At the moment the bullet leaves the muzzle of a barrel, its trajectory (or path) is somewhat straight, but as it continues to fly, itspath becomes an arc.

While a bullet accelerates within a barrel owing to rifling, the moment it leaves the muzzle, it loses energy and slows down as the distance grows, partly because of gravity, air resistance and wind drifts.

In other words, at some distance, which is usually 100 yards, the bullet begins to drop below the straight path. And the drop grows larger as the distance increases. The extent of drop depends on the behavior of your gun and cartridge.

In some, the bullet drop is larger at the same distance. Larger rounds seem to have bigger drops than smaller counterparts. For example, consider the extent of drop of .308 Winchester round compared to a smaller round like .2.

Anything greater than 300 yards is considered long-range, although it starts at between 500 yards and 1000 yards, depending on the experience and sight of the shooter.

The effects of bullet drop and wind drifts become more apparent with distance. That’s partly why the margin of error is bigger at greater distances. For a long-range shooter, it’s crucial to make hold-overs and hold-offs.

To compensate for bullet drop, you must tilt the barrel upwards when you fire rounds. Technically, this is holding over (the barrel). But there are crosswinds, which can sway your bullet from side to side.

These crosswinds have different values, which range between 0 and over 10 miles per hour (we are going to consider how to gauge wind speed and direction later in this article). You must account for wind drifts if you want to shoot on a windy day.

To compensate for wind drifts, you must know the direction and strength of wind. Then, you can hold off, or make necessary hold-offs (shooting against the wind direction).

Fortunately, you no longer have to make these adjustments manually. With the aid of a good scope, you can make necessary adjustments, but only if you understand what hash marks (or sub-tensions) on your reticle and dials on your turret mean.

There are different types of reticles, but the most popular ones include minute of angle (MOA) and milli-radians (milrad).

However, the focus of this article is MOA: what it is and how to range your targets on MOA scope. Let’s learn more.

**What’s Minute of Angle (MOA)**

To understand the minute of angle, let’s consider an hour.

One hour has 60 minutes. Hence, a minute of an hour is one-sixtieth (1/60) of an hour. Then, what about a minute of what angle?

*A minute of a degree.*

But there are 60 minutes in a degree. Therefore, a minute of a degree is one-sixtieth of a degree (1/60°). And just as in time, one minute has 60 seconds; hence, there a second of an angle is 1/3600°.

You’ll cover 360 degrees going round a circle. Therefore, if you go round a full circle you’ll cover 21,600 minutes (1,296,000 seconds).

**How to Understand Minute of Angle?**

Consider an arc of a circle, which subtends an angle of 1/60° at the center. This angle is too narrow to measure using a protractor, though, but we can imagine.

The arc is a curved distance between two points on the circumference. When you draw a line from either point to the center of the circle, the length of the line gives you the radius. Both lines converge at the center but diverge at the circumference to form an arc.

The straight distance between the two points is the chord – it’s what we’re interested in when determining the size of targets and range. The chord and the arc subtend the same angle at the center: 1/60°.

So, how does this concept apply to hunting?

You want to determine the distance between you and the target: the range, right?

Imagine your vantage point is the centerof the circle. When you drop a perpendicular from the center, it’ll divide the chord into two equal parts. The perpendicular is the range (the distance between you and the target).

Interestingly, the perpendicular also divides the angle subtended at the center by the chord, which, in this case, is 1/60°. Thus, the angle between the radius and the perpendicular (range) is 1/120 °.

Now, imagine that you’re firing shots from your vantage point. Your position is the tip of a cone whose size ever increases with distance.

At a particular target distance, the diameter of the circular part of the cone is equal to the chord of the circle that subtends1 MOA at your position. This principle is applicable in making corrections for windage and elevation in scopes (we’ll see that later on).

Now, let’s go back to basic trigonometry (you’ll need it for long-range shooting).

We’re interested in the length of the chord, but we can only find half its length using trigonometry. To do that, we need to find the tangent of 1/120 °.

The side opposite to the angle is half of the chord. The adjacent side to the angle is the range.

Let’s take the range to be 100 yards.

We want to find the length of the opposite side to the angle (x).

