Table of Contents
- 1. Introduction
- 2. Grouping
- 3. Getting on paper
- 4. Making adjustments
- 5. Troubleshooting
- 6. Sidebars
- 7. Further reading
This article will give an introduction about how to sight in a scope on a rifle. This article assumes that the scope is already mounted, and you are ready for your first range session with the new scope.
Sighting in a scope is not difficult, but there are some important concepts that will make the task a lot easier. While this article will focus on scoped rifles, many of the principles apply to any type of sight on any type of firearm.
First, let's discuss what "sighting in" really means. When you sight in a rifle, your goal is to adjust the sight so that all of your shots form a group which is centered on your intended point of impact.
The statement above may seem trivial, but there are two points in that statement that might not be obvious. One point is the term "point of impact" as opposed to "point of aim." The distinction between these terms is discussed later in this article.
The other important point is that the goal is to shoot a group. People often think that the important part of sighting in is to adjust the sight. But the first and most important step is to make sure that the rifle shoots acceptable groups. If the rifle will not group well, then there may be a mechanical problem. And you will need to understand that problem before you can get satisfactory results.
So logically, the process of sighting in a rifle is: shoot an acceptable group, then adjust the scope so the groups land where you want them.
However, in the real world, you cannot shoot a group until your shots are hitting paper. So you may have to adjust the scope enough to get on paper, then shoot a group, then make the rest of your adjustments. The rest of this article will discuss these steps. Shooting groups will be covered first because it is a central principle.
There are a few terms you should be familiar with if you are working with scopes.
- The reticle is the crosshairs or other markings which are used to identify the aiming point. Modern scopes are available with a wide range of reticle designs.
- The knobs which are used to adjust a scope are called turrets.
- Adjustment clicks
- Scope adjustments are often described in clicks. When you turn the adjustment turrets, you should feel mechanical clicks. Each click will only require a very slight movement of the turret. On some scopes the clicks are very defined, and on other scopes, the clicks are harder to feel. If you turn the turret gently, you should feel the clicks.
1.2 Useful supplies
You may find some supplies helpful during the process of zeroing your scope.
- You will want a large piece of paper for your target. The larger the paper is, the easier it will be to get your shots on paper. You do not necessarily want a large bullseye since that can create a coarse sight picture. But the paper should be at least 2 feet square.
- It is very helpful if you can see bullet holes in the target. If your scope does not have enough magnification to see bullet holes, then a spotting scope is helpful. Binoculars may be OK if nothing else is available.
- To shoot good groups, you need to be in a comfortable position with a rest for your rifle. A shooting sled, sandbags, pieces of carpet or other supplies may be helpful. Consider what supplies might help you get in a comfortable shooting position.
- A pencil and paper can be useful to make notes.
When you mount a new scope on a rifle, you want to make sure that you can shoot acceptable groups before you try to adjust the point of aim. If the groups are not good enough, then there may be a problem with the mount, the scope or the rifle. You need to identify the problem before you go further. If you go ahead and adjust the scope, it is likely that you will need to adjust it again after the problem is resolved. In that case, the time and ammunition spent adjusting the scope would be wasted.
Most of the time you will have no problems shooting a group. But if you do have an issue, you will find more information in the troubleshooting section of this article.
2.1 Shooting groups
To test your groups, you want to shoot from a comfortable rested position. And you want to do everything as consistently as possible from shot to shot. The goal is to get all of your shots as close together as possible. As long as the shots are on paper, it does not matter if they are close to the bullseye. After you have established that the groups are good, then we will discuss how to zero in the scope so the groups hit the center of the target.
To shoot consistently, you need to take a consistent sight picture on every shot. Aiming for the center of a fairly small bullseye often gives a good visual reference. But some people get a better visual picture if they put the crosshairs right at the bottom of the black bullseye. And some people prefer to use a sight in target with a red diamond or square. The important thing is to choose a visual picture that you can hold consistently.
Remember that the only goal is to get all your shots close together. If your first shot is one foot high and left, that is fine. Try to shoot the next shot the exact same way you shot the first one. If all your shots are close together, but the group is high and left, then you are in great shape. Do not try to adjust your point of aim so the shots will hit the bullseye, just continue to hold the same picture for each shot.
2.2 What is an acceptable group?
Earlier, I said that you need to make sure the groups are "acceptable." Well, what does acceptable mean? Acceptable means that the groups are good enough to meet your requirements for this rifle.
For a lever action carbine that will be used in dense brush, a 4" group at 75 yards might be acceptable. And for a precision rifle, a 2" group at 100 yards might be terrible. The definition of acceptable is based on your own requirements. Also, on your first day with a new scope, you may not shoot to your full potential. So it is OK if the groups are a little short of your expectations. But they should not be too far off.
