Here are some formulae that you may find useful in your long range shooting. But first, a few words concerning Minutes of Angle (MOA) and Mil (milliradian) dots.
Both MOA and mils are used to measure angles. There are 360 degrees in a complete circle. There are 60 minutes in a degree. A radian is defined as the plane angle with its vertex at the center of a circle that is subtended by an arc (not a line) equal in length to the radius. There are 2 times Pi (6.283...) radians in a complete circle. A milliradian is simply one one-thousandth of a radian. We take the mil to mean a distance equal to one one-thousandth of the distance to the target. (The Army further confuses things by defining a milliradian as 1/6,400th of a circle. Don't worry about that unless you get assigned to an artillery unit.)
As shooters we tend to think of one MOA as equaling one inch at 100 yards. Our scopes are usually calibrated to give us one quarter (or one eighth, or one half, or one, unless it's metric then you get about one third) inch adjustment per click at one hundred yards. The scope manufacturers don't say "quarter minute clicks" but that's how we interpret it. A true MOA is equal to 1.047 (rounded off) inches at 100 yards. The difference is minor. Even at 1,000 yards it's slightly less than a half an inch, but it is there. Where we get into trouble is when we start running numbers up on the calculator. One true milliradian equals 3.438 (rounded off) true MOA. This means one true milliradian equals a very tiny bit less than 3.6 inches at one hundred yards. 3.6 inches at one hundred yards or 36 inches at 1,000 yards is exactly how we want to use the mil. If you think your calculator is telling you that a mil equals 3.438 inches at 100 yards you are mistaken. Fortunately, the differences are too minor to make a difference.
Just remember that for shooting purposes, virtually all scopes, reticles, and shooter's formulae are calibrated so that one MOA equals one inch at 100 yards and one mil equals one yard at 1,000 yards.
1 actual MOA = 1.047 inches at 100 yards
1 actual milliradian = 3.438 actual MOA
1 actual milliradian = 3.600 inches at 100 yards
1 actual MOA = .291 actual milliradians
1 shooter's MOA = 1 inch per 100 yards of range
1 shooter's MOA = .278 mils
1 mil = 3.6 shooter's MOA
MOA adjustment times the range in hundreds of yards (600 yards = 6) equals change of impact in inches.
MOA X R = Inches
Inches adjustment divided by the range in hundreds of yards equals MOA.
Desired MOA adjustment divided by the resolution of one click equals total adjustment in clicks.
= 20 clicks
1/4 (.25) minute clicks
I prefer to memorize my come-ups in clicks rather than MOA.
Total drop in clicks from a 100 yard zero minus the total clicks of all come-ups to the new zero range equals your comeup to that range. Start at 200 yards and work out.
Clicks at 500 yards minus come-ups to 200, 300, and 400 yards totaled equals come-up from 400 to 500 yards in clicks.
The height of an object in yards times 1,000 divided by the apparent height of the object in mils equals the range in yards. Height in meters yields range in meters.
Height X 1000
The apparent angle from vertical of mirage divided by 8 equals the windspeed in miles per hour. Mirage angle must be read with the wind blowing directly from the right or left. Turn your spotting scope if you have to.
The apparent angle from vertical of smoke, flags, or the arm pointing at lightly balled piece of paper dropped from the shoulder divided by 4 equals the windspeed in miles per hour.
The Marine Corps Windage formula:
Range in 100s of yards (600 yards = 6) times the wind in miles per hour divided by the constant C equals MOA change.
Range X MPH
For the M118 round at sea level
C = 15 for 100 to 500 yards
C = 14 for 600 yards
C = 13 for 700 to 800 yards
C = 12 for 900 yards
C = 11 for 1000 yards
For the M852 round at sea level
C = 13 for 100 to 200 yards
C = 12 for 300 to 400 yards
C = 11 for 500 to 600 yards
C = 10 for 700 to 900 yards
C = 9 for 1000 yards
To adjust wind speed for differences in wind direction from ninety degrees from sightline multiply total wind speed by the constant C.
MPH X C = adjusted MPH
If wind direction is 90 degrees from sightline C = 1.0
If wind direction is 65 degrees from sightline C = .9
If wind direction is 45 degrees from sightline C = .75
If wind direction is 30 degrees from sightline C = .5
If wind direction is 15 degrees from sightline C = .25
If wind direction is 0 degrees from sightline C = 0
To adjust range for an up or down angle shot multiply the actual range by the Constant C.
