Minute of Angle (MOA) for Scope Adjustment

Minute of Angle (MOA) for Scope Adjustment

Minute of Angle (MOA) for Scope Adjustment

Leupold's Firedot Wind-Plex Minute of Angle Reticle
Leupold's Firedot Wind-Plex MOA Reticle

Minute of Angle (MOA) Scope Adjustments and Holds

I think most rifle shooters know the term “minute of angle” (MOA) refers to a measurement you dial onto your scope, to change the point of impact on target by the same measure.

For example, my target scopes are calibrated so eight “clicks” on the turret, either for windage or elevation, will move the bullet on target by one minute of angle.  That's my March scope featured at the top of the post.  This is a relatively fine adjustment, used by the benchrest crowd.

In contrast, some scopes will be calibrated four clicks per MOA for hunting, and others one click per MOA for long-range applications.

If you need to dial 24 MOA elevation onto your scope, you won't be using one graduated in 1/8th MOA!  But the fine MOA adjustable optic is perfect for short-range benchrest.  I zero the rifle to shoot dead-center in a calm condition, and then hold for windage.  Once I've adjusted the scope zero for range conditions, I will rarely make any further windage adjustments to the turrets during a competition, no matter how hard the wind blows.

The image above is a Leupold scope reticle dubbed the FireDot Wind-Plex.  The reticle aids in compensating for crosswinds.  The hash marks are in one MOA increments, and extend to ten MOA on each side.  You can read more about this scope, and find other examples of MOA (and Mil-Dot) scopes on Leupold's website.

But just what is a minute of angle, and how is it used to dial, or hold, for the wind?

In the following I'll explain what MOA means, without drilling down too deep into the math behind the unit of measurement.  You'll understand how to add windage onto your scope, or hold the same distance using minutes of angle.

The “Angle” in Minute of Angle

Angles are measured in degrees, but they may also be measured in radians–more on that in an upcoming post.

We're familiar with degrees; for example, a right angle has 90 degrees.  There are 360 degrees in a circle.  Cut the circle in half, and the straight line that bisects it is said to have an angle of 180 degrees.

One degree can be further subdivided into minutes.

Just like an hour is divided into sixty minutes of time, the degree is divided into sixty minutes of angle.

So one MOA is 1/60th of a degree.  In our context I'll use the term “minute” to be interchangeable with MOA.

Now, how wide is a minute?

The Width of a Minute of Angle

Although an angle has no width, you can measure the distance between two lines drawn at an angle, for a specified distance.  Think of it this way.

If you held a flashlight close to a wall, it would make a very small circle of light.  Shine it on the wall in the next room, and the cone of light will have spread out.  Point it downrange, and the lighted circle will be very large at, say, 100 yards.

The angle of light shining from the lamp is the same over the entire distance.  The angle itself is dimensionless, but it can be defined by trigonometry, calculated using the length of a line drawn from the source to the target, and the radius of the circle (from the center line to the circle's edge) at the target.

So how wide is a minute of angle at 100 yards?

Picture yourself at a shooting range, in the center of a large imaginary circle.  The target is at zero degrees, which on the clock face is 12 o'clock.  To put the degree in perspective, winds from 9 or 3 o'clock are 90-degree winds, since they come at right angles to the bullet trajectory; that is, the line from muzzle to target.

The circle arc from the 9 o'clock position to your left, through the target, and reaching around to the 3 o'clock position on your right, is 180 degrees.  At 100 yards, one degree along this circle will measure about 63 inches–too wide to be a practical measure for shooting.

Here's the Math

(only if you're interested) 🙂

Briefly, if you want to know how I got here, remember the formula for the circumference of a circle is 2πr, where π (pi) equals ~ 3.14 and r is the circle's radius (100 yards, or 3600 inches).  Divide the circumference by 360 degrees, and you have 62.8 inches for one degree of arc.

Now that you know a minute is 1/60th of a degree, you can visualize one minute as about one inch (62.8 inches / 60 minutes = 1.047 inches/minute) distance on your target at 100 yards.

You can also repeat the calculation using metric units of measurement, if you prefer to think in centimeters of bullet deflection.  It doesn't matter, because the angle itself is devoid of units, it's just an angle.  In our non-virtual world we attach units to describe the physical width of the angle at a selected distance.

One MOA is One Inch at 100 Yards

The width increases linearly with distance, because a minute is an angle.  One minute of angle at 100 yards, is still one minute of angle at 1000 yards.  The circle's circumference is 2πr.  Increase the radius r by 10 times, and the circumference increases by 10 times.  It's linear.

One minute of angle then is one inch at 100 yards, two inches at 200 yards, three inches at 300 yards, and ten inches at 1000 yards.

OK, one MOA is actually 10.47 inches at 1000 yards, and that difference may or may not be important depending on your shooting application.  But I'm going to keep the numbers as simple as possible for discussion purposes.

If you're interested in hearing more on the topic, Ryan Cleckner discusses minute of angle in his National Shooting Sports Foundation (NSSF) video “Understanding Minute of Angle (MOA)–Long Range Shooting Technique”.  Ryan's the ultimate expert; he was a Sniper Team Leader in the military, and worked for years as a sniper instructor for military and police snipers.

