Ryan Cleckner [above] was a special operations sniper team leader in the US Army’s 1st Ranger Bn (75th) and a sniper instructor with multiple combat deployments. Click here to order his book Long Range Shooting Handbook- A Beginner’s Guide to Precision Rifle Shooting from Amazon. Here’s chapter 9 on measurements . . .
There are many measurements that we must take into consideration when shooting long range: distance to the target, size of the target, elevation compensation, windage compensation, barometric pressure, temperature, and others. You need to get familiar with all of them.
9.1 Linear Measurements
Linear measurements are generally used to describe the distance to a target. However, they are also sometimes used to describe a target’s size for range estimation purposes.
9.1.1 Yards (yds)
A yard is an English/Standard unit of measurement. It equals exactly 3 feet (36 inches).
9.1.2 Meters (m)
A meter is a metric unit of measurement. It’s the basic linear unit in the metric system. From this unit of measurement, we add prefixes to describe different lengths. For example, since the metric prefix for 1000 is “Kilo,” 1000 meters is 1 kilometer (also knows as a “click”). Likewise, “Centi” is the metric prefix for 1/100th. One hundred centimeters make up 1 meter.
9.1.3 Converting Between Yards and Meters
There is about a 10 percent difference in size between yards and meters. To be accurate, 1 meter
equals 1.09 yards and 1 yard equals 0.91 meters. That’s closer to a nine percent difference. For simplicity’s sake, I prefer to just use 10 percent in my calculations, since I can easily calculate 10 percent of a number by moving the decimal place one position to the left. For example,to find 10 percent of 450, move the decimal point one spot to the left for an answer of 45.0. The ability to calculate percentage in your head is better than relying on a calculator in the field.
If I want to convert meters to yards, I add 10 percent. If I want to convert yards to meters, I subtract 10 percent. For example, to convert 500 yards to meters, I move the decimal place one position to the left and end up with 50 as my 10 percent figure. I then subtract that 10 percent figure from the original 500 and end up with 450. Five hundred yards is approximately 450 meters (note: actual conversion is 455 meters). (See Figure 9.1-1).
Notice how the number for the meters is smaller than the number for yards. This will always be the case. It’s a good way to confirm your math, when you’re cold, tired and hungry.
(answers at end of chapter)
- Which unit of measurement is longer, a yard or a meter?
- When converting from yards to meters, will the number for meters be larger or smaller than the number for yards?
- 900 yards equals approximately how many meters?
- 420 meters equals approximately how many yards?
9.1.4 Linear Conversion Charts
The following charts (Figures 9.1-2 and 9.1-3) are used for converting linear measurements.
9.2 Angular Measurements
Angular measurements are used to describe linear size relative to distance. The most common uses: incremental adjustments to the bullet impact, estimating the distance of a known-size target, “holding” for windage or elevation, and measuring accuracy by shot-group size.
The most important thing to understand about these measurements is that they are angular!
For example, when we adjust our scopes, we move the reticle inside the scope which then forces us to move the barrel of the rifle up, down, left, or right in order to get the reticle back on to the target.
This difference between where the rifle’s barrel was pointed prior to an adjustment in windage or elevation and where the barrel is pointed after the adjustment is a change in angle. This same angular adjustment creates smaller changes to the bullet’s impact point at closer distances and larger changes at greater distances.
To help you understand how an angular measurement translates into a different sizes at different distances, imagine holding two laser pointers next to each other and pointing them down range.
If you spread the two laser pointers apart at a certain angle, the lasers would gradually get further and further apart from each other as they went down range. For a certain angle, however, the rate at which the dots spread apart is consistent. The dots will be twice as far apart at 200 yds – and ten times as far apart at 1000 yds – as they were at 100 yds. See Figure 9.2-1.
9.2.1 Minute of Angle (MOA)
In the term Minute of Angle, the word “minute” means 1/60th (for example, there are 60 minutes in 1 hour so 1 minute of time is 1/60th of 1 hour) and the word “angle” refers to one of the 360 degrees in a circle. So, 1 Minute of Angle is 1/60th of a degree. See Figure 9.2-2.
