Rifle Scopes Mils / MOA and the Range Estimation Equations

[Bags]

I first wrote this paper in 2007, then updated it in 2016 to a much better version. It's an academic paper and a " down to the basics" about what a Mil and MOA are and a, "how did they come up with the range equations". Although you don't need this info to use your scope, it's great for understanding your scope 's reticle and also for getting to sleep at night. I'll be glad to send it to anybody via email if for some reason you can't download it here or get it on Scribd. I have two versions of it, one a simple version where I left out most of the math, and one a more in depth version for this interested in the math. Thank you.

Note: In 2007 when I first posted it on SH, it was under the name "runner" (I used my sons login) . Now I have my own name.

They're in the Resources page under, "https://www.snipershide.com/shootin...-range-equations-and-the-math-behind-them.25/"

I also have Links below to the two versions of it for friends who aren't on SH. One an in depth version and the other without the detailed math.

https://www.scribd.com/doc/251836084/Mils-MOA-and-the-Range-Estimation-Equations

Simple version with no math:

https://www.scribd.com/document/265985865/Mils-MOA-A-Basic-Study-for-Shooters

 

[AIAW]

Very nice! I posted your "old" version as a "resource" here. You should add these as resources and I will take the "old" version that I posted down. Either that, or I can simply update the one I posted with this version. Up to you, given that you are the author.

MILs and MOA - A Shooters Guide to Understanding (Conversion, Range Estimation Formulae, etc.)

Very nice job on these papers by the way.

 

[patriot07]

Just curious - why not just use a rangefinder?

 

[AIAW]

Just curious - why not just use a rangefinder?

This is material that every shooter should know. Sure, a rangefinder gets the job done real quick but the math behind the reticle is something that should be known by all serious shooters. On top of that and equally as important, the reticle takes no batteries.

 

[Bags]

patriot07 said:
Just curious - why not just use a rangefinder?


Yes, absolutely use a range finder first. But what if your batteries die, or there's some weather interference or some other reason you can't use it , these basics might get you there. Think of it as the S has HTF and the only car left is a standard shift. Thank god the millenial who tried to drive it before you didn't know the basics, and now you're on your way escaping with your road map that OBTW he didn't know how to read either since cell service is down.

 

[Bags]

Very nice! I posted your "old" version as a "resource" here. You should add these as resources and I will take the "old" version that I posted down. Either that, or I can simply update the one I posted with this version. Up to you, given that you are the author.

MILs and MOA - A Shooters Guide to Understanding (Conversion, Range Estimation Formulae, etc.)

Very nice job on these papers by the way.

First, thank you. Second, yes, I would like to add these newer ones to the resources page and take down the old ones. Thank you.

 

[patriot07]

This is material that every shooter should know. Sure, a rangefinder gets the job done real quick but the math behind the reticle is something that should be known by all serious shooters. On top of that and equally as important, the reticle takes no batteries.

Understood - I just didn't understand if I was missing something. I certainly understand the math behind reticles, but the lack of accuracy in ranging estimates seem like it would make it very, very difficult to make the technique useful at longer ranges when small differences in yardage make big differences in elevation adjustment. But maybe I'm way off base - I'm definitely not a serious shooter, and I don't hunt at all.

 

[Jefe's Dope]

Just curious - why not just use a rangefinder?

Same reason you should know how to use a fire starter. Yes, the Bic lighter will likely work and be reliable. Until it isn't.

 

[AIAW]

Understood - I just didn't understand if I was missing something. I certainly understand the math behind reticles, but the lack of accuracy in ranging estimates seem like it would make it very, very difficult to make the technique useful at longer ranges when small differences in yardage make big differences in elevation adjustment. But maybe I'm way off base - I'm definitely not a serious shooter, and I don't hunt at all.

For ELR perhaps not exactly the most accurate, but for ranging lets say under 1500 yards you'd be surprised how accurate it can be if you know the exact height (or width) of a target. Best way to know if you are missing anything would be to read over the papers and see if anything catches your eye.

I get what you are saying, and technology is fun and easy: until it stops functioning.

 

[AIAW]

First, thank you. Second, yes, I would like to add these newer ones to the resources page and take down the old ones. Thank you.

Just click on the top of the website where is says "Resources". You can then upload from there under your username!

