Posted: 11/29/2009 7:42:12 PM EDT
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How do you calculate MOA?
Things I know. -1 MOA at 100 yards is roughly 1 inch (1.047 to be exact) -1 MOA is 1/60th of 1 degree -Therefore 1 MOA is 1/21600 of a whole circle So... how do you calculate MOA at various ranges - not using proportions! What is the formula? As in, I was shooting at this distance, and my group size was this big, therefore my MOA is this...... Thanks. |
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How do you calculate MOA? Things I know. -1 MOA at 100 yards is roughly 1 inch (1.047 to be exact) -1 MOA is 1/60th of 1 degree -Therefore 1 MOA is 1/21600 of a whole circle So... how do you calculate MOA at various ranges - not using proportions! What is the formula? As in, I was shooting at this distance, and my group size was this big, therefore my MOA is this...... Thanks. A quick way is to compute the circumference of a circle with the radius being the distance from you to the target (formula is 2*pi*[r]adius). You then divide by 21,600 (the number of MOA in a circle). This will give you 1 MOA at any distance. It works better if you keep all units in inches. For example, distance=200 yards=7200 inches. (2*pi*7200)/21600=1 MOA@ 200 yards-2.094395102393195" If your group was, say 1.25 inches, you would divide your group size by the MOA value to get your group size in MOA. 1.25/2.094395102393195 =0.596831036594608 MOA There are more elegant methods, but this one is basic arithmetic. |
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Quoted: You are so close. Circumference is twice the radius (in your case, range) multiplied by pi. So at 100 yards, that is 300 feet or 3600 inches so the circumference is about 22,619 inches. Divide that by 21600 and there you have it.How do you calculate MOA? Things I know. -1 MOA at 100 yards is roughly 1 inch (1.047 to be exact) -1 MOA is 1/60th of 1 degree -Therefore 1 MOA is 1/21600 of a whole circle So... how do you calculate MOA at various ranges - not using proportions! What is the formula? As in, I was shooting at this distance, and my group size was this big, therefore my MOA is this...... Thanks. |
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Roughly 1 inch per 100 yards is usually good enough. This. MOA is always MOA. Meaning that 1 inch groups at 100 yards is 1 MOA, and 5 inch groups at 1000 yards (aside from phenomenal) is 1/2MOA, despite the larger group size. How do you calculate MOA? Easy. How far away is the target? Multiply the distance by 0.01. The answer is your group size for MOA in inches. Examples: 100 * 0.01 = 1 500 * 0.01 = 5 1000 * 0.01 = 10 872 * 0.01 = 8.72 424 * 0.01 = 4.24 Now that you've seen a few examples, you're beginning to notice the pattern, right? Even easier than multiplying by 0.01 –– just move the decimal two places to the left, and that's your MOA group size in inches at that distance. Well, all that in "shooter's MOA" (s-MOA) anyway. I'm not going to bother confusing you with milliradians, but I think those are even easier 
_MaH |
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How do you calculate MOA? Things I know. -1 MOA at 100 yards is roughly 1 inch (1.047 to be exact) -1 MOA is 1/60th of 1 degree -Therefore 1 MOA is 1/21600 of a whole circle So... how do you calculate MOA at various ranges - not using proportions! What is the formula? As in, I was shooting at this distance, and my group size was this big, therefore my MOA is this...... Thanks. I really don't know what your asking to tell you the truth. "MOA" represents fixed amount,it's no different than an inch or centimeter. It doesn't change with range. |
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Roughly 1 inch per 100 yards is usually good enough. This. MOA is always MOA. Meaning that 1 inch groups at 100 yards is 1 MOA, and 5 inch groups at 1000 yards (aside from phenomenal) is 1/2MOA, despite the larger group size. How do you calculate MOA? Easy. How far away is the target? Multiply the distance by 0.01. The answer is your group size for MOA in inches. Examples: 100 * 0.01 = 1 500 * 0.01 = 5 1000 * 0.01 = 10 872 * 0.01 = 8.72 424 * 0.01 = 4.24 Now that you've seen a few examples, you're beginning to notice the pattern, right? Even easier than multiplying by 0.01 –– just move the decimal two places to the left, and that's your MOA group size in inches at that distance. Well, all that in "shooter's MOA" (s-MOA) anyway. I'm not going to bother confusing you with milliradians, but I think those are even easier
_MaH Please, confuse me.
I'm a bit of a math nerd. Not an all star by any means, but I get it. |
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Roughly 1 inch per 100 yards is usually good enough. This. MOA is always MOA. Meaning that 1 inch groups at 100 yards is 1 MOA, and 5 inch groups at 1000 yards (aside from phenomenal) is 1/2MOA, despite the larger group size. How do you calculate MOA? Easy. How far away is the target? Multiply the distance by 0.01. The answer is your group size for MOA in inches. Examples: 100 * 0.01 = 1 500 * 0.01 = 5 1000 * 0.01 = 10 872 * 0.01 = 8.72 424 * 0.01 = 4.24 Now that you've seen a few examples, you're beginning to notice the pattern, right? Even easier than multiplying by 0.01 –– just move the decimal two places to the left, and that's your MOA group size in inches at that distance. Well, all that in "shooter's MOA" (s-MOA) anyway. I'm not going to bother confusing you with milliradians, but I think those are even easier
_MaH Please, confuse me.