If we spread two laser pointers apart 1 MOA (1/60th of a degree), the dots would be about one inch apart at 100 yards, about 2 inches apart at 200 yards, about 3 inches apart at the 300 yards and so on. Simply stated, this means that 1 Minute of Angle is about 1 inch per adjustment.
This is a point of contention among shooters. Many will argue that it is crucial to use 1.047 inches per 100 yards. I agree that it’s more accurate, I just don’t notice enough of an impact to use the more accurate number.
Let me qualify that. At 1000 yards, when I use 1 inch per 100 yards, 1 MOA equals 10 inches. When 1.047 inches per 100 yards is used, 1 MOA equals 10.47 inches. The difference is less than one half of an inch and barely wider than the width of my bullet.
To be fair, there’s a counter argument to my point. Half an inch difference is per MOA. When you’re adjusting up about 42 MOA to shoot a .308 caliber rifle at 1000 yards, that half of an inch is realized 42 times over. The extra 0.47 inches per MOA at 1000 yards times 42 MOA equals a 19.74 inch difference.
Although this seems like a significant number, it is hard to imagine a chance for this number to affect you.
I believe strongly in gathering your own data for your own rifle. Go out to a range, shoot at 1000 yards and record how many MOA you needed to come up with your rifle and your scope to hit at 1000 yards. Regardless of how you calculate a MOA per 100 yards (1” or 1.047”), if you need to come up 42 MOA on your scope to hit at 1000 yards, then you come up 42 MOA.
If you use someone else’s data (such as a store-bought “ballistic card” or ballistic software), you’re likely to get an estimated elevation adjustment of somewhere between 40 and 44 MOA.
Again, regardless of how you calculate a MOA per 100 yards (1” or 1.047”), you’re going to simply dial the estimated MOA adjustment into your scope and shoot. Only then, when you are a few inches high or low are you going to need to calculate how many MOA to come up or down.
If you tried 40 MOA for your first time shooting at 1000 yards and ended up being 15 inches low, you will need to come up about 1.5 MOA. By using 1 MOA per 100 yards, I can quickly see that 10 (the rough number of inches 1 MOA equals at that distance) goes into 15 (the number of inches I need to correct) 1.5 times and therefore I need to come up 1.5 MOA.
However, by using the more accurate 1.047 inches per 100 yards, I would need to find out how many times 10.47 (the precise number of inches 1 MOA equals at that distance) goes into the needed 15 inch adjustment. Since 15 divided by 10.47 equals 1.43 (hardly a calculation I can do in my head), I would need to come up 1.43 MOA.
Because most scopes don’t adjust more precisely than 0.25 MOA per click, I’d be forced to choose between 1.25 MOA or 1.5 MOA. I would end up choosing the closer 1.5 MOA adjustment which is precisely what the rough 1 MOA per 100 yards got me.
I understand that I hand-picked this example to prove my point. But the only time I could see the difference affecting your shooting is if you were trying to calculate how to adjust up 420 inches in order to hit a 1000 yard target instead of just adjusting in MOA.
Only if you read some data from a pre-filled ballistic card or from some ballistic software that told you to adjust up 420 inches (instead of the much more likely 42 MOA which directly dials into your scope) would you notice a 19” difference at 1000 yds. Bottom line – use 1 inch per MOA. It’s way easier and in the field it gets you hits just as precisely.
(answers at end of chapter)
- A MOA is how many degrees?
- Approximately how many inches on the target is 1 MOA at 300 yards?
- Approximately how many MOA are in 18 inches on a target at 600 yards?
9.2.2 Milliradian (Mil)
Just as the meter is the metric equivalent of the yard for distance, the Milliradian is the metric equivalent of the MOA for angular measurement.
In the term Milliradian, the prefix “Milli-” means 1/1000th and the root “radian” is the metric unit of angular measurement. So, 1 Milliradian is 1/1000th of a radian.
