# MOA vs MilDot.......

#### Murphy

##### Moderator
What is one MOA and why do we use it to measure a group?

A Minute of Angle.......What does that mean and why do we use it as a unit of measure?

What is a MilDot? Is that a unit of measure?

The MOA, minute of angle is often used to describe the accuracy potential of certain rifles. Some makers even offer guarantees their rifle will shoot to one MOA or even 1/2 MOA. One might ask; How good is that?

Lets look at a rifle shooter taking aim with his new rifle. He places a target up at 100 yards distant and seats himself at the bench, sand bags his rifle and prepares to make the shot. Lets move above the shooter in a low hover. Looking down upon the shooter, we draw a line from the muzzle of his rifle to the 100 yard distant target. This line is 100 yards, 300 feet, 3600 inches in length. Now lets draw a circle around our shooter starting at the target and making a complete, perfect circle, around behind our shooter and back to the target. This circle will be 200 yards in diameter but how far around?

Now lets move on to some simple math:

The circle:
Always measures 360 degrees.
There are 60 Minutes of Angle in one degree.
There are 60 * 360 or 21,600 minutes of angle in one complete circle.
This is true regardless the size of the circle so we can call this number a constant.

The circle is further measured in diameter, linear measure expressed in inches, feet, centimeters or furlongs. One half its diameter is the Radius. Our shooters circle has a radius of 3600 inches.
The Radius can be expressed in linear measure or angular measure,
Angular measure is defining the radius of a circle in degrees.
The radius of any circle, though a straight line, will equal 57.296 degrees when wrapped around the circle.

It is from this relationship we derive the quantity of pi.
One pi radius, now called a radian when we wrap it around the circle, will equal 180 degrees.

pi = 3.14159 One radian = 57.296 degrees.

When we multiply these together we get a number pretty close to 180. This 180 degrees is half the circle.
We can further measure any circle or partial circle in radians, or more correctly pi radians. One complete circle is 2 pi radians or 360 degrees.

2* 3.14159 * 57.296 = 360

We are now almost ready to make the shot, or several shots actually and measure the spread of those shots in MOA.

Remember our circle always has 21,600 minutes of angle but this circle of 100 yards radius has a certain linear measure we have yet to calculate.

The radius of this circle must be known to calculate the linear length of the circle.
Our shooters circle has a radius of 100 yards or 3600 inches.

100 yards = 300' = 3600" (inches).

This 3600 " equals 57.296 degrees.

If we multiply 3600 times 2 pi, we get;

3600" * 6.28318 (2pi) = 22,619.448"
This is the distance around our shooters circle in inches.

Now that our shooter has had time to shoot several shots to test his new rifle, lets look at the group and determine the group size in MOA.

Two sets of numbers are needed for this;

The angular distance around the circle. 21,600 MOA

And the linear distance around the circle. 22,619.448"

We divide the distance by the constant (21,600) we get;

22,619.448"/21,600 = 1.047"
1.047" = one MOA.

So, a rifle guaranteed to shoot 1/2 MOA should group three or five shots within, plus or minus, .524". This means the rifle will keeps it's shots within .524" of the point of aim (POA).

They could be .524" left or .524" right, high or low of POA and still meet the accuracy guarantee.

We could also just measure a group fired from a known distance and convert that to MOA. Generally when measuring a group we measure from center to center of the widest shots, in inches or centimeters, and convert to MOA.

If I have a group fired at 200 yards which measures 1.750" we can calculate the MOA size of that group.

200 yards = 7200" (r)
7200" * 2 pi = 45,238.9"
45,238.9/21,600 = 2.094" = one MOA @ 200 yards.

1.75"/2.094" = .8357 MOA

A very good group. Less than one MOA accuracy at 200 yards.

That's MOA as used to describe shooting accuracy.

So where does Mil Dot come from? What does it mean?

Mil is an abbreviated way of saying Milli-Radian (mr).

Remember a radian is 57.296 degrees.