I'm a bit of a math nerd. Not an all star by any means, but I get it. All right, then. A milliradian (mrad) is 36" at 1000 yards. Or, in other words, 1 yard at 1000 yards. A milliradian will always be 1/1000th of the unit of measure at the distance it's measured. So what's 1 mrad at 2000 meters? 1 mrad at 100 feet? I find mrads more useful because it removes an element of conversion if you have MOA turrets and a true mil-dot scope reticle. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Now convert this to MOA for adjustment to be on target." vs. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Fortunately my turrets adjust by 0.1mrad, so I make a two-click adjustment and smack a bullseye." The only disadvantage mrads have to MOA is that MOA is a smaller unit of measure. As said before: 1 MOA at 1000 yards = 10 inches 1mrad at 1000 yards = 36 inches However, this difference is usually compensated for in the scope turret design. Most mrad scope turrets adjust by 0.1mrad per click, and most MOA scope turrets adjust by 1/4MOA. Meaning: 1/4MOA at 1000 yards = 2.5" adjustment 0.1mrad at 1000 yards = 3.6" adjustment A difference of 1.1" at 1000 yards. Measure your head. Your chest. If you're pretty much on dead center point-of-aim, hitting 1.1" to the right or left of the center of your head or chest is still a kill. It would seem that MOA is the advantage at longer distances, as it allows finer adjustments than mrads, however many shooters forget that 1 MOA is, in fact NOT 1" @ 100 yards. It's 1.047" at 100 yards. Start shooting 2000+ yard distances with larger calibers and that extra 0.047" will make the difference. Though, from a practical shooting stand-point, I'll quote a former co-worker of mine who I think summed it up rather well: "Minute of Angle and milliradian. Six one way, half-a-dozen the other." _MaH |
buy one of those handy dandy mil calculator/computer things but costly, better yet get a "Mildot Master" its a chart that has all the stuff you need on it looks like this  , or just read a LOT at the various sniper forums and take geometry and trigonometry for the concepts behind it.
http://www.mil-dot.com/Mil_Dot_User_Guide.htm |
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buy one of those handy dandy mil calculator/computer things, better yet get a "Mildot Master" its a chart that has all the stuff you need on it looks like this http://www.mil-dot.com/Content%20Images/image014.jpg, or just read a LOT at the various sniper forums and take geometry and trigonometry for the concepts behind it. http://www.mil-dot.com/Mil_Dot_User_Guide.htm This should be a back-up to a calculator, if your calculator runs out of batteries. Your mind should be a backup to the mil-dot master, if you lose it or it becomes tattered, soiled, burned, or unusable. That being said, there's one thing I know I'll always need to rely on a calculator or mil-dot master for: Cosine angle of shot. Sine, cosine and tangent are mathematical functions that I have not yet been capable of performing in my mind alone
_MaH |
| Agreed, thats why I balk at the computer and even GPS's. Sure they make life easy, but goddammit if you better know how to read a map. I like a little cheat card made from that rite in the rain paper in my range book to list out all the equAtions, I cant remember them all off the top of my head but I know how to use them and thats the most important part. |
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Roughly 1 inch per 100 yards is usually good enough. This. MOA is always MOA. Meaning that 1 inch groups at 100 yards is 1 MOA, and 5 inch groups at 1000 yards (aside from phenomenal) is 1/2MOA, despite the larger group size. How do you calculate MOA? Easy. How far away is the target? Multiply the distance by 0.01. The answer is your group size for MOA in inches. Examples: 100 * 0.01 = 1 500 * 0.01 = 5 1000 * 0.01 = 10 872 * 0.01 = 8.72 424 * 0.01 = 4.24 Now that you've seen a few examples, you're beginning to notice the pattern, right? Even easier than multiplying by 0.01 –– just move the decimal two places to the left, and that's your MOA group size in inches at that distance. Well, all that in "shooter's MOA" (s-MOA) anyway. I'm not going to bother confusing you with milliradians, but I think those are even easier
_MaH Please, confuse me.