 

[Bags]

Just click on the top of the website where is says "Resources". You can then upload from there under your username!

I just added the new ones to the resources page, but I want to take down the older version. Can I do it or do you have to? Thanks, Bags

 

[patriot07]

For ELR perhaps not exactly the most accurate, but for ranging lets say under 1500 yards you'd be surprised how accurate it can be if you know the exact height (or width) of a target. Best way to know if you are missing anything would be to read over the papers and see if anything catches your eye.

I get what you are saying, and technology is fun and easy: until it stops functioning.

What if you don't know the target size?

Same reason you should know how to use a fire starter. Yes, the Bic lighter will likely work and be reliable. Until it isn't.

LOL. 34 years old and never used one, and don't anticipate ever needing to anytime soon. Maybe now I need to learn ranging and fire starting!

 

[Jefe's Dope]

LOL. 34 years old and never used one, and don't anticipate ever needing to anytime soon. Maybe now I need to learn ranging and fire starting!

2 is 1 and one is none. Should apply to your training too. At worst, you've gained some knowledge. It's just like algebra. You'll never need it when you grow up until you do. Algebra, or mathematics in general, train your brain to solve problems. That skill can be applied to many things and situations beyond mathematics.

 

[AIAW]

I just added the new ones to the resources page, but I want to take down the older version. Can I do it or do you have to? Thanks, Bags

No problem. I just took the version that I had uploaded down, so now your new version that you uploaded is the only one up.

 

[Bags]

No problem. I just took the version that I had uploaded down, so now your new version that you uploaded is the only one up.

Thank you Sir.

 

[patriot07]

2 is 1 and one is none. Should apply to your training too. At worst, you've gained some knowledge. It's just like algebra. You'll never need it when you grow up until you do. Algebra, or mathematics in general, train your brain to solve problems. That skill can be applied to many things and situations beyond mathematics.

I'm a mechanical engineer. I use algebra daily and the math for ranging is elementary stuff, except that variability in your estimation of target size results in huge variance in the result. And I just can't imagine a scenario where you know the exact target size but don't know the range and can't use a RF.

Fire starting...not so much my thing....

 

[Bags]

patriot07, my papers are just academic papers to give shooters an understanding of the basic math behind Mils / MOA and the Range equations. It's just for fun knowledge, or like I said, for help in putting yourself to sleep. I also stated that you don't have to know the math to use your scope or range finders, just info for those inquisitive minds.

 

[Gunfighter14e2]

And I just can't imagine a scenario where you know the exact target size but don't know the range and can't use a RF.

All weapons, gear an transport conveyance items on this rock have known numbers. Plus you have all civi listed items categorized as well. Issue comes with animals yet even they have a size chart. A good hunter will have all these numbers depending venue. A LRF emits a active beam bad juju,,... in some venues

 

[Jefe's Dope]

I'm a mechanical engineer. I use algebra daily and the math for ranging is elementary stuff, except that variability in your estimation of target size results in huge variance in the result. And I just can't imagine a scenario where you know the exact target size but don't know the range and can't use a RF.

Fire starting...not so much my thing....

You asked "why not just use a rangefinder?" I and some others have tried to give you some 'reasons'. You don't seem to be satisfied with those 'reasons'. So, I'm not sure what you're driving at, but my last advice is, use your rangefinder. I think this should satisfy 'your' needs.

The rest of us are just happy to have another resource. ?

 

[Gunfighter14e2]

I'm a mechanical engineer. I use algebra daily and the math for ranging is elementary stuff, except that variability in your estimation of target size results in huge variance in the result. And I just can't imagine a scenario where you know the exact target size but don't know the range and can't use a RF.

Fire starting...not so much my thing....

The math is first/second grade stuff however there is another item that comes into play with all items unless they are subdued, that is color. If you don't know "YOUR" color correction factors, you will get out of your "thats a give me" range real quick. The other thing many forget is the skill required to break the ret down to the finer points when ranging. As miss ranging a target past 600 yds can an often equals a miss with a .308 on a minute of chest shot.. Ya the Gucci chamberings do better but, past 8-900 the same issue starts to crop up. Know your gear, know your ability/limitations, but most of all know what question/s to ask.
Not everything is as it appears at times.

 

[RedRyder]

Bags - thanks for all the work that went into this. I have a question/observation to make.