A radian is an angle based on a circle’s radius, or half of its diameter. When the length of a section of a circle equals the radius of that circle, the resulting angle is a radian.
In simpler terms, if you placed a string, which is the same length as the radius (“A” in Figure 9.2-3), around the outer edge of the circle (“B”), the angle formed from the center of the circle to each end of the string would be one radian (“C”). Now, if you divided that angle into 1000 equal smaller angles, one of those smaller angles would be one Milliradian.
This is where the simplicity of using Milliradians comes in.
If you imagine yourself standing at the center of the circle in Figure 9.2-3 and you spread two laser pointers 1 Milliradian apart and shine them along the radius to the edge of the circle (“A” distance), then the dots will spread exactly 1/1000th of the length of the radius (“A” distance) apart.
I’ve heard many people argue over whether 1 Milliradian equals 1 meter at 1000 meters or whether it equals 1 yard at 1000 yards. They’re both right! 1 Milliradian equals 1/1000th of any distance. It is 1 inch at 1000 inches and 1 mile at 1000 miles.
Bottom line: it doesn’t matter what unit of measurement you use as long as you keep using that unit of measurement.
1 Mil is exactly 10 centimeters (cm) at 100 meters (m), 20 cm at 200 m, 30 cm at 300 m, and so on. Because we’re dealing with the metric system, we can simply move the decimal place from 100.0 meters to the left three places to find 1/1000th. The result is 0.1 meters (0.1000) or 1/10th of a meter. Because there are 100 cm in a meter, 1/10th equals 10 cm.
Most Mil scopes adjust in 0.1 (1/10th) Mil increments. 1/10th of 10 cm is 1 cm. Therefore, a single 0.1 Mil adjustment on a Mil scope will move the bullet impact 1 cm per 100 meters.
(answers at end of chapter)
- How big is a Mil at any given distance?
- How many centimeters on the target is 1 Mil at 300 meters?
- How many Mils are in 30 cm on a target at 600 meters?
9.2.3 Using MOA and Mils
When learning how to use MOA or Mils, always think in whole increments for a particular distance. Start with the target’s distance and ask yourself how big 1 MOA or 0.1 Mil is at that distance. Then, determine how many of those “chunks” you need to adjust. For example . . .
Using MOA, if your target is 600 yards away, you should first calculate that 1 MOA is about six inches and then ask yourself how many six inch “chunks” you need to adjust your bullet’s impact. If you need to move three inches at 600 yards, that’s ½ of a 6-inch “chunk.” So you need to move ½ MOA. Likewise, if you need to move 12 inches at 600 yards, that is two six-inch “chunks” so you need to move two MOA.
With Mils, if your target is 500 meters away, you should first calculate that 0.1 Mil is five centimeters (or 1 Mil is 0.5 meters) and then ask yourself how many five cm “chunks” you need to adjust the bullet’s impact.
9.2.4 Converting Between MOA and Mils
Approximately 3.5 MOA equal one Mil. To be accurate, there are two different precise conversions because there is a difference between a true Milliradian and a NATO Milliradian. The number of true Milliradians in a circle is not an even number (its actually 6,283.18…) and it is not easily divided into equal parts.
Because of this, many militaries have rounded the number up to 6,400. Therefore, there are 6,283 true Milliradians and 6,400 NATO Milliradians in a circle. One true Mil equals 3.438 MOA and one NATO Mil equals 3.375 MOA.
For practical purposes, when converting from Mils to MOA, multiply the Mils by 3.5. To convert from MOA to Mils, divide the MOA by 3.5. As with my use of one inch per 100 yds for MOA, I don’t think it’s necessary to use the precise conversion from MOA to Mils.
First off, when I’m converting between the two, precision is generally not required. For example, when I was first learning to read wind, I would calculate the wind hold in MOA and then convert to Mils so that I could use the reticle in my scope. Generally, a wind call is not precise enough to have the difference between 3.375 or 3.5 matter. Also, using the precise figure for MOA and Mil doesn’t make much of a difference.