But, 1 yard=36 inches

Therefore, x=0.01454 ×36=0.5236 inches (rounded off to 4 sf)

Hence, the length of the chord = 2x = 1.0471 inches (rounded off to 4 decimal places)

So, why is 1.047” significant?

It’s because it’s a length (chord) that subtends 1 MOA at the center (which is your vantage point, by the way).

Thus, famously, 1 MOA is equivalent to 1.047” at 100 yards.

And the beauty of this angular measurement is that it’s independent of the range.

As in, an angle doesn’t change with range, but the chord grows longer in proportion to the distance.

At 200 yards, 1 MOA is 2.094”. At 300 yards, it’s 3.141”, and so forth.

MOA | Range (yards) | Divergence (inches) |
---|---|---|

1 | 100 | 1.047” |

1 | 200 | 2.094” |

1 | 300 | 3.141” |

1 | 400 | 4.188” |

1 | 500 | 5.235” |

1 | 600 | 6.282” |

1 | 700 | 7.329” |

1 | 800 | 8.376” |

1 | 900 | 9.423” |

1 | 1000 | 10.47” |

Notice that that divergence increases with range.

Most shooters prefer to round off the divergence. For example, 1 MOA at 300 yards is 3”. However, at longer ranges, the margin of error increases significantly.

Hence, for distances longer than 500 yards, it’s important to not round off. At 1000 yards, an error of .47 is huge and can affect your accuracy by a big margin.

Now that you’ve understood what MOA is, let’s see why it’s used in scopes and what they mean for your turret adjustment.

Most scopes come as ¼ MOA. That means “at 100 yards, ¼ MOA is equal to ¼ inches”. But you’ll find some scopes calibrated as 1 MOA, 3 MOA and 6 MOA.

**What MOA Means for Long-range Shooting**

As said, the bullet’s downrange flight doesn’t follow a straight trajectory – the bullet travels in a curve or an arc.Wind swings bullet sideways as it drops under the influence of gravity while at the same time overcoming air resistance.

And so, when you fire a shot, the bullet will fly out of a muzzle following a straight curve initially, but when it hits a 100-yard mark, it begins to drop consistently until it hits the ground. Then there is wind drifts to account for.

The extent of drop and drift is of interest to a long-range shooter, because it affects your precision.

It’s important to note that you zero your rifle before going outdoors to hunt or shoot targets.

When zeroing, you:

- Perform bore sighting
- Set up known targets e.g. bullseye, at a chosen distance, say, 25 yards
- Fire a three-shot groupingat a bullseyeas accurately as possible
- Note the spacing between the point of impacts of the three shots
- Measure the average deviation (in inches) from target – it could be above, below, left or right of the bullseye
- Make corrections for windage and elevation based on the correction
- Fire a three-shot grouping again
- Repeat the procedure if there’s deviation

It’s also during zeroing that you’ll understand the behavior of your cartridge and gun. That is, you’ll understand what deviation from target your round would make at a certain longer-range distance than 100 yards.

Let’s say you fire a shot during zeroing, and the bullet hits 2” below and 6” left of the target or bullseye at 300 yards. What does this mean?

You need to move the point of impact of the bullet 2” above and 6” right to be dead-on at 300 yards.

1 MOA at 100 yards is 1”. Thus, 1 MOA at 300 yards is 300 yards.

If you’ve got a scope with a ¼MOA calibration, then ¼ MOA at 100 yards is ¼”.

¼ MOA at 300 yards would be ¾”.

*How many ¾” pieces fit in 2”?*

So, when you round off, you get approximately 3 pieces.

Thus, to move the point of impact 2” above, you need to rotate the turret to hear 3 clicks (or ticks) to make that correction.

*How many ¾” pieces fit 6”?*

You need 8 chunks. That means you need to rotate the turret to hear 8 clicks to make that correction.

**Corrections for Wind Outdoors After Zeroing**

After zeroing, you go outdoors to shoot targets or hunt. You mustn’t postpone hunting or target shooting on a windy day. It’s important to learn how to make windage corrections if you want be a consistent hunter.

Crosswinds have different values. Winds that run in a perpendicular direction to the bullet trajectory can have a significant impact in moving it away from the target in that direction.