I'm a bit of a math nerd. Not an all star by any means, but I get it. All right, then. A milliradian (mrad) is 36" at 1000 yards. Or, in other words, 1 yard at 1000 yards. A milliradian will always be 1/1000th of the unit of measure at the distance it's measured. So what's 1 mrad at 2000 meters? 1 mrad at 100 feet? I find mrads more useful because it removes an element of conversion if you have MOA turrets and a true mil-dot scope reticle. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Now convert this to MOA for adjustment to be on target." vs. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Fortunately my turrets adjust by 0.1mrad, so I make a two-click adjustment and smack a bullseye." The only disadvantage mrads have to MOA is that MOA is a smaller unit of measure. As said before: 1 MOA at 1000 yards = 10 inches 1mrad at 1000 yards = 36 inches However, this difference is usually compensated for in the scope turret design. Most mrad scope turrets adjust by 0.1mrad per click, and most MOA scope turrets adjust by 1/4MOA. Meaning: 1/4MOA at 1000 yards = 2.5" adjustment 0.1mrad at 1000 yards = 3.6" adjustment A difference of 1.1" at 1000 yards. Measure your head. Your chest. If you're pretty much on dead center point-of-aim, hitting 1.1" to the right or left of the center of your head or chest is still a kill. It would seem that MOA is the advantage at longer distances, as it allows finer adjustments than mrads, however many shooters forget that 1 MOA is, in fact NOT 1" @ 100 yards. It's 1.047" at 100 yards. Start shooting 2000+ yard distances with larger calibers and that extra 0.047" will make the difference. Though, from a practical shooting stand-point, I'll quote a former co-worker of mine who I think summed it up rather well: "Minute of Angle and milliradian. Six one way, half-a-dozen the other." _MaH I understand all of this. What I want to know is: how did we arrive at the number 1.047 ??? I found this on wikipedia, but it doesn't make sense when I plug in the numbers in my own calculator. equivalent group size = tan(MOA/60) × distance Therefore 3600 tan(1 MOA/60) inches = 1.047. But when I plug in these numbers into my calculator, it doesn't work. I get 60.0055 ETA So I guess I needed to convert from degrees to radians
When I convert 60.0055 to radians I get 1.047294525 |
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Roughly 1 inch per 100 yards is usually good enough. This. MOA is always MOA. Meaning that 1 inch groups at 100 yards is 1 MOA, and 5 inch groups at 1000 yards (aside from phenomenal) is 1/2MOA, despite the larger group size. How do you calculate MOA? Easy. How far away is the target? Multiply the distance by 0.01. The answer is your group size for MOA in inches. Examples: 100 * 0.01 = 1 500 * 0.01 = 5 1000 * 0.01 = 10 872 * 0.01 = 8.72 424 * 0.01 = 4.24 Now that you've seen a few examples, you're beginning to notice the pattern, right? Even easier than multiplying by 0.01 –– just move the decimal two places to the left, and that's your MOA group size in inches at that distance. Well, all that in "shooter's MOA" (s-MOA) anyway. I'm not going to bother confusing you with milliradians, but I think those are even easier
_MaH Please, confuse me.
I'm a bit of a math nerd. Not an all star by any means, but I get it. All right, then. A milliradian (mrad) is 36" at 1000 yards. Or, in other words, 1 yard at 1000 yards. A milliradian will always be 1/1000th of the unit of measure at the distance it's measured. So what's 1 mrad at 2000 meters? 1 mrad at 100 feet? I find mrads more useful because it removes an element of conversion if you have MOA turrets and a true mil-dot scope reticle. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Now convert this to MOA for adjustment to be on target." vs. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Fortunately my turrets adjust by 0.1mrad, so I make a two-click adjustment and smack a bullseye." The only disadvantage mrads have to MOA is that MOA is a smaller unit of measure. As said before: 1 MOA at 1000 yards = 10 inches 1mrad at 1000 yards = 36 inches However, this difference is usually compensated for in the scope turret design. Most mrad scope turrets adjust by 0.1mrad per click, and most MOA scope turrets adjust by 1/4MOA. Meaning: 1/4MOA at 1000 yards = 2.5" adjustment 0.1mrad at 1000 yards = 3.6" adjustment A difference of 1.1" at 1000 yards. Measure your head. Your chest. If you're pretty much on dead center point-of-aim, hitting 1.1" to the right or left of the center of your head or chest is still a kill. It would seem that MOA is the advantage at longer distances, as it allows finer adjustments than mrads, however many shooters forget that 1 MOA is, in fact NOT 1" @ 100 yards. It's 1.047" at 100 yards. Start shooting 2000+ yard distances with larger calibers and that extra 0.047" will make the difference. Though, from a practical shooting stand-point, I'll quote a former co-worker of mine who I think summed it up rather well: "Minute of Angle and milliradian. Six one way, half-a-dozen the other." _MaH I understand all of this. What I want to know is: how did we arrive at the number 1.047 ??? I found this on wikipedia, but it doesn't make sense when I plug in the numbers in my own calculator. equivalent group size = tan(MOA/60) × distance Therefore 3600 tan(1 MOA/60) inches = 1.047. But when I plug in these numbers into my calculator, it doesn't work. I get 60.0055 ETA So I guess I needed to convert from degrees to radians
When I convert 60.0055 to radians I get 1.047294525 
Not 100% on that, but a MOA is a subset measurement of degrees –– not radians (that would be mrads). 360 degrees in a circle. 60 "minutes" in a degree. "Minute of Arc" = 1 minute within 1 degree (aka –– Minute of Angle). _MaH |
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Roughly 1 inch per 100 yards is usually good enough. This. MOA is always MOA. Meaning that 1 inch groups at 100 yards is 1 MOA, and 5 inch groups at 1000 yards (aside from phenomenal) is 1/2MOA, despite the larger group size. How do you calculate MOA? Easy. How far away is the target? Multiply the distance by 0.01. The answer is your group size for MOA in inches. Examples: 100 * 0.01 = 1 500 * 0.01 = 5 1000 * 0.01 = 10 872 * 0.01 = 8.72 424 * 0.01 = 4.24 Now that you've seen a few examples, you're beginning to notice the pattern, right? Even easier than multiplying by 0.01 –– just move the decimal two places to the left, and that's your MOA group size in inches at that distance. Well, all that in "shooter's MOA" (s-MOA) anyway. I'm not going to bother confusing you with milliradians, but I think those are even easier
_MaH Please, confuse me.