For an example, with my rounding of one inch per 100 yds for MOA and 3.5 MOA to 1 Mil, I calculate that one Mil equals about 3.5 inches at 100 yds. If I use the precise numbers of 1.047 inches per 100 yds for MOA and 3.375 MOA to one Mil, I calculate that one Mil equals precisely 3.53 inches at 100 yds. By rounding, I was able to calculate approximately 3.5 inches in my head quickly instead of a precise 3.53 inches slowly. The difference at 100 yds is only 0.03 inches. Even at 1000 yds, the difference is only 0.3 inches.
(answers at end of chapter)
- Approximately how many MOA are in 1 Mil?
- How many Mils are in 7 MOA?
9.2.5 MOA vs. Mil
The decision to have a scope which adjusts in MOA or Mil is a personal choice. My simplest advice: use whatever’s comfortable for you. If you normally think in inches and yards and have experience with MOA then stick with MOA. If you’re comfortable with the metric system — or starting fresh and don’t already have MOA experience — you might want to go with Mils.
Mils are not more precise than MOA. Because most Mil scopes adjust in increments of 0.1 Mil, you can actually adjust in smaller increments when using a 1/4 MOA scope. No matter which number you use for mils (rounded, NATO, or true), 0.25 MOA equals 0.07 Mil. This is not a meaningful difference.
I have some rifles with scopes that adjust in 1 MOA per click because I often want faster, instead of finer, adjustments. I want to be able to adjust out to 1000 yards without using more than one complete revolution of my turret.
Regardless of which unit of measurement you choose, I recommend using a scope which uses the same unit for its turrets and reticle. Newer scopes are available in Mil/Mil and MOA/MOA combinations which are much easier to use than a scope which has turret adjustments in MOA and a reticle with marks in Mil.
Something else to consider: what unit your peers will be using. Regardless of my personal preference, I’d rather use whatever my shooting buddies use so that we can speak the same language at the range.
9.3 Other Measurements
9.3.1 Mass / Weight
The terms mass and weight are often used interchangeably even though they’re different things. Simply, mass is an inherent property of an object and the weight is the result of gravity’s effect on that mass.
In long range shooting we’re concerned about the weight of our bullets and, if you reload your own ammunition, the weight of your powder charge. Both of these are measured in “grains.”
A “grain” is an old-fashioned unit of measurement. A “grain” equals 64.79891 milligrams (mass) or 1/7000th of a pound (weight). Seven thousand grains equals a pound.
You will encounter three classifications of speed measurements: speed, velocity, and acceleration. Although each of these refer to how fast an object is moving, they are each unique measurements.
In long range shooting, we’re concerned about the speed of our bullets. The faster our bullet gets to the target, the less wind and gravity can change its original path. Also, if we keep the bullet traveling faster than the speed of sound (about 1,100 fps), we won’t have to deal with the effects of the transonic zone (discussed in Chapter 10 – Ballistics).
The speed of an object is the amount of distance the object will cover in a given amount of time. In America, we measure the speed of our bullet in feet per second (fps). This measurement tells us how many feet our bullet will travel in one second.
Velocity is speed with direction. Velocity is a “vector”: a scientific/mathematical term for a value with both magnitude (speed) and direction (towards the target). Although it could be argued that we’re concerned with the velocity of our bullets and not just the speed, it’s usually important to know only the speed of the bullet regardless of which direction you are shooting.
On the other hand, the velocity of the wind, and possibly of our target, does matter. This is because wind of a certain speed has drastically different effects based on the direction it’s blowing. Likewise, a target’s speed is only half the story. You need to know in which direction it’s moving, too.
Velocity is described with the object’s speed and direction.
Although we typically use miles per hour (mph) to describe the speed of both the wind and targets it’s up to the shooter to determine how they describe direction. Personally, I like to use clock positions to describe direction. For example, “the wind is blowing 10 mph from 3 o’clock (the right).” I like clock directions because it is easy to remember that 12 o’clock is always the direction you’re facing.