As an aside, I know some readers may scoff at a 4" group at 75 yards. But I consider anyone who can deliver that accuracy quickly from a standing position to be an effective rifleman.
2.3 How many shots do I need in a group?
An important question about shooting groups is "How many shots will it take to know that the groups are acceptable?" The answer is either "about five" or "it depends." A better answer might be that you need continue shooting a group until you are confident that you understand the results. If you shoot five shots and they are all in a tight group, then are ready to make adjustments. In rare cases, you might shoot three excellent shots and be fully confident that everything is fine. That is OK, but be aware that with a small number of shots, you can get misleading results due to coincidence.
A common result when you shoot with a new scope is that the groups are hard to understand. For example, suppose you expect your rifle to shoot 2" groups at 100 yards. You fire five shots, and you know that you pulled one shot off target. Three of the four good shots form a 2.5" group, but the fourth shot spreads the group to 4". So what does this mean? It means that you need to shoot more to get a clear result. And you need to have patience, because this issue is very common.
Also, since you know you pulled a shot, that shot doesn't count, and you need to reshoot it. But in this case, you should shoot several more shots. Catch your breath, recheck that your position is stable and comfortable, and shoot three to five more shots. If the rest of your shots are pretty close to a 2" group, then you are ready to make adjustments. If the group is too large, or there are flyers you can't explain, then you will find more suggestions in the troubleshooting section.
2.4 Groups scale proportionally with distance
Another important concept about groups is that group size scales proportionally with distance. In other words, if you move to twice the distance, then your groups will be twice as large. Similarly, at half the distance the groups will shrink by half. So if your goal is to get 2" groups at 100 yards, but you are sighting in at 50 yards, then you should expect 1" groups at 50 yards. Also, if you are sighting in at a shorter distance than you intend to shoot, then you should check your groups at the longer distance as soon as you can.
3 Getting on paper
Ideally, you would like to shoot your first group before making adjustments to the scope. But as a practical matter, you can't check groups if you are not hitting paper. So you may need to make a coarse adjustment to get on paper before you can shoot your first group.
3.1 Taking your first shots
When you take your first shot with a newly mounted scope it is very important to be careful. You really do not know where your first shot will land. I have seen the first shot with a newly mounted scope miss by 6 feet at 100 yards. That is a wide enough miss that on some ranges the shot might not hit a safe part of the backstop. The best option is to take the first shots at a much shorter distance. If your range will allow it, 25 yards is a good distance for the first shot. Most of the time your first shot at 25 yards will land on a 2 foot square piece of paper. Keep in mind, that at one quarter the distance, your misses will be off by a quarter as much. So a shot that would miss by 4 feet at 100 yards will only miss by 1 foot at 25 yards.
If your first couple of shots are on paper at 25 yards, then you could go ahead and shoot your first group at 25 yards. Or if your shots are quite close to the bullseye, you could safely move back to a longer distance. However, you may find that you are far from the bullseye at 25 yards, but you still prefer to test your first group at 100 yards. In this case, you can adjust the scope enough to get on paper at 100 yards. You do not need to get the scope perfectly adjusted, you just need to be close enough to hit paper at longer distance. The section of this article on making adjustments will describe how to figure out the number of clicks to move the scope.
If you do shoot groups at shorter distance, just remember to scale things appropriately. So if you expect 4" groups at 100 yards, then you should expect 1" groups at 25 yards.
3.2 Bore sighting
Bore sighting is a process for aligning a scope with the bore without firing the rifle. If you are working with scoped rifles, you should have a general understanding of bore sighting. Bore sighting is often done with a special laser device. On some rifles, bore sighting can also be done by visually looking down the bore.
A common way to bore sight a rifle is to use a laser bore sighter. A laser bore sighter is a device that aligns with the bore of a rifle and shines a laser where the bore is pointed. The laser can be seen on a surface some distance away, and then the scope can be aligned with the laser. Because the scope sits above the bore, the crosshair usually needs to be centered above the laser. A bore sighter will come with instructions describing exactly how the scope should be aligned with the laser at specific distances.
On bolt action rifles, you can remove the bolt and look directly down the bore. Since you can see down the bore, it is possible to bore sight these rifles visually. To visually bore sight a rifle, you need a way to hold the rifle firmly in place. First you look carefully through the bore and align the bore with a target. Then you lock the rifle in place with the bore pointed at the target. Now that you know where the bore is pointed, you can align the scope reticle to the same spot. Note that it is possible to visually bore sight an AR15 type rifle by using just the upper receiver with the bolt carrier removed.