I'm a bit of a math nerd. Not an all star by any means, but I get it. All right, then. A milliradian (mrad) is 36" at 1000 yards. Or, in other words, 1 yard at 1000 yards. A milliradian will always be 1/1000th of the unit of measure at the distance it's measured. So what's 1 mrad at 2000 meters? 1 mrad at 100 feet? I find mrads more useful because it removes an element of conversion if you have MOA turrets and a true mil-dot scope reticle. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Now convert this to MOA for adjustment to be on target." vs. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Fortunately my turrets adjust by 0.1mrad, so I make a two-click adjustment and smack a bullseye." The only disadvantage mrads have to MOA is that MOA is a smaller unit of measure. As said before: 1 MOA at 1000 yards = 10 inches 1mrad at 1000 yards = 36 inches However, this difference is usually compensated for in the scope turret design. Most mrad scope turrets adjust by 0.1mrad per click, and most MOA scope turrets adjust by 1/4MOA. Meaning: 1/4MOA at 1000 yards = 2.5" adjustment 0.1mrad at 1000 yards = 3.6" adjustment A difference of 1.1" at 1000 yards. Measure your head. Your chest. If you're pretty much on dead center point-of-aim, hitting 1.1" to the right or left of the center of your head or chest is still a kill. It would seem that MOA is the advantage at longer distances, as it allows finer adjustments than mrads, however many shooters forget that 1 MOA is, in fact NOT 1" @ 100 yards. It's 1.047" at 100 yards. Start shooting 2000+ yard distances with larger calibers and that extra 0.047" will make the difference. Though, from a practical shooting stand-point, I'll quote a former co-worker of mine who I think summed it up rather well: "Minute of Angle and milliradian. Six one way, half-a-dozen the other." _MaH I understand all of this. What I want to know is: how did we arrive at the number 1.047 ??? I found this on wikipedia, but it doesn't make sense when I plug in the numbers in my own calculator. equivalent group size = tan(MOA/60) × distance Therefore 3600 tan(1 MOA/60) inches = 1.047. But when I plug in these numbers into my calculator, it doesn't work. I get 60.0055 ETA So I guess I needed to convert from degrees to radians
When I convert 60.0055 to radians I get 1.047294525 OK so I got the formula down to figure out the equivalent group size for any given MOA of accuracy. Now I'm trying to solve the formula equivalent group size = tan(MOA/60) × distance For MOA. I have (equivalent group size)/(distance) = tan(MOA/60) I forget what to do from there... |
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Roughly 1 inch per 100 yards is usually good enough. This. MOA is always MOA. Meaning that 1 inch groups at 100 yards is 1 MOA, and 5 inch groups at 1000 yards (aside from phenomenal) is 1/2MOA, despite the larger group size. How do you calculate MOA? Easy. How far away is the target? Multiply the distance by 0.01. The answer is your group size for MOA in inches. Examples: 100 * 0.01 = 1 500 * 0.01 = 5 1000 * 0.01 = 10 872 * 0.01 = 8.72 424 * 0.01 = 4.24 Now that you've seen a few examples, you're beginning to notice the pattern, right? Even easier than multiplying by 0.01 –– just move the decimal two places to the left, and that's your MOA group size in inches at that distance. Well, all that in "shooter's MOA" (s-MOA) anyway. I'm not going to bother confusing you with milliradians, but I think those are even easier
_MaH Please, confuse me.