Some people like to use degrees to determine direction. Although this may be more precise, it can quickly confuse people. For example, if you’re facing due East and someone tells you that “the target is moving three mph towards 90 degrees,” are they trying to say the target is moving to your right (90 degrees from where you are facing) or straight away from you (because you are facing 90 degrees ‘East’ on a compass)?
Gravity is an acceleration. Acceleration is the measurement of the rate of change of a velocity (speeding up or slowing down).
Objects falling due to gravity fall faster and faster the longer they fall, until they reach their “terminal velocity.” The terminal velocity of an object is the downward speed at which the force of gravity on that object is equal to the wind resistance of the object.
Gravity causes object to fall at an acceleration of 9.8 meters per second per second (9.8 m/s2). After the first second of free fall, an object fallsat a velocity of 9.8 m/s. It will continue at that 9.8 m/s velocity and accelerate an additional 9.8 m/s for every additional second it falls.
It’s helpful to understand that your bullet falls faster and faster the longer it takes to get to the target. It’s one of the reasons you need to add elevation the further away you shoot.
In shooting, we’re usually concerned with the energy of our bullet. The energy of the bullet matters both for when the bullet strikes the target and also when you fire the rifle. Too much energy and you’re not going to enjoy shooting that rifle.
Energy in shooting in the U.S. is usually measured in foot pounds (ft-lbs). A foot pound is the energy transferred by applying one pound of force over a one foot surface. Elsewhere, energy is measured in Joules.
9.3.4 Bullet Efficiency
The efficiency of a bullet to travel through the air is measured by the bullet’s Ballistic Coefficient (BC). At its simplest level, you calculate the BC of a bullet by a mathematical model based off of a bullet’s density (a ratio of a bullet’s mass and its cross-sectional area) and its shape. The higher the BC, the less drag on the bullet. The less drag on a bullet, the faster it gets to the target and the less it is affected by wind and gravity.
BC is a relative measurement. It can change depending on the bullet’s speed and atmospheric conditions. Do not make the mistake of laying all of your bullet selection judgment at the “BC altar.” A bullet’s BC is just one variable. Equally, I don’t trust all published BCs. (Some manufacturers have been know to get creative with their marketing materials.)
There are two main drag models for BCs of bullets – G1 and G7. G1 is the older/standard drag model. G7 is gaining popularity as a drag model for bullet BCs. Each of these models compare the bullet being measured to a standard bullet shape.
G1 Drag Model
The standard shape for the G1 drag model bullet is based on a stereotypical bullet shape with a flat base. Critics say
the G1 doesn’t accurately represent modern long range bullets and it’s too speed sensitive.
A good BC based on a G1 drag model is in the 0.5-0.6 range.
G7 Drag Model
The standard shape for the G7 drag model bullet is a more modern and aerodynamic profiled round with a boat-tail base. Because this more closely matches modern long range bullets, the number for the G7 BC will not be as high as the number for a G1 BC for the same bullet. The efficient bullet is closer in shape to the G7 model than it is to the G1 model.
A good BC based on a G7 drag model is in the 0.2-0.3 range.
Section Quiz Answers
- 810 meters (estimated) / 819 meters (calculated). 10% of 900 is 90. 90 subtracted from 900 is 810.
- 462 yards (estimated) / 457.8 yards (calculated). 10% of 420 is 42. 42 added to 420 is 462.
- 1/60th of a degree.
- 3 inches. 1 MOA at 100 yds is about 1 inch. 1 inch times 3 is 3 inches.
- 3 MOA. 1 MOA at 600 yards is about 6 inches. 18 inches divided by 6 inches is 3.
- 1/1000th of the distance.
- 30 centimeters. 1 Mil at 100 meters is 10 cm. 10 cm times 3 is 30 cm. Or another way to solve this answer:
- 1/1000th of 300 meters is 0.3 meters. 0.3 meters is 30 cm.
- 0.5 Mils. 1 Mil at 600 meters is 60 cm. 30 cm divided by 60 cm is 0.5.
- 3.5 MOA.
- 2 Mils. 3.5 MOA equals 1 Mil. 7 MOA divided by 3.5 MOA per Mil is 2.