# Gun sighting equation and trigonometry **URL:** \ **Category:** Factual Questions\ **Tags:** science-math\ **Created:** [January 14, 2026, 10:08pm UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697 "2026-01-14T22:08:03Z")\ **Posts on this page:** 16\ **Page:** 1
**Author:** ![carnivorousplant](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/carnivorousplant/32/3563_2.png) [@carnivorousplant](https://boards.straightdope.com/u/carnivorousplant)\ **Post date:** [January 14, 2026, 10:08pm UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/1 "2026-01-14T22:08:03Z")
There is an equation for aligning the rear sight of a firearm. The rear sights can be moved left or right. The movement = (error/distance)x(sight radius) Error=the distance between the point of aim and the actual place bullets go. Distance=length to target. Sight radius=distance between the front and rear sights. I can see that a right triangle is created by the muzzle to the gun, the bulls eye and the place where bullets actually hit. Given opposite/adjacent, the equation gives the tangent of the angle between bulls eye and actual place where bullets go. Why the sight radius? I see that it preserves units, and presumably gives us a sine to change the tangent into an x coordinate, but it is along the the distance to the target. I hope someone better at trig than I can explain it. ---
**Author:** ![Timz](https://avatars.discourse-cdn.com/v4/letter/t/6a8cbe/32.png) [@Timz](https://boards.straightdope.com/u/Timz)\ **Post date:** [January 14, 2026, 10:11pm UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/2 "2026-01-14T22:11:50Z")
Don’t see what’s puzzling you. The rear sight moves in a straight line, perpendicular to the muzzle? If so, two similar triangles: front sight to bullseye to where the bullet hits, and front sight rearward along the barrel centerline, then right-angle to the rear sight. ---
**Author:** ![carnivorousplant](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/carnivorousplant/32/3563_2.png) [@carnivorousplant](https://boards.straightdope.com/u/carnivorousplant)\ **Post date:** [January 14, 2026, 10:16pm UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/3 "2026-01-14T22:16:57Z")
Eureka! Thanks, Timz. I love the ‘Dope. ---
**Author:** ![Timz](https://avatars.discourse-cdn.com/v4/letter/t/6a8cbe/32.png) [@Timz](https://boards.straightdope.com/u/Timz)\ **Post date:** [January 14, 2026, 10:20pm UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/4 "2026-01-14T22:20:02Z")
I should have thought a little more. We’re assuming the bullet goes where the riflebarrel is pointed, so the above similar triangles aren’t right. ---
**Author:** ![carnivorousplant](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/carnivorousplant/32/3563_2.png) [@carnivorousplant](https://boards.straightdope.com/u/carnivorousplant)\ **Post date:** [January 15, 2026, 12:18am UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/5 "2026-01-15T00:18:43Z")
I think our error is the way the barrel is situated in relation to the rest of the gun. The barrel forms an arm of the triangle, we must adjust the sight to follow the same (similar) arm. ---
**Author:** ![Isilder](https://avatars.discourse-cdn.com/v4/letter/i/cc9497/32.png) [@Isilder](https://boards.straightdope.com/u/Isilder)\ **Post date:** [January 15, 2026, 7:45am UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/6 "2026-01-15T07:45:26Z")
Think of it as correction = error x ( sight radius/distance ). There are two similar triangles, 1. the triangle to target, with error at the far end. 2. the triangle with the sights and the sight radius, with correction in the place of error. If the error is 1 metre ( = 1000mm) out at the target, but the sight radius is a 1000th the distance to target, the adjustment of this sight is a 1000th the error, ie, 1 mm. ---
**Author:** ![Spoons](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/spoons/32/3141_2.png) [@Spoons](https://boards.straightdope.com/u/Spoons)\ **Post date:** [January 15, 2026, 9:11am UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/7 "2026-01-15T09:11:24Z")
> [@carnivorousplant](#): > > The rear sights can be moved left or right. Known as “windage.” The rear sight can also be moved up or down, known as “elevation.” At least, that’s how things were on my competition rifle, with iron sights. Does elevation affect your formula? If so, how? (I know nothing about trigonometry, and very little about equations, so my question might seem dumb, but I do know how to sight in a rifle. Maybe I knew both of those without realizing it.) ---