I'm a bit of a math nerd. Not an all star by any means, but I get it. All right, then. A milliradian (mrad) is 36" at 1000 yards. Or, in other words, 1 yard at 1000 yards. A milliradian will always be 1/1000th of the unit of measure at the distance it's measured. So what's 1 mrad at 2000 meters? 1 mrad at 100 feet? I find mrads more useful because it removes an element of conversion if you have MOA turrets and a true mil-dot scope reticle. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Now convert this to MOA for adjustment to be on target." vs. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Fortunately my turrets adjust by 0.1mrad, so I make a two-click adjustment and smack a bullseye." The only disadvantage mrads have to MOA is that MOA is a smaller unit of measure. As said before: 1 MOA at 1000 yards = 10 inches 1mrad at 1000 yards = 36 inches However, this difference is usually compensated for in the scope turret design. Most mrad scope turrets adjust by 0.1mrad per click, and most MOA scope turrets adjust by 1/4MOA. Meaning: 1/4MOA at 1000 yards = 2.5" adjustment 0.1mrad at 1000 yards = 3.6" adjustment A difference of 1.1" at 1000 yards. Measure your head. Your chest. If you're pretty much on dead center point-of-aim, hitting 1.1" to the right or left of the center of your head or chest is still a kill. It would seem that MOA is the advantage at longer distances, as it allows finer adjustments than mrads, however many shooters forget that 1 MOA is, in fact NOT 1" @ 100 yards. It's 1.047" at 100 yards. Start shooting 2000+ yard distances with larger calibers and that extra 0.047" will make the difference. Though, from a practical shooting stand-point, I'll quote a former co-worker of mine who I think summed it up rather well: "Minute of Angle and milliradian. Six one way, half-a-dozen the other." _MaH I understand all of this. What I want to know is: how did we arrive at the number 1.047 ??? I found this on wikipedia, but it doesn't make sense when I plug in the numbers in my own calculator. equivalent group size = tan(MOA/60) × distance Therefore 3600 tan(1 MOA/60) inches = 1.047. But when I plug in these numbers into my calculator, it doesn't work. I get 60.0055 ETA So I guess I needed to convert from degrees to radians
When I convert 60.0055 to radians I get 1.047294525
Not 100% on that, but a MOA is a subset measurement of degrees –– not radians (that would be mrads). 360 degrees in a circle. 60 "minutes" in a degree. "Minute of Arc" = 1 minute within 1 degree (aka –– Minute of Angle). _MaH When I multiply by pi/180 I get the proper answer. |
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Roughly 1 inch per 100 yards is usually good enough. This. MOA is always MOA. Meaning that 1 inch groups at 100 yards is 1 MOA, and 5 inch groups at 1000 yards (aside from phenomenal) is 1/2MOA, despite the larger group size. How do you calculate MOA? Easy. How far away is the target? Multiply the distance by 0.01. The answer is your group size for MOA in inches. Examples: 100 * 0.01 = 1 500 * 0.01 = 5 1000 * 0.01 = 10 872 * 0.01 = 8.72 424 * 0.01 = 4.24 Now that you've seen a few examples, you're beginning to notice the pattern, right? Even easier than multiplying by 0.01 –– just move the decimal two places to the left, and that's your MOA group size in inches at that distance. Well, all that in "shooter's MOA" (s-MOA) anyway. I'm not going to bother confusing you with milliradians, but I think those are even easier
_MaH Please, confuse me.
I'm a bit of a math nerd. Not an all star by any means, but I get it. All right, then. A milliradian (mrad) is 36" at 1000 yards. Or, in other words, 1 yard at 1000 yards. A milliradian will always be 1/1000th of the unit of measure at the distance it's measured. So what's 1 mrad at 2000 meters? 1 mrad at 100 feet? I find mrads more useful because it removes an element of conversion if you have MOA turrets and a true mil-dot scope reticle. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Now convert this to MOA for adjustment to be on target." vs. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Fortunately my turrets adjust by 0.1mrad, so I make a two-click adjustment and smack a bullseye." The only disadvantage mrads have to MOA is that MOA is a smaller unit of measure. As said before: 1 MOA at 1000 yards = 10 inches 1mrad at 1000 yards = 36 inches However, this difference is usually compensated for in the scope turret design. Most mrad scope turrets adjust by 0.1mrad per click, and most MOA scope turrets adjust by 1/4MOA. Meaning: 1/4MOA at 1000 yards = 2.5" adjustment 0.1mrad at 1000 yards = 3.6" adjustment A difference of 1.1" at 1000 yards. Measure your head. Your chest. If you're pretty much on dead center point-of-aim, hitting 1.1" to the right or left of the center of your head or chest is still a kill. It would seem that MOA is the advantage at longer distances, as it allows finer adjustments than mrads, however many shooters forget that 1 MOA is, in fact NOT 1" @ 100 yards. It's 1.047" at 100 yards. Start shooting 2000+ yard distances with larger calibers and that extra 0.047" will make the difference. Though, from a practical shooting stand-point, I'll quote a former co-worker of mine who I think summed it up rather well: "Minute of Angle and milliradian. Six one way, half-a-dozen the other." _MaH I understand all of this. What I want to know is: how did we arrive at the number 1.047 ??? I found this on wikipedia, but it doesn't make sense when I plug in the numbers in my own calculator. equivalent group size = tan(MOA/60) × distance Therefore 3600 tan(1 MOA/60) inches = 1.047. But when I plug in these numbers into my calculator, it doesn't work. I get 60.0055 ETA So I guess I needed to convert from degrees to radians
When I convert 60.0055 to radians I get 1.047294525 OK so I got the formula down to figure out the equivalent group size for any given MOA of accuracy. Now I'm trying to solve the formula equivalent group size = tan(MOA/60) × distance For MOA. I have (equivalent group size)/(distance) = tan(MOA/60) I forget what to do from there... Inverse Tangent of both sides... |
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Roughly 1 inch per 100 yards is usually good enough. This. MOA is always MOA. Meaning that 1 inch groups at 100 yards is 1 MOA, and 5 inch groups at 1000 yards (aside from phenomenal) is 1/2MOA, despite the larger group size. How do you calculate MOA? Easy. How far away is the target? Multiply the distance by 0.01. The answer is your group size for MOA in inches. Examples: 100 * 0.01 = 1 500 * 0.01 = 5 1000 * 0.01 = 10 872 * 0.01 = 8.72 424 * 0.01 = 4.24 Now that you've seen a few examples, you're beginning to notice the pattern, right? Even easier than multiplying by 0.01 –– just move the decimal two places to the left, and that's your MOA group size in inches at that distance. Well, all that in "shooter's MOA" (s-MOA) anyway. I'm not going to bother confusing you with milliradians, but I think those are even easier
_MaH Please, confuse me.