Milli is represents the quantity of 1 * 10 to the -3 (Ten to the third negative power).
Basically .001 or 1 one thousandth. Or a thousandth of a radian.
Or quite simply, 57.296/1000 = .0573 degrees.

To convert this to MOA we simply multiply by 60 (number of minutes in a degree.)
.057296 * 60 = 3.43776 MOA

Or

3.43776 (MOA in 1 mr) * 1.047" (inches in MOA at 100 yards) = 3.599" = 1 mr

Thus one milli radian is equal to approximately 3.6" at 100 yards or 36" at 1000 yards.

Two milliradians at one thousand yards is approximately the height of adult male human.

More on the Mil Dot system of range finding will be found in the Mil Dot section.

From the book The Science of Shooting
By Jim Clopton

#### marshall

##### New member
That's a nice bit of information Murphy. I choose a TMR recital in my 8.5-25x50mm MK-IV atop a recent McMillan TAC338 Lapua build. I'm sure you're familiar with it. My feelings are that it offers less cover up on small targets at long range. I would love to have a class on the proper use of it's ranging capabilities.

My math skills are strong and I'm a fast learner but the classes I've attended are large and they seem to prefer shooting a lot of ammo versus illustrations and use of the reticle. There has been very little discussion about ranging and holder over using the reticle. To clarify, they dial correction based on ranging with a laser and hold off for wind with the MIL system. I feel that this is a waste of the optics ability. I would like to learn consistent ranging with the reticle then shoot some ammo to confirm my math.

Do you have any links or recommend reading that I can benefit from?

#### back country

##### New member
I may be mistaken but I "thought" that part of the mil-dot principle was using it to range your target, a man's torso - IF you know the basic size in inches of your intended target you can teach yourself to calculate the range on pretty much any quarry - Laser RF's are wonderful, wouldn't be without my Geovid BUT what if it quits you ? Knowing how to range with your mil-dot reticle leaves you "foolproof" (as long as the brain doesn't "quit ya") I have "taught" myself to use one shooting prairie dogs and it does work ...

#### Murphy

##### Moderator
Yep!!

Two milliradians at one thousand yards is approximately the height of adult male human.

That's two dots ground to crown....if he's six feet tall.

Yes it is ranging and requires that the target be of known size. The size of the dots and other points help with the ranguesstimation. (that's a new word)

#### evandailey

##### New member
Wow Murphy, that blew out some cobwebbs. I knew all of that, but it has been a while since I saw it all expressed geometrically/trigonometrically. Good write up.

#### marshall

##### New member
Back Country,

It's the quick math that I need to work on for odd size targets at all ranges. It's easy to do the math at 500 and 1000 yards on a 72" man or a 36" gut to spine. However when the target is between 600 - 1400 yards your drop rate is vastly different and a 25 yard error in ranging can make a huge difference in point of impact.

I have a really good ballistic card made up for a variety of altitudes and temperatures but I need to be more proficient with ranging. I found a disc that I can drop in to the computer CD drive and practice ranging with an on screen reticle. I'm looking forward to it's arrival.

#### Vek

##### New member
If you're stronger with triangle trig than with circles and arclengths, then it's pretty easy to put together a right triangle describing your MOA group or target at a given range using the following relationship:

tan (angle) = group size / range

example, for a MOA group at 100 yards:

Tan (1/60 degrees) = x / (100yds * 36"/yd)
x = 3600" * tan(1/60) = 1.047"

If your ballistics program gives inches of drop at range (say, 60" at 500 yds) and you want to convert to MOA drop in order to easily manipulate your MOA-based elevation adjustment turret on your scope, use the formula:

tan (angle) = 60"/(500yds * 36"/yd) = 0.0033
angle = arctan(0.0033) = .1910
MOA = angle * 60 = .1910 * 60 = 11.5 MOA

Easy to program this into a spreadsheet. Or hunt around for a freebie ballistic program that spits out both inches of drop and MOA.

