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Zero a red dot ?

If your AR rifle's red dot sight has its center 2.5" above the center of your rifle's bore...
(and I'm taking that figure from this LuckyGunner article on "mechanical offset"
which means height of sights over bore)

https://www.luckygunner.com/lounge/mechanical-offset-why-your-ar-15-shoots-low/

then I here's what I get from the GunData.Org ballistic calculator for a standard 55 gr. FMJ load,
when the zero distance is 40 yards:

20 yards = your bullets hit 1.2" low, compared to your point of aim.
40 yards = zero, dead-on.

100 yds. = 2.6" high

175 thru 200 yards = all about 3.5" high, give or take a fraction of an inch.

250 yds. = bullet is back down to only 1.6" above aiming point.

275 yds = Second Zero point. Dead-on .

(Now look how fast the bullet drops over the next 100 yards, compared to how little it rose above the line of sight in the first 100 yards.)

300 yards = 1.75" low.
325 yds. = 4" low.
350 yds. = 7" low.

and at 400 yards, it's 14" low, and I hope you remembered to aim a bit high, since that much drop would be bad if you didn't compensate for it.

Still, the 40-yard zero, on an AR in .223 with 55 gr. bullets that have an initial velocity of 3200 f/sec,
can be sighted at 40 yards and you can just "forget it" for any shot out to 325 yards.
Just aim dead-on, and your bullet will ALWAYS be within 4" of your aiming spot.
Could be 4" high around 175 yards, or 4" low around 325, but from point-blank to 325 you just put the crosshairs on your target and press the trigger.
 
Depends. If just a red dot - 100 yards. If something like an EOTech with a BDC ish reticle - either zero at 50 (where most are designed to be zero'd, and that is also your 200'ish mark), or still zero at 100 and work your ballistics around the extra reticle reference points.
Eotechs reticle is actually meant for 100yd for the bottom tic to do the 7&10 holds if I Remember correctly
 
I like 50 yard zero for irons and an optic that is co-witnessed to the irons. It gives a nice flat trajectory from 0-200 yards. Just remember that hold over inside 50 yards. See yellow line:

1205A46E-E80F-4F5E-86CF-77AF4A570D2B.jpeg
 
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