The actual dot is called a reticle, there are different types of reticles available on red dot scope...here are some examples:
MOA is what they are usually measured in. MOA is: (From Wikipedia - very good definition)
"Sights that use dot reticles are almost invariably measured in minutes of angle, or "MOA". One of the most common reticles used in red dot sights is a small dot, covering 5 MOA (1.5 mrad), illuminated by a red LED, hence the common term "red dot sight". MOA is a convenient measure for shooters using English units, since 1 MOA subtends approximately 1.0472 inches at a distance of 100 yards (91.44 m). This is generally rounded to 1 inch at 100 yards, which makes MOA a handy unit to use in ballistics. The 5 MOA (1.5 mrad) dot is small enough not to obscure most targets, and large enough to quickly acquire a proper "sight picture". For many types of action shooting, a larger dot is preferred; 7 (2.0 mrad), 10 (2.9 mrad), 15 (4.4 mrad) or even 20 MOA (5.8 mrad) dots or rings are used; often these will be combined with horizontal and/or vertical lines to provide a level reference."
Red dots usually mount to a rifle or pistol like any other scope would fit on a rail of some type, typically picatinny or weaver. The only difference between those types of rails is the spacing of the slots in them. The actual sight is adjusted or sighted in using a vertical and horizontal dial that adjust the dot in relation to the point of impact of the projectile. The object here is consistency. The "technical" name for horizontal and vertical adjustments are windage and elevation.
I usually mount the scope to a weapon then I use a tool call a bore sight to adjust the site so it is on the paper. A bore sight is a small laser you insert into the barrel of the weapon that points to the target. Adjust your red dot so that the red dot reticle lines up perfectly with the bore sight laser. This will get you on the paper. I then shoot a few rounds to warm the barrel up. Once this is done change to a sighting in target...it usually has a grid on it. Shoot one round and adjsut...rinse and repeat until the bullet hits the same spot consistently where the red dot reticle is.
Red dot sights usually have really good eye relief, this mean that unlike most scopes, where your eye needs to be within a certain distance from the scope to use it effectively, the red dot can be utilized from all distances (or most). Red dots are also usually low magnification, if you need something to really reach out and touch someone go with a regular scope.
Red dots also use batteries so keep that in mind and have extras because it would suck to lose the dot when you need it most....which leads me to this...be an expert with your iron sights before worrying about scopes of any type!!!
...that is all.
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