MOA trivia

[Deerstalker]

MOA Trivia 
(best with your morning coffee or when you have absolutely nothing to do)
MOA = Minute of Angle
1 MOA at 100 yards = 1” 
1 MOA at 100 Meters = 1.145” or 2.66 CM (39.37” = 1 meter)
(Note, how is the 1” at 100 yards calculated?)
1.   There are 7,200” in the diameter of a 100 yard circle.  36” x 100 yards x 2 = 7,200”.
2.   There are 21,600 minutes in a circle.  360 degrees x 60 minutes in one degree = 21,600 minutes.
3.   Formula for circumference of a circle = Diameter x Pi, 3.14159.  7,200” x Pi = 22,619.4” in the circumference of a 100 yard circle.
4.   1 MOA circumference at 100 yards = 22,619” divided by 21,600 minutes = 1.04719” for 1 MOA at 100 yards.
5.   1 MOA of 1.04719” at 100 yards is rounded to 1”.
6.   1 MOA at 200 yards = 2”, at 400 yards = 4”, at 800 yards = 8”, etc.
7.   1 MOA at 50 yards = ½”, 1 MOA at 25 yards = Ό”.
8.   1 MOA at 1 mile = 18.43”
9.   1 MOA on the Moon = 69.5 miles. (238,900 miles to the Moon)
The 1 MOA = 1” is an ARC measurement and not a straight line as it is a very small section, 1” of the overall circle circumference at 100 yards.

[dtdtdtdt]

Just for grins, now do the same analysis on radians and milliradians used by the military.  It remains a mystery to me. 

[Deerstalker]

Radians and MOA, Minute of Angle, Trivia
(Best with a 6 pack of BUD)

Circumference of a circle = 2 x Pi, Pi = 3.14159, 7200” in diameter of a 100 yard circle.
Circumference of a circle at 100 yards = 22,619.448”, 7200” x 3.14159 Pi.
6,283.18 MILLIRADIANS = 1 CIRCLE (Pi x 2, 3.14159 x 2 x 1000 = 6,283.18), Mathematical actual (MRAD)
6,400 MILLIRADIANS = 1 CIRCLE,  NATO rounded (MRAD)
21,600 MINUTES = 1 CIRCLE (360 degrees x 60 Minutes in 1 degree = 21,600 minutes)
1 MOA = 1.04719” at 100 yards, 22,619.448”/21,600 Minutes.  1 MRAD = 3.6” at 100 yards, 22,619.448”/6283.18 MRAD, Mathematical.  1 MRAD = 3.534” at 100 yards, 22,619.448/6400 MRAD, NATO rounded.
Scope settings MOA or MRAD.
It also depends on what your scope's notion of 1 milliradian is, because the NATO milliradian differs from the mathematical definition of a milliradian.

A mathematically accurate radian is that part of a circle where 2 * PI radians is a full circle, and a milliradian is 1/1000th of a radian, so a full circle is equal to approximately 6283.18 milliradians (2000 * PI).

But the NATO definition of a milliradian for use in ballistics is that a full circle is split into 6400 NATO milliradians.

Anyway, the difference is not very large, with mathematically accurate MRADs, 1 MRAD is 100 cm @ 1000 m, with 1 NATO MRAD, it is 98.2 cm @ 1000 m. For this reason, if your scope uses mathematically accurate MRADs, 1 MRAD is about 3.44 MOAs, but if it uses NATO MRADs, then 1 MRAD is 3.375 MOAs.

The distance of the reticle's movement per click is tan(angle) * distance, however, at longer distances this is not exactly equal to the change in point of impact, because of the difference between changes to the line of sight and changes in the bullet's trajectory.

degrees = MOAs / 60
MOAs = degrees * 60

degrees = MRADs / (PI * 1000) * 180
degrees = (MRADs / 6400) * 360 [with NATO MRADs]
MRADs = (degrees / 180) * PI * 1000
MRADs = (degrees / 360) * 6400 [with NATO MRADs]

MOAs = MRADs / (PI * 1000) * 10800
MOAs = (MRADs / 6400) * 21600 [with NATO MRADs]
MRADs = (MOAs / 10800) * PI * 1000
MRADs = (MOAs / 21600) * 6400 [with NATO MRADs]

[Fate]

Radians and MOA, Minute of Angle, Trivia
(Best with a 6 pack of BUD)