Half-value winds move at a particular direction to the bullet path, and their impact on direction may not be significant.

But how do you gauge the strength and speed of a crosswind?

A reliable way is to find a mirage using your scope. And the good thing is that a mirage would be present as long as heat is present.

A mirage with a vertical heat wave indicates a weak crosswind. Experts say that wind speed could be between 0 and 3 miles per hour.

As the heat wave of the mirage becomes more diagonal, so is the wind strength.

Speed can range between 5 and 7 mph. A completely horizontal heat wave indicates a strong crosswind whose speed is beyond 10 mph.

The constant depends on range, and reduces with range. Over 500 yards, a constant of 10. Let’s take a look constants used for each yards.

Range (yards) | Constant |
---|---|

100 | 14 |

200 | 13 |

300 | 12 |

400 | 11 |

500 and beyond | 10 |

If you know wind speed and range, you can determine MOA.

For example, if you estimate that a crosswind has a speed of 6 mph and your target is 400 yards away, how far will your bullet deviate from the target?

You need to hear 9 clicks to make the correction.

**How to Estimate Distance to Target Using Your MOA Scope**

Reticles on MOA scopes have hash marks or sub-tensions. You can use these calibrations to estimate the distance between you and your target. The marks are scales you find on your ruler, caliper or screw gauge, but, instead of being in cm or mm, they are in MOAs.

Most hunting scopes lack hash marks. However, for a hunter who wants to take down game at long-range, precision is important.

You must have previous knowledge of the average size or height of your target. For example, if you intend to shoot deer at a distance of 600 yards, you must know that deer stand 18” high on average. The width is usually half of the height. Hence, in this case, it’s 9”.

Ensure the origin (center) of the reticle is in contact with your target. Then, you can begin counting the hash marks.

For example, if you determined that deer’s height is 2.6 MOA on your scope’s reticle, the width must be 1.3 MOA.

Use the W.E.R.M formula,

So, the deer is about 661 yards away from your position.

**Use Cosines to Resolve Uphill or Downhill Distances**

Sometimes, the target is uphill or downhill from your position. In most cases, your line of sight; hence, scope won’t always straight toward the target. Your barrel doesn’t have to be in line with your scope (making turret adjustments tilts the barrel).

- Determine as usual distance to your target
- Determine the angle between the horizontal distance to the target and the hypotenuse
- Resolve that distance by multiplying it with cosine of the angle

**Performance of MOA at Long-range Shooting**

At a longer-range than 500 yards, rounding off values of bullet deviation can make you miss a target by a mile, because the margin of error increases. Most shooters hate the math and decimals. However, if you want to take down targets at long-range, you’ll need to do math – lots of it.

In a fast-paced environment that requires quick reaction, MOA calculations can be a big letdown, considering time you’ll take. It can be challenging to do the calculations for yardages, which don’t carry zero.

Unfortunately, many hunters aren’t good in math. Unit conversion can be a big problem if your scope uses MOA and your turret is in milli-radians. Always ensure your scope and turret are all in MOA or otherwise, if you’ve got a spotter, ensure she uses the same units.

For a tactical (precision) shooter, like a sniper or spotter, who doesn’t need to switch positions (because he’s hidden), MOA is king.

## Use a MOA calculator

Once you understand the math behind the calculations needed for MOA shooting, it's best to use a MOA calculator, to avoid spending time calculating instead of focusing on the game.

## More information

Check out this NSSF video with more information about MOA math:

**Conclusion**

MOA reticles are suitable for tactical or precision shooting. It means you’re not shifting positions. There’s lots of math involved, and that’s a problem in and on itself. You’ll be in problems if a target spots you from a distance, and especially if that target is dangerous and wants to take you down, too (as in case of snipers). If that target is close enough, it’ll take you down before you’ve even completed your calculations, unless you’re a very quick mathematical thinker.

It’s advisable that before you go outdoors at great distances, you’ve a record of the bullet drops at various distances, so you don’t have to calculate them again. All you need to worry about is making corrections for crosswinds. Bottom line: MOA favors long-range shooters or hunters who’re hidden and who’ve time to make corrections to take down targets precisely.

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