I'm a bit of a math nerd. Not an all star by any means, but I get it. All right, then. A milliradian (mrad) is 36" at 1000 yards. Or, in other words, 1 yard at 1000 yards. A milliradian will always be 1/1000th of the unit of measure at the distance it's measured. So what's 1 mrad at 2000 meters? 1 mrad at 100 feet? I find mrads more useful because it removes an element of conversion if you have MOA turrets and a true mil-dot scope reticle. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Now convert this to MOA for adjustment to be on target." vs. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Fortunately my turrets adjust by 0.1mrad, so I make a two-click adjustment and smack a bullseye." The only disadvantage mrads have to MOA is that MOA is a smaller unit of measure. As said before: 1 MOA at 1000 yards = 10 inches 1mrad at 1000 yards = 36 inches However, this difference is usually compensated for in the scope turret design. Most mrad scope turrets adjust by 0.1mrad per click, and most MOA scope turrets adjust by 1/4MOA. Meaning: 1/4MOA at 1000 yards = 2.5" adjustment 0.1mrad at 1000 yards = 3.6" adjustment A difference of 1.1" at 1000 yards. Measure your head. Your chest. If you're pretty much on dead center point-of-aim, hitting 1.1" to the right or left of the center of your head or chest is still a kill. It would seem that MOA is the advantage at longer distances, as it allows finer adjustments than mrads, however many shooters forget that 1 MOA is, in fact NOT 1" @ 100 yards. It's 1.047" at 100 yards. Start shooting 2000+ yard distances with larger calibers and that extra 0.047" will make the difference. Though, from a practical shooting stand-point, I'll quote a former co-worker of mine who I think summed it up rather well: "Minute of Angle and milliradian. Six one way, half-a-dozen the other." _MaH I understand all of this. What I want to know is: how did we arrive at the number 1.047 ??? I found this on wikipedia, but it doesn't make sense when I plug in the numbers in my own calculator. equivalent group size = tan(MOA/60) × distance Therefore 3600 tan(1 MOA/60) inches = 1.047. But when I plug in these numbers into my calculator, it doesn't work. I get 60.0055 ETA So I guess I needed to convert from degrees to radians
When I convert 60.0055 to radians I get 1.047294525 OK so I got the formula down to figure out the equivalent group size for any given MOA of accuracy. Now I'm trying to solve the formula equivalent group size = tan(MOA/60) × distance For MOA. I have (equivalent group size)/(distance) = tan(MOA/60) I forget what to do from there... Either I have no idea what it is you're trying to say, or you're making this way more complicated than it needs to be. What is the distance you're shooting? Let's say 750 yards. What is your group size? Let's say it's 9.3". At 750 yards, 1 s-MOA is 7.5" - so you already know it's more than that. Now you just need to figure out that fraction. So do this: 9.3 (group size) - 7.5 (s-MOA at distance you were shooting) = 1.8 1.8 (remainder from above) / 7.5 (s-MOA from above) = 0.24 1 s-MOA + 0.24 (remainder) = 1.24 s-MOA was your group size. _MaH |
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Roughly 1 inch per 100 yards is usually good enough. This. MOA is always MOA. Meaning that 1 inch groups at 100 yards is 1 MOA, and 5 inch groups at 1000 yards (aside from phenomenal) is 1/2MOA, despite the larger group size. How do you calculate MOA? Easy. How far away is the target? Multiply the distance by 0.01. The answer is your group size for MOA in inches. Examples: 100 * 0.01 = 1 500 * 0.01 = 5 1000 * 0.01 = 10 872 * 0.01 = 8.72 424 * 0.01 = 4.24 Now that you've seen a few examples, you're beginning to notice the pattern, right? Even easier than multiplying by 0.01 –– just move the decimal two places to the left, and that's your MOA group size in inches at that distance. Well, all that in "shooter's MOA" (s-MOA) anyway. I'm not going to bother confusing you with milliradians, but I think those are even easier
_MaH Please, confuse me.