**Author:** ![Crafter\_Man](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crafter_man/32/458_2.png) [@Crafter\_Man](https://boards.straightdope.com/u/Crafter_Man)\ **Post date:** [January 15, 2026, 11:14am UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/8 "2026-01-15T11:14:35Z")
> [@Spoons](#): > > The rear sight can also be moved up or down, known as “elevation.” Or the front sight; on my FALs and Ruger 10/22s, elevation is adjusted by moving the front sight up or down. Also note that simple trigonometric models are _very_ approximate. There are a lot of variables that affect PoI. A model that accounts for all variables is quite complex. Practically speaking, sight adjustments are performed during target practice. Shoot three rounds, measure PoI error (for elevation and windage), adjust sights, shoot three rounds, measure PoI error, adjust sights - lather, rinse, repeat. Each “click” in the adjustment screw roughly equates to an MOA value. ---
**Author:** ![thelurkinghorror](https://avatars.discourse-cdn.com/v4/letter/t/7c8e57/32.png) [@thelurkinghorror](https://boards.straightdope.com/u/thelurkinghorror)\ **Post date:** [January 16, 2026, 4:09am UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/9 "2026-01-16T04:09:09Z")
Yeah, usually windage is on the back sight and elevation on the front. Scopes and red dots of course only require 1 point of attachment, so they have both on separate controls. > Each “click” in the adjustment screw roughly equates to an MOA value. Or increasingly, milliradians. _Usually_, 1 click = 1/4 MOA or 1/10 MIL. Each has their own fans, usually MOA for hunting as it’s less controlled but 1 MOA ≅ 1 inch at 100 yards (really 1.047”) but MIL is metric adjustments. ---
**Author:** ![carnivorousplant](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/carnivorousplant/32/3563_2.png) [@carnivorousplant](https://boards.straightdope.com/u/carnivorousplant)\ **Post date:** [January 17, 2026, 10:34pm UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/10 "2026-01-17T22:34:16Z")
> [@Spoons](#): > > Does elevation affect your formula? If so, how? It does not consider elevation. ---
**Author:** ![carnivorousplant](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/carnivorousplant/32/3563_2.png) [@carnivorousplant](https://boards.straightdope.com/u/carnivorousplant)\ **Post date:** [January 17, 2026, 10:35pm UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/11 "2026-01-17T22:35:40Z")
> [@Crafter\_Man](#): > > Also note that simple trigonometric models are _very_ approximate. There are a lot of variables that affect PoI. A model that accounts for all variables is quite complex. It worked spot on with the pistol rest. In my hands is another matter. ---
**Author:** ![thelurkinghorror](https://avatars.discourse-cdn.com/v4/letter/t/7c8e57/32.png) [@thelurkinghorror](https://boards.straightdope.com/u/thelurkinghorror)\ **Post date:** [January 19, 2026, 7:26pm UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/13 "2026-01-19T19:26:11Z")
Welp, looks like not even SDMB is safe from bot answers… ---
**Author:** ![engineer\_comp\_geek](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/engineer_comp_geek/32/504_2.png) [@engineer\_comp\_geek](https://boards.straightdope.com/u/engineer_comp_geek)\ **Post date:** [January 20, 2026, 8:43pm UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/14 "2026-01-20T20:43:59Z")
> [@thelurkinghorror](#): > > looks like not even SDMB is safe from bot answers… The spammer-bot has been wished away to the cornfield. ---
**Author:** ![carnivorousplant](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/carnivorousplant/32/3563_2.png) [@carnivorousplant](https://boards.straightdope.com/u/carnivorousplant)\ **Post date:** [January 21, 2026, 4:42pm UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/15 "2026-01-21T16:42:24Z")
To what do you refer? ---
**Author:** ![jnglmassiv](https://avatars.discourse-cdn.com/v4/letter/j/f07891/32.png) [@jnglmassiv](https://boards.straightdope.com/u/jnglmassiv)\ **Post date:** [January 21, 2026, 4:49pm UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/16 "2026-01-21T16:49:21Z")
There was some spam, gone now. I’ve had some experience with the long distance shooting hobby with regard to their scales, for weighing. They load their own rounds and, of course, the bullets are carefully selected for weight & dims but they also measure the powder charge. It’s one of the few places that the grains unit of measure remains standard. And some humidity specs. ---
**Author:** ![carnivorousplant](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/carnivorousplant/32/3563_2.png) [@carnivorousplant](https://boards.straightdope.com/u/carnivorousplant)\ **Post date:** [January 21, 2026, 4:56pm UTC](https://boards.straightdope.com/t/gun-sighting-equation-and-trigonometry/1026697/17 "2026-01-21T16:56:44Z")
Thank you.