Circumference of a circle = 2 x Pi, Pi = 3.14159, 7200” in diameter of a 100 yard circle.
Circumference of a circle at 100 yards = 22,619.448”, 7200” x 3.14159 Pi.
6,283.18 MILLIRADIANS = 1 CIRCLE (Pi x 2, 3.14159 x 2 x 1000 = 6,283.18), Mathematical actual (MRAD)
6,400 MILLIRADIANS = 1 CIRCLE,  NATO rounded (MRAD)
21,600 MINUTES = 1 CIRCLE (360 degrees x 60 Minutes in 1 degree = 21,600 minutes)
1 MOA = 1.04719” at 100 yards, 22,619.448”/21,600 Minutes.  1 MRAD = 3.6” at 100 yards, 22,619.448”/6283.18 MRAD, Mathematical.  1 MRAD = 3.534” at 100 yards, 22,619.448/6400 MRAD, NATO rounded.
Scope settings MOA or MRAD.
It also depends on what your scope's notion of 1 milliradian is, because the NATO milliradian differs from the mathematical definition of a milliradian.

A mathematically accurate radian is that part of a circle where 2 * PI radians is a full circle, and a milliradian is 1/1000th of a radian, so a full circle is equal to approximately 6283.18 milliradians (2000 * PI).

But the NATO definition of a milliradian for use in ballistics is that a full circle is split into 6400 NATO milliradians.

Anyway, the difference is not very large, with mathematically accurate MRADs, 1 MRAD is 100 cm @ 1000 m, with 1 NATO MRAD, it is 98.2 cm @ 1000 m. For this reason, if your scope uses mathematically accurate MRADs, 1 MRAD is about 3.44 MOAs, but if it uses NATO MRADs, then 1 MRAD is 3.375 MOAs.

The distance of the reticle's movement per click is tan(angle) * distance, however, at longer distances this is not exactly equal to the change in point of impact, because of the difference between changes to the line of sight and changes in the bullet's trajectory.

degrees = MOAs / 60
MOAs = degrees * 60

degrees = MRADs / (PI * 1000) * 180
degrees = (MRADs / 6400) * 360 [with NATO MRADs]
MRADs = (degrees / 180) * PI * 1000
MRADs = (degrees / 360) * 6400 [with NATO MRADs]

MOAs = MRADs / (PI * 1000) * 10800
MOAs = (MRADs / 6400) * 21600 [with NATO MRADs]
MRADs = (MOAs / 10800) * PI * 1000
MRADs = (MOAs / 21600) * 6400 [with NATO MRADs]

Having two MIL reticle scopes and realizing their elevation and windage adjustments are in MOA... and reading up on all that stuff so I could interpolate, I decided it wasn't happening and was overcomplicating my life. Not in the military. Not in NATO forces. Not a sniper. Soooo...

I have a new scope coming tomorrow with a glass MOA reticle. See how that goes.

[Jshooter71]

Good stuff~

[Yogi]

One mil-radian is 10 cm at 100 meters.
Work backwards from there...

-Y

[HectorMedina]

Just for grins, now do the same analysis on radians and milliradians used by the military.  It remains a mystery to me.

Mrads are easy . . . as long as you are not "subject" of NATO, LOL!

Perhaps you would find interesting to read this:

https://www.ctcustomairguns.com/hectors-airgun-blog/mil-as-in-milliradian

;-)

Keep well and shoot straight!





HM

[Deerstalker]

One mil-radian is 10 cm at 100 meters.
Work backwards from there...

-Y

1 MRAD at 100 meters = 10 cm. (2 x PI x 1000 = 6283.185 MRADS in a circle). 100 meters = 10,000 cm x 2 = 20,000 cm in diameter of 100 meter circle.  20K x PI = 62,831.85/6,283.18 MRADS = 10 cm; for  (1 MRAD at 100 meters = 10 centimeters).

[avator]

Moving to optics gate for subject matter....

[mobilehomer]

1 MOA is 1.047" at 100 yards.  For simplicity sake, one mil = 1/1000 of distance to target.

[sscoyote]

I love playing the math game with shooting. Recently I've become reinterested in applying angular math for both downrange zeroing and rangefinding to iron sights in MOA. One part of the equation has a factor of 3438 for MOA, and while I was playing with it I though hey that 3438 factor is similar to 3.438 MOA to 1 Mil. (x 1000=3438), so I figured that if I replaced the 3438 factor with 1000 then the calculation would be in milliradians, and it worked. My testing platform is a simple 1377 which has a great iron sight system for this application. This is about the only thing I've ever found in my life where math is actually fun.