This app was mentioned in 12 comments, with an average of 1.92 upvotes
For anything closer than your primary zero.
When you zero in your weapon (let's say at 25 yards, but the distance is technically irrelevant), you have a primary and a secondary zero. That means your pellet will intersect at that elevation at 25 yards, and then again at that same elevation let's say 70 yards. This is because every round that you shoot, be it a pellet gun, or 7mm hunting rifle, is effected by gravity. What this does to your round is make the pellet trajectory travel in an arc.
The easiest way to figure out how much hold under you need is to test it! I'd set up targets at 25 yards and 10 & 5 yards, and then 50 yards. Sight your scope or iron sights on for dead center at 25 yards. After that's done, aim at a target at 10 yards and see how much lower the pellet hits from where you aimed. Do it again at 5 yards, and it will be significantly lower than what 10 yards was. At 50 yards, you may have to hold under a bit, because your pellet is probably still rising, but at 125 yards, you'll probably need some hold over so your pellet won't land too low.
Now just remember where those points are at, and you are ready to go!
But there is something else you can do too, and install this ballistics calculator app on your phone!
https://play.google.com/store/apps/details?id=com.borisov.strelok
Have you tried Strelok? I have no idea about shooting, so I don't know if it will cover your needs, but some of my friends who visit the range frequently use it a lot.
The free version of Strelok is already a good start ... available on Android. https://play.google.com/store/apps/details?id=com.borisov.strelok&hl=en
You can also find online ballistic calculators..
You will need things like
bullet weight
bullet length
Ballistic Coeff ( g1 or g7 )
muzzle velocity of your load
some will require twist rate of barrel
This will already give u an idea. Then other factors like
wind
temp
humidity
atmospheric pressure
This is the one that Generalfeldmarschall Erwin Rommel preferred to use when on manouevers:
> https://play.google.com/store/apps/details?id=com.borisov.strelok
Using this, they say that he could hit a Bedouin Camel Jockey right between the humps from over 4 km away with the main gun of his command Panzer.
With a proper zero there are two points of line-of-sight convergence. It's possible that you don't have the same zero for both sights, but they have a similar point of convergence.
Move your target and see if you're still on. Try using Strelok to calculate your zero for a Maximum Point Blank Range with a threshold of ~1.5 inches-3 inches, depending on how parabolic you like your flight. The threshold is how far from zero(above or below) the round is allowed to get during flight.
Go with the recommended distance to keep the BDC true. If you want to deviate, get a chronograph and calculate the zero with Strelok
Strelok is a decent free ballistic calculator: https://play.google.com/store/apps/details?id=com.borisov.strelok&hl=en
And Shot Timer is, well, a shot timer: https://play.google.com/store/apps/details?id=com.futurewisetechnologies.mobile.shottimer&hl=en
Before I got a laser rangefinder, you used to be able to use Google Maps in map or satellite view to give you a point-to-point range to your target too, if you could locate where it and yourself were on a map.
A fifty yard zero can easily be adjusted to 25. Use this: https://play.google.com/store/apps/details?id=com.borisov.strelok&hl=en
This rifle?
http://www.hobbyconsolas.com/sites/default/files/users/F%C3%A1tima%20Elidrissi/shooter_dentro_0.jpg
As for the range computers, long-range shooters absolutely use them. Military uses them a whole lot. They even had analog ones on battleships for the same reasons.
Basically: Everything falls to the ground at 9.8m/s^2. That's gravity. You shoot a bullet, it's gonna drop. To make a hit at long-range, you need to know by how much it's going to drop.
Then, you've got wind. Wind is a bitch. You're never really sure what wind is doing, and it's always changing.
Next, air resistance. More drag = less speed. Less speed= more drop because it takes longer for the round to get there. Different elevations have different air pressures. More pressure = more air hitting the bullet = more resistance and more drop.
There are TONS of factors once you get into long-range. A 'range computer' (or cell phone calculator like Strelok just makes the math easier.
http://i.imgur.com/W7wkDas.jpg?1
Also note: If you're a sniper in position to take a shot, you've probably got a few hours to sit around ranging and calculating things. Also, the 'longest kill-shot ever' back in 2010 was because the insurgents walked into their practice area. They were already dialed in with their DOPE for that spot, and pew pew. Done.
(Dope = Data On Previous Engagement, aka the scope settings and wind holds to ensure a round on target)