I'm a bit of a math nerd. Not an all star by any means, but I get it. All right, then. A milliradian (mrad) is 36" at 1000 yards. Or, in other words, 1 yard at 1000 yards. A milliradian will always be 1/1000th of the unit of measure at the distance it's measured. So what's 1 mrad at 2000 meters? 1 mrad at 100 feet? I find mrads more useful because it removes an element of conversion if you have MOA turrets and a true mil-dot scope reticle. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Now convert this to MOA for adjustment to be on target." vs. "Okay, so we're measuring a target of known size to be two mrads tall, and we missed by 1/5 mrad. Fortunately my turrets adjust by 0.1mrad, so I make a two-click adjustment and smack a bullseye." The only disadvantage mrads have to MOA is that MOA is a smaller unit of measure. As said before: 1 MOA at 1000 yards = 10 inches 1mrad at 1000 yards = 36 inches However, this difference is usually compensated for in the scope turret design. Most mrad scope turrets adjust by 0.1mrad per click, and most MOA scope turrets adjust by 1/4MOA. Meaning: 1/4MOA at 1000 yards = 2.5" adjustment 0.1mrad at 1000 yards = 3.6" adjustment A difference of 1.1" at 1000 yards. Measure your head. Your chest. If you're pretty much on dead center point-of-aim, hitting 1.1" to the right or left of the center of your head or chest is still a kill. It would seem that MOA is the advantage at longer distances, as it allows finer adjustments than mrads, however many shooters forget that 1 MOA is, in fact NOT 1" @ 100 yards. It's 1.047" at 100 yards. Start shooting 2000+ yard distances with larger calibers and that extra 0.047" will make the difference. Though, from a practical shooting stand-point, I'll quote a former co-worker of mine who I think summed it up rather well: "Minute of Angle and milliradian. Six one way, half-a-dozen the other." _MaH I understand all of this. What I want to know is: how did we arrive at the number 1.047 ??? I found this on wikipedia, but it doesn't make sense when I plug in the numbers in my own calculator. equivalent group size = tan(MOA/60) × distance Therefore 3600 tan(1 MOA/60) inches = 1.047. But when I plug in these numbers into my calculator, it doesn't work. I get 60.0055 ETA So I guess I needed to convert from degrees to radians
When I convert 60.0055 to radians I get 1.047294525 OK so I got the formula down to figure out the equivalent group size for any given MOA of accuracy. Now I'm trying to solve the formula equivalent group size = tan(MOA/60) × distance For MOA. I have (equivalent group size)/(distance) = tan(MOA/60) I forget what to do from there... Inverse Tangent of both sides... OK. Here's the final verdict. Please check me. If you know the distance and the MOA you want to shoot then, you use this formula to find the group size you must achieve. GROUP_SIZE_TO_ACHIEVE = DISTANCE * (tan(DESIRED_MOA/60)) Because MOA is a measure of degrees, and you obviously cannot have a group size in degrees, you must convert to radians. Multiply the entire thing by (pi/180) If you know the distance and the group size, you can compute your MOA with the following formula... MOA = arctan(GROUP_SIZE/DISTANCE)*60 Since arctan returns the number you need to yield a specific angle, in this case, the MOA, you must convert your final thing back to degrees, since MOA is a measure of degrees after all. Multiply everything by (180/pi) With these formulas you can use any units too! Just make sure they're consistent. If you want to achieve a 1 MOA group at 10 feet, then your group size must be .002909 feet. If you want to achieve a 1 MOA group size at 25 meters, you must shoot a .007273 meter group. You can use centimeters too. 1 MOA group at 5000 centimeters, you must shoot a 1.4546 centimeter group. Link to Excel Spreadsheet to do this for you. Right click and "save as" |
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http://i728.photobucket.com/albums/ww284/ronin083/Math1.jpg eta: yeah i'm being a smartass but you seem to be on the right track Yeah I think I finally got it. I know there's the whole shooter's MOA with basically 1 MOA = 1 inch at 100 yards, but I wanted the formula and the precision. I'm a bit of a nerd like that. 
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| it's better to be a bit of a nerd figuring all this out, that's why the militaries best snipers are usually picked from the smartest of the group, its good shit, your average couch commando knows how to plink budweiser cans at 50 meters but shooting at high distances is more of an art/science than anything else, glad to talk to others who take it seriously |
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So... how do you calculate MOA at various ranges - not using proportions! Took you awhile, but TAN function is about the quickest way without having to give a damned about how many degrees or minutes of angle are in a complete circle. Never gave two shits about a whole circle. Even with radian measure and figuring out a mil-radian for being able to use a ranging reticle, never gave a shit about the entire circle. Yeah, took trig as well as 2nd year and 3rd year calc during Jr College. |
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So... how do you calculate MOA at various ranges - not using proportions! Took you awhile, but TAN function is about the quickest way without having to give a damned about how many degrees or minutes of angle are in a complete circle. Never gave two shits about a whole circle. Even with radian measure and figuring out a mil-radian for being able to use a ranging reticle, never gave a shit about the entire circle. Yeah, took trig as well as 2nd year and 3rd year calc during Jr College. Yeah... got geometry, trig, precalc, and calc 1 in HS. Then got a repeat of calc 1 and a course in calc 2 in college.