#### Murphy

##### Moderator
If you're stronger with triangle trig than with circles and arclengths, then it's pretty easy to put together a right triangle describing your MOA group or target at a given range using the following relationship:

tan (angle) = group size / range

example, for a MOA group at 100 yards:

Tan (1/60 degrees) = x / (100yds * 36"/yd)
x = 3600" * tan(1/60) = 1.047"

If your ballistics program gives inches of drop at range (say, 60" at 500 yds) and you want to convert to MOA drop in order to easily manipulate your MOA-based elevation adjustment turret on your scope, use the formula:

tan (angle) = 60"/(500yds * 36"/yd) = 0.0033
angle = arctan(0.0033) = .1910
MOA = angle * 60 = .1910 * 60 = 11.5 MOA

Easy to program this into a spreadsheet. Or hunt around for a freebie ballistic program that spits out both inches of drop and MOA.

Very good and actually I do prefer Trig and Triangles. I can remember S=O/H, C=A/H, T=O/A. I don't use ballistic programs,.....I use the noodle to stay in shape. I can calculate BC with a pencil.

But you,re right that's a good way to do it. I think when we master math we have a full tool box.

#### Vek

##### New member
Practical application, fully developed:

1. Work up a load that groups well for you close in (100-200) and chrono it.
2. Enter chrono number and bullet advertised BC into ballistic calculator
3. Use math above, solid body mechanics and fluid mechanics textbook info, or ballistic calculator output to spit out drop sheet out to desired distance (say, 1000 yards). Drops in MOA easiest, but you want to know how those came to be. See math above. Make sure scope centerline height above bore centerline dimension is close. Choose a range at which your load prints dead on - say 200 yards - as the basis for your drop chart.
4. Stretch load out to 600/800/1000 yards. Zero rifle first at 200 yards. Use M1 elevation on Leupold scope in 1/4 MOA scale to dial in elevation corrections. Compare performance with that shown on drop sheet.
5. Adjust drop sheet input (bullet BC) to make computer output drop sheet match field observations
6. Print drop sheet, tape to stock, and off you go.
7. Restart/repeat as desired until dialed in. Don't muck with your load once found...

8. Don't bother with any sort of custom dial from leupold that's built around a bullet and load - the system above is both more general and more precise. And, any scope so equipped with the M1 turret can be swapped to another rifle as whim dictates.

Very good and actually I do prefer Trig and Triangles. I can remember S=O/H, C=A/H, T=O/A. I don't use ballistic programs,.....I use the noodle to stay in shape. I can calculate BC with a pencil.

But you,re right that's a good way to do it. I think when we master math we have a full tool box.

#### back country

##### New member
marshall - elk are pretty "simple" to do but deer, moose, etc. are a bit more complicated but when you "get your mind around the concept" it is not too bad a deal to memorize for huntin' "eatin' critters" - I like having a tool like a mil-dot reticle at my disposal because mechanical AND electronic stuff fails and we ALL know when they fail ( I guess a guy could carry TWO rangefinders! )

#### elmerkeithclone

##### New member
Back in the 70's I got an A+ in Algebra and a B+ in Trig. Right now I feel like the dumb kid that sat next to the fat girl in the back row way back then.

Yup Murphy I got it but I don't care to admit to how many times I had to read it before it sunk in. I even had to tell mother to go watch tv in the bedroom cuz I was studying!

Funny thing is, I bet I'm not alone!

#### marshall

##### New member
Back country,

I don't have any problems at 500 and 1000 with center mass hits on 18"X30" IPSC steels. It's when they are different sizes and odd ball ranges that I need to improve my ranging abilities. The wind is the real voodoo beyond 500 yards.

I have a great 300gr Berger Hybrid load that is consistently grouping under 1.5" at 300 yards. I also spent a lot of time working up a data book in 25 yard increments from 500 - 1800 yards in a variety of atmospheric conditions. Shots under 500 yards are a no brainer with this rifle.

Current and former military guys that I shoot with have had formal training with the Mil Dot system and endless practice over the years. I'm trying to do it in my head and on paper before I go out and waste ammo. Once the range is determined I have 100% confidence in my equipment.