Let's take this into the practical realm of shooting.

Point of Impact on Target

Bullets will print on target in increasingly wide groups, as target distance increases from short range (100 to 300 yards), to mid-range (300 to 600 yards) and long range (out to 1000 yards and beyond).

In a vacuum, the bullet would fly straight to the target affected only by gravity.  However even in the absence of wind, the barrel will impart some deflection to each bullet that exits the muzzle, a.k.a. loss of precision–caused by barrel wear, inconsistencies in loaded ammunition, and other factors beyond the scope of our discussion here.

So in the purest of conditions, and shot from the steadiest rest, any particular barrel will be capable of sending projectiles downrange with a baseline precision, or spread if you will, measured in minutes of angle.  This is where you hear talk of a one MOA rifle (or better).  Then factors such as the shooter's skill, and the wind conditions come into play, to determine the final precision of shots on target.

Real World Precision

In the real world, external forces between the muzzle and target affect bullet trajectory.  The ballistic coefficient of the bullet, and pressures inside the action and barrel that may destabilize the bullet, will also affect group spread.  So at farther and farther distances, the linear nature of the angle is lost, as forces further deflect the bullet as it travels downrange.

That's why a rifle capable of shooting low MOA at short range can't achieve the same precision at longer distances–while in theory a minute of angle increases linearly, the action of the wind will increase bullet spread non-linearly over increased range, and more so if the bullet lacks stability due to poor reloading technique.  Add errors imparted by poor gun handling skills, and the projectile may well be off target at distance.

Let's shift gears and discuss how to use MOA to adjust for windage.

How to Dial for Windage

First, determine your wind call.  That's the average wind speed after factoring wind value (i.e., angles).  A range chart will tell you how many inches the bullet will be deflected for a specified yardage and cartridge.

Yes, that's a bit complicated, but estimating wind speed isn't that difficult, and you can always build your own range chart based on experience (that's using DOPE, or doping the wind using Data On Previous Engagement).

If you've reasonably determined how many inches the wind will push the bullet, you can translate that into minutes of angle, i.e., one minute is one inch at 100 yards, two inches at 200 yards, and so on.

If you want to dial windage onto your scope, this is easily enough done as long as you:

  1. Dial in the correct direction, and
  2. Dial the turret the correct number of clicks depending on whether the scope is calibrated for 1/8, 1/4, 1/2 or one minute increments.

Tip:  You won't go wrong on direction if you look through the scope while dialing, since you can see the direction the reticle is moving.

Dial the Reticle to the Bullet's Point of Impact

As an end result of adjusting your optics, you want to aim the rifle muzzle into the wind, like spitting into the wind.  To do this, dial the reticle in the direction the wind would take the bullet.  It's counter-intuitive, but if you dial the reticle to the left, the projectile's point of impact will move to the right.

You learned this when bore sighting a rifle–if you can get a shot on paper, then you simply dial the reticle to the bullet's point of impact.  What an expert shooter does, is dial the turret the correct windage before taking the first shot.

Therefore dial the reticle in the direction the wind would take the bullet.  In a left wind (from 9 o'clock), picture the bullet landing on the right side of the target.  Hold the scope at the center of the target, and dial the windage turret the estimated number of minutes while watching the reticle move to the right, to where the bullet would have landed, had you pulled the trigger without adjusting your scope.

You've now (in theory, at least) added the correct amount of windage to the scope, so the bullet should hit the X-ring in that wind condition.  Remember how many clicks are on your windage turret, so you can quickly come back to zero should the wind die down, or switch direction.

Holding Off (Instead of Dialing) for Windage

What if you have a good wind zero on your scope, and would rather hold for additional changes in wind speed and direction, instead of continuously dialing the windage turret?  If you have a standard printed target, you'll have the MOA graduations needed to hold for windage.

300-yard benchrest target showing a 0.3 Minute of Angle group
300-yard target sporting a 1-inch 5-shot group (gusting conditions, Krokodilspruit, South Africa)

For example, an international benchrest target measures one minute across the nine-ring, or a half-minute across the ten-ring.  From the center dot to the nine ring is a half minute.  Between rings is a quarter minute.

The lines on the rings have a standard width, as does the distance between rings–get out a digital caliper (or a low-tech ruler) and explore the target.  Then, when you need to hold for MOA, you can use the lines on the target for measurement.

Hold Using Hash Marks on the Reticle

Similarly, of you have a reticle with MOA graduations, like the Leupold reticle featured at the beginning of the post, you can hold for windage using the hash marks in your scope.  This is the preferred method for hunters or tactical shooters in the real world, where paper targets with graduations don't exist in the field.

Estimate the wind call, and convert it into MOA.  Then hold that distance using the reticle graduations, aiming into the wind.  It's faster than dialing your scope.  And you can achieve the same accuracy.  I would argue better accuracy, since you can get your shot downrange before the wind changes.

You may be frustrated at this point that I haven't discussed how to call the wind!  In another post we'll do a deep dive into wind reading skills.  And next, we'll demystify the Milliradian (Milrad, or Mil for short).

Until then, let's stay on target!

cheers,

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