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So... how do you calculate MOA at various ranges - not using proportions! Took you awhile, but TAN function is about the quickest way without having to give a damned about how many degrees or minutes of angle are in a complete circle. Never gave two shits about a whole circle. Even with radian measure and figuring out a mil-radian for being able to use a ranging reticle, never gave a shit about the entire circle. Yeah, took trig as well as 2nd year and 3rd year calc during Jr College. Yeah... got geometry, trig, precalc, and calc 1 in HS. Then got a repeat of calc 1 and a course in calc 2 in college. Honestly, if I get enough money to replace all my scopes on my rifles, I'm going to standardize and go either Mil-Radian reticle with mil-adjustment turrets or MOA reticle with MOA turrets. It really is amazing that people have gone so long with mil-radian reticle and MOA turrets. I can work mil-radian math in my head faster than I can with MOA conversions, however many drop charts are in MOA unless you've converted them to mil already. |
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This is what you should take away from this thread
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Quoted: You are so close. Circumference is twice the radius (in your case, range) multiplied by pi. So at 100 yards, that is 300 feet or 3600 inches so the circumference is about 22,619 inches. Divide that by 21600 and there you have it. Is the MOA a projection of the arc onto a straight line? Yes, I know it's an insignificant difference. |
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How do you calculate MOA? Things I know. -1 MOA at 100 yards is roughly 1 inch (1.047 to be exact) -1 MOA is 1/60th of 1 degree -Therefore 1 MOA is 1/21600 of a whole circle So... how do you calculate MOA at various ranges - not using proportions! What is the formula? As in, I was shooting at this distance, and my group size was this big, therefore my MOA is this...... Thanks. Sorry I realize others have probably got this nailed but here’s my, hopefully, clear explanation. So, where does the number 1.047 come from? A true MOA (minute of angle) equals 1.047” at a distance of 100 yards. Hence the quick down and dirty approximation sometimes referred to as ‘the rifleman’s moa’ of 1” @ 100yds. Without too many extra formulas here’s how you get there: Everything must be in inches so 100yds x 3 ft/yd x 12 in/ft = 3600 inches. Visualize that as the radius of a circle and apply 2πr to get its circumference: 2 x 3.1416 x 3600 in = 22,619.52 in. Since there are 360 degrees in a circle and 60 minutes in a degree (moa): 22,619.52 in ÷ 360 ÷ 60 = 1.0472 in. So, do you use 1” or 1.047” to calculate your corrections? Let’s assume you need to correct for a shot that’s 20” off at 1,000 yds. Using the rifleman’s moa 1,000 yds is 10 units of 100 yds so you divide 20” by 10 and get 2 MOA. With ¼ minute clicks that works out to 8 clicks (2 x 4 = 8). If you want to calculate the true MOA simply divide the rifleman’s 2 MOA by 1.047 and you get a correction of 1.91 MOA (true). Since we can’t split the ¼ minute clicks any finer you must go to the nearest click. Guess what? It’s 2 MOA! We’re talking about a difference in this example of less than 1” at 1,000 yds! It’s not until you have to make a correction of about 22” at 1,000 yds that you will finally round your true MOA correction down ¼ minute from your rifleman’s MOA correction. This is truly more of a rounding error than an actual difference because you can go further on up to around a 75” correction at 1K and still have only ¼ minute of difference between the two methods. Fairly minor difference. Just go with the simple 1 MOA = 1” @ 100 yds. BUT! Do you know whether your scope corrects 1” per MOA or 1.047” per MOA? Food for thought. gk |
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You could just use milliradians, the natural unit of angular measurement.
mils = 1000*size/distance Way easier, IMHO. It makes more sense to measure angles based upon the ratio of chords/radii rather than using a system based arbitrarily upon the (incorrect) number of days in a year according to some Egyptian who's been dead for 4000 years. |
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Quoted: BUT! Do you know whether your scope corrects 1” per MOA or 1.047” per MOA? 1" is not 1 MOA - it's an approximation. The scope is most likely designed to be adjusted by some sort of a radial measure. The point is probably moot anyway, as the 0.047" difference is more precise than the operator's ability to measure the distance under field conditions. |
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BUT! Do you know whether your scope corrects 1” per MOA or 1.047” per MOA? 1" is not 1 MOA - it's an approximation. The scope is most likely designed to be adjusted by some sort of a radial measure. The point is probably moot anyway, as the 0.047" difference is more precise than the operator's ability to measure the distance under field conditions. Bingo! That's what I was getting at in my post. Whether or not you want to use the 1.047 to be 'precise' or 1" to simplify the whole process is of no consequence because you can't realistically tell the difference anyway. My comment which you quoted above was meant to also say - What does it matter if we don't know how the scope maker set the scope up in the first place? 1" is so close and simple it makes no sense to think of it any other way. As for the pros and cons of MOA vs Milradian it makes absolutely no difference. It is all in what you want to get used to and what type of units you wish to think in. Angles are angles. The high power competive crowd will probably stay with MOA and the military crowd will stay with Milradian. gk |