracy. Because both MRAD and MOA track angular movement, the further a bullet travels, the further off course it would be at the same angle.
For example, if a sportsman is shooting a target 10 meters away, being off by a single degree means being .17 meters off target. That same one degree difference at 100 meters away would make him 1.75 meters off target. That’s enough to completely miss what he’s aiming to hit. At 1,000 meters away, that same one degree difference becomes a disastrous 17.5 meters off target. Being able to make more precise adjustments is essential to actually hitting the mark at greater distances.
MOA scopes have different types of adjustments available. Adjustments come in half-minute, quarter-minute, and eighth-minute, each giving a greater fraction of precision. Eighth-minute is the most precise, but it’s suitable only for stationary target shooting. This is due to the number of adjustment clicks that have to be made to get even a small amount of difference in angle. For any type of precision shooting, either with a moving target or where adjustments have to be made quickly, quarter-minute and half-minute are better choices. They give the desired increase in precision over distance without taking so long to set up that the target has already changed positions.
MRAD scopes have one standard adjustment, one-tenth. This makes it much easier to adjust the scope using simpler base-10 math rather than tracking different fractions, as MOA requires. The ease of finding, noting, and communicating precision angles in MRAD is what makes it more popular for military and engineering applications. Because of the difference in size between minutes and milliradians, a tenth of a milliradian is about one third of a minute. It is therefore a more precise adjustment than a half-minute click, but less precise than a quarter-minute click. Since it has nearly-identical precision to adjustable MOA, and since the notation is much easier to reproduce quickly without involving multiple types of fractions, MRAD is superior to MOA for longer-distance shooting of anything but stationary targets.
Here’s a video of NSSF’s Mr. Cleckner covering MOA details.
MRAD vs MOA in Reticles
MRAD and MOA are applied in exactly the same way in reticles as in turrets, with similar advantages and disadvantages. MOA is more precise for distances that are short enough not to need much additional adjustment. MRAD is better for longer distances where keeping track of fractional adjustments gets unwieldy. The biggest thing to watch for is ensuring the reticle is the same angular measurement type as the turret. When the reticle is marked with mil-dots (showing milliradians), always pair it with a MRAD turret. Similarly, always put a MOA reticle with a MOA turret so there’s no confusion about the different measurements.
Just like miles vs. kilometers, choosing MRAD vs MOA is largely a matter of comfort and familiarity with either system. MOA has a clear advantage for shorter-range shooting where no fine adjustments are needed. MRAD is better for most precision sport shooting at a distance.
For additional in-depth reading, you can check out Richard Mann’s article on Mil, MOA, or Inches here.