Range X C = adjusted range
For an up or down slope of 5 degrees from horizontal C = .99
For an up or down slope of 10 degrees from horizontal C = .98
For an up or down slope of 15 degrees from horizontal C = .96
For an up or down slope of 20 degrees from horizontal C = .94
For an up or down slope of 25 degrees from horizontal C = .91
For an up or down slope of 30 degrees from horizontal C = .87
For an up or down slope of 35 degrees from horizontal C = .82
For an up or down slope of 40 degrees from horizontal C = .77
For an up or down slope of 45 degrees from horizontal C = .70
For an up or down slope of 50 degrees from horizontal C = .64
For an up or down slope of 55 degrees from horizontal C = .57
For an up or down slope of 60 degrees from horizontal C = .50
For an up or down slope of 65 degrees from horizontal C = .42
For an up or down slope of 70 degrees from horizontal C = .34
For an up or down slope of 75 degrees from horizontal C = .26
For an up or down slope of 80 degrees from horizontal C = .17
For an up or down slope of 85 degrees from horizontal C = .09
For an up or down slope of 90 degrees from horizontal C = 0
To adjust elevation for an up or down angle shot multiply your total drop from the horizontal boreline by the constant C and hold low by that amount from your estimated zero.
Drop X C = hold UNDER
For an up or down slope of 5 degrees from horizontal C = .004
For an up or down slope of 10 degrees from horizontal C = .015
For an up or down slope of 15 degrees from horizontal C = .034
For an up or down slope of 20 degrees from horizontal C = .060
For an up or down slope of 25 degrees from horizontal C = .094
For an up or down slope of 30 degrees from horizontal C = .134
For an up or down slope of 35 degrees from horizontal C = .181
For an up or down slope of 40 degrees from horizontal C = .235
For an up or down slope of 45 degrees from horizontal C = .293
For an up or down slope of 50 degrees from horizontal C = .357
For an up or down slope of 55 degrees from horizontal C = .426
For an up or down slope of 60 degrees from horizontal C = .500
Bullet time of flight times the speed of the target lateral to the sightline equals total lead. Speed in feet per second yields lead in feet.
Time X Speed = Lead
Whenever I change ammunition, rifle, or altitude I work up a complete set of tables. A chronograph and a good ballistics program make this a whole lot easier. I record all my values in inches, MOA, and mils. For moving target leads I will also figure leads. I run all my charts from 100 to 1,000 yards in 100 yard increments. For no-reflex hits I also run a set of charts from 25 to 200 yards in 25 yard increments. I record the total drop from the muzzle at each range. I also record the bullet time of flight. I figure my come-ups, and back calculate from the windage tables to get my constants for the Marine windage formula. With those two progressions memorized I can handle most of my shooting chores without my tables, if needs be.
For my elevation tables I record the drop in inches, MOA, and mils at each range for a zero at each range. That's one hundred sets of numbers for the long range charts. I only calculate my short range tables for a 100 yard zero. That's 8 sets of numbers. For my short range elevation charts I don't bother converting to mils. I also record my actual sight settings for each zero range.
My windage tables yield inches, MOA, and mils for each range and run from 5 to 30 miles per hour in 5 MPH increments.
My moving target chart is calculated for a walk (3 MPH), a trot (6 MPH), and a dash (10 MPH). I figure each range and speed (30 sets of numbers) in inches, MOA, mils and "leads." A lead is equal to the approximate width of a human body in profile 12 inches. Leads are very easy to visualize. All moving target leads are figured from the center of the target.
I run my up/down slope adjustment charts from 5 degrees from horizontal to 60 degrees in 5 degree increments and list inches, MOA, and mils. Since this chart will not be used for quick targets-of-opportunity I calculate the hold under to be adjusted for, after the initial elevation adjustments have been made. Short range slope adjustment charts are critical for no-reflex shooting.
I also have charts listing the mil height and range for men 6 feet, 5 feet 9 inches, and 5 feet 6 inches tall as 6 feet is unusually tall for most parts of the world. That's another reason I use yards instead of meters. A six foot (2 yards) man appears 2 mils tall at 1000 yards. The mil-dot formula is easy to calculate for two yards. A man would have to be 6 feet 6 inches tall to measure two meters. They're even rarer than six footers. To plug an average man into the mil-dot formula you'd have to use 1.77 meters. A little less handy than 2 yards.
6 feet = 2 yards
5 feet 9 inches = 1.9 yards
5 feet 6 inches = 1.8 yards
The SEALs found the following changes in elevation applied to their M852 rounds with changes in temperature. The higher the temperature, the higher the bullet impact.
At 300 yards there is 1 MOA change in elevation per 20 degree change in
At 600 yards there is 1 MOA change in elevation per 15 degree change in temperature.
At 1000 yards there is 1 MOA change in elevation per 10 degree change in temperature.
Only by firing your rifle under field conditions can you determine how much effect temperature will have on your ammunition. If your computer generated charts don't match your field data you must go with the field data. Sometimes a change in ballistic coefficient will bring the computer in line with the real world.
The more of this information you memorize the better off you will be.