The ranging game that I'm waiting on is "The long range shooting solution". From what I've seen it gives a variety of targets at various ranges and lets the shooter do the ranging with the Mil Dot reticle before the bullet is sent down range, it should be a decent learning tool.

#### Murphy

##### Moderator
Practical application, fully developed:

1. Work up a load that groups well for you close in (100-200) and chrono it.
2. Enter chrono number and bullet advertised BC into ballistic calculator
3. Use math above, solid body mechanics and fluid mechanics textbook info, or ballistic calculator output to spit out drop sheet out to desired distance (say, 1000 yards). Drops in MOA easiest, but you want to know how those came to be. See math above. Make sure scope centerline height above bore centerline dimension is close. Choose a range at which your load prints dead on - say 200 yards - as the basis for your drop chart.
4. Stretch load out to 600/800/1000 yards. Zero rifle first at 200 yards. Use M1 elevation on Leupold scope in 1/4 MOA scale to dial in elevation corrections. Compare performance with that shown on drop sheet.
5. Adjust drop sheet input (bullet BC) to make computer output drop sheet match field observations
6. Print drop sheet, tape to stock, and off you go.
7. Restart/repeat as desired until dialed in. Don't muck with your load once found...

8. Don't bother with any sort of custom dial from leupold that's built around a bullet and load - the system above is both more general and more precise. And, any scope so equipped with the M1 turret can be swapped to another rifle as whim dictates.

I shoot through the chrony at 15' from muzzle and at the 300 yard line. These two velocities can be used to calculate BC at that mean velocity. bullet makers wee in the past very optimistic with BC until the last decade or so when better equipment to measure velocities down range. I have an Oehler 43 system and an 35P chrony for home use and have access to some pretty sophisticated equipment at work to measure tunnel velocity as well as pressures, etc. So I'm pretty fortunate equipment wise.

I agree about the ballistic cam as related to a certain cartridge/bullet/BC/velocity. I much prefer clicking my own scope. I learned that a few decades back when there were no handheld lasers and ranging and wind estimation were part of the shooters skill set. I've expanded on that with a well rounded set of math skills and ballistic knowledge.......albeit a knowledge that is frequently challenged around here but not necessarily elsewhere.

You obviously have a good understanding of the principles as well as the math skill set. You also have come up with very good system that works well. Others could well benefit from your expertise. Thanks for your pointers on down range dope, I do appreciate your efforts. I like the way you condense and simplify. You bring up a good point about scope height above bore. The long line multiplies errors in that estimation, a 1/4" can make a difference.

#### back country

##### New member
elmerkeithclone - GOOD ONE ! (and my sentiments precisely)

marshall - the good thing about game in the boiler room is pretty big on most and more horizontal than a human target - experience is the best teacher, I have popped 1000's of caps on prairie dogs and sage rats with 223's and 6mm's - the lowly 223 with 40 grain v-max will teach you volumes about wind doping and don't sell short the value of .22 LR shooting - have fun !

#### elmerkeithclone

##### New member
I dunno fellas but I'm thinking "The Science of Shooting" by Jim Clopton is something that I want to put my mitts on!

#### jim in anchorage

##### New member
A MOA is one inch at 100 yards because Jack O'Conner and Warren Page told me so.

#### Smokey

##### New member
If I ever get in a situation that requires this much thinking I will likely just sneak up closer or become a vegetarian....
My system is a bit simpler - if'n I miss I will aim someplace else on the next shot...:lol:

#### ytlogger

##### New member
I dunno fellas but I'm thinking "The Science of Shooting" by Jim Clopton is something that I want to put my mitts on!

Anyone know where to find it?

#### marshall

##### New member
Anyone know where to find it?

I started looking too, no luck in two large chain book stores. They don't even have the author or the title in their data base.

#### Murphy

##### Moderator
The book is yet to be published. It is the combination of two different manuscripts, put together and renamed.
The editing process is much larger than anticipated and has slowed it's release. This post was meant to judge the interest in this subject.