At the very top of page 19, "H inches x 95.5 / X MOA" appears. The value 95.5 suddenly appears and is not defined until, I believe, the Note which appears nearly at the bottom of page 19. I'm puzzled as to why you didn't define 95.5 earlier in the text?

 

[Bags]

Bags - thanks for all the work that went into this. I have a question/observation to make.

At the very top of page 19, "H inches x 95.5 / X MOA" appears. The value 95.5 suddenly appears and is not defined until, I believe, the Note which appears nearly at the bottom of page 19. I'm puzzled as to why you didn't define 95.5 earlier in the text?

RedRyder, if you go back one page to the bottom of page 18, you'll see I said:

"Recall from page 12 that H/36 will convert inches to yards. Substituting that into the basic equation above, with H measured in inches and the output D in yards, the MOA distance equation now is: H inches × 95.5 / X MOA= D yards.

So look at the basic equation just a few sentences above that sentence and it is, "H x 3,437.75 / X = D" . Therefore substituting H/36 for H in the top of this equation gives you, "3437.75 / 36 = 95.5".

On that note you're talking about (below), recall, at 100 yards, 1 MOA = 1.047 inches. I was just asking at what distance does 1 MOA give you 1 inch, and that answer is at 95.5 yards. Do the math with the knowns 1 MOA and 1 inch in the equation and solving for the yards X: You get 95.5 yards. So 1 MOA = 1 inch at 95.5 yards and 1.047 inches at 100 yards.

"Note: If you solve for the distance at where 1 MOA would give you exactly 1 inch, you would get 95.5 yards. That is, at 95.5 yards, 1 MOA equals 1-inch".

RedRyder, I'm not sure if you realized it, but I have two versions of the paper. A long version with a lot of math and a short version where I kept most of it out for those not interested in it. You're looking at the "short version" paper with very little detailed math. Download the long version of it and look at the top of page 30 for a more detailed mathematical explanation of your question. Feel free to ask me again if anything I said is not clear.

 

[highhope]

Nice paper, like it!

 

[spife7980]

I wouldnt say that its first or second grade math, trig is definitely high school level (at least when I learned it) but I think so ling as someone took basic algebra they should be able to follow this paper (provided they take the time to actually read something on the internet). Very comprehensive and excellent job.

 

[Bags]

I wouldnt say that its first or second grade math, trig is definitely high school level (at least when I learned it) but I think so ling as someone took basic algebra they should be able to follow this paper (provided they take the time to actually read something on the internet). Very comprehensive and excellent job.

I left most the trig out in the simplified version, but even in the more comprehensive version, I still give the reader the option of skipping over the math if they don't want to get bogged down by it. I clearly delineate where you should skip over and start reading again in the paper if that is what you choose to do. Also, thanks for the compliment Spife7980.

 

[Ravenworks]

Thanks for posting this up.

 

[Bags]

I want to edit my original post above but can't seem to do it anymore. Is there a time limit on making edits?

P.S. The link to the resources page in my original post no longer works as I changed the resource to an updated version. I merely want to insert this new link (below) in the original post. Either way, here is a direct link to my papers.

https://www.snipershide.com/shootin...-range-equations-and-the-math-behind-them.25/

 

[Forrest84]

I'm a mechanical engineer. I use algebra daily and the math for ranging is elementary stuff, except that variability in your estimation of target size results in huge variance in the result. And I just can't imagine a scenario where you know the exact target size but don't know the range and can't use a RF.

Fire starting...not so much my thing....

Ok man look at it like this. You don’t have a range finder or it doesn’t work for whatever fuckin reason or we are 5 years into a post apocalyptic world and your fresh out of double a batteries.
Your in a good firing position and your staring down some commie dickheads that you want to send to whatever god they warship.
Well fuck how far away are they!? Dont have a range finder guess I’ll be an amateur bitch and pack it up for the day.






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Ooorrrr you notice they are standing next to a derelict late model dodge/Chevy pick up and you remember they have 20” factory wheels........ There you go! (Or whatever other object you can confidently gauge the size of)Do your math, dial your turret or hold your reticle and send a screaming match king or ELD or whatever you prefer down range into some those assholes to Jesus.


Or you can just keep asking why and not use your imagination to easily creat any number possible scenarios it could be usefule knowlede to have.