If a gunsmith mounted your scope for you, he probably bore sighted it. When someone professionally mounts a scope, bore sighting is generally a part of the job.
But the most important thing to know about bore sighting is that it is not very precise. Whether it is done with a laser or visually, bore sighting is difficult to do accurately. Laser bore sighters seem like they would be very accurate, but in the real world, the results are mixed. A rifle that has been properly bore sighted should be on paper at 25 yards, but it may not be on paper at a longer distance. This is one of the reasons that you should take your first shots at a short distance.
3.3 Getting on paper with help from a spotter
If your shots do not hit paper, then you often can't tell where they landed. And if you don't know where the shots landed, then you don't know which way to adjust the scope. The ideal thing to do in this situation is move closer, but on some ranges that is not possible. If your range has a backstop where hits are visible, then there is another way to get on paper. You can have someone help you by spotting your shots. At the range where I shoot, the backstop is a dirt berm, and this method works well in that environment.
To get on paper with the help of a spotter, you and your spotter need to agree on an easily visible target. A piece of orange clay pigeon on the berm works well. Then you shoot at the target and your spotter tells you where the shot landed. You should shoot at least two shots to be sure the results are consistent, but this does not need to be an extremely precise process. The only goal here is to figure out where the shots hit, and then adjust the scope to get your shots on paper. Once your shots are within 10 inches of the bullseye, you should be able to hit paper and shoot your first real group.
4 Making adjustments
Adjusting a scope seems pretty straightforward, and indeed it is not difficult. But there are still some questions which frequently arise.
To find the basic information about adjusting your scope, you should look in the manual. But usually the most important information is printed on the scope itself. The key things you need to know are which way to turn the adjustment turrets and how much each click of adjustment moves the reticle. However, if this information is unavailable, it is possible to figure it out. I will describe how to figure out the adjustments work later in this section.
It is common for a scope to be pretty far off initially, so your first adjustments may be quite large. Keep in mind that the scope adjustments are proportional to distance just like group size. Let's consider a scope where each adjustment click is 1/4 inch at 100 yards. So at 25 yards, each click would only be 1/16 inch. So to make a 10" adjustment at 25 yards, you would figure 16 clicks per inch, times 10 inches, equals 160 clicks. Note that if you are 10" off at 25 yards then you would be 40" inches off at 100 yards, and most likely would be off the paper.
To make a large adjustment like 10" at 25 yards, do not try to count 160 clicks. Just count the number of clicks in 1/4 turn of the turret. Then make your adjustments in 1/4 turns until you are pretty close. For example, if there are 15 clicks in a quarter turn, then 10 quarter turns will be 150 clicks, which is close enough to 160 for the first adjustment. And 10 quarter turns is 2.5 rotations of the turret, so it is easy to do. Sometimes people are hesitant to move more than a few clicks at a time. But if you really need to move 160 clicks, then doing it in little bits would take all day.
When you make large adjustments it will become clear how well calibrated the clicks are. In this case, you expect 2.5 turns of the turret to move the point of impact a bit less than 10 inches. If the adjustment actually moves more or less than that, then you will be able to estimate how much each click really moved the point of impact. With inexpensive scopes, imprecise adjustments are not uncommon. One click might move the reticle 1/3" instead of 1/4". If you only moved a few clicks you would not notice the difference, but if you move 30 clicks the difference is noticeable.
Making a significant adjustment is also how you can figure out how the adjustments work if you have no documentation. Just shoot a group, then turn one turret a half turn and shoot another group. You will know which way the shots moved, and by how much.
I have also seen a case where a scope was documented to have 1/4 inch clicks, but they were actually 1/2 inch. This became apparent after I turned one turret a full turn and the adjustment went too far. After that, I understood how the adjustments really worked. And you should not be afraid of adjusting too far. If you overshoot, just adjust back.
After each adjustment, you need to shoot a few shots to see where you are hitting. But since you already know that the rifle is grouping acceptably, two or three shoots is usually enough.
When you are making large adjustments, it is possible that you will hit the adjustment limit of the scope. If the adjustment turret feels like it has hit a stop, do not try to turn it further. You might damage the scope if you try to force it. If the scope will not adjust enough to get it sighted in, then you will probably have to take the scope off and remount it. This is an uncommon problem, but it does happen occasionally. The troubleshooting section of this article has advice about what to do if you run out of adjustment.
The total amount of adjustment varies with different scopes. For many scopes, the adjustments allow about 5 feet of adjustment in each direction at 100 yards. That means there would be 15" of adjustment at 25 yards. However, some scopes have more than 5' of adjustment, and others have considerably less. The manual usually states the total range of adjustment, but for some scopes it may not be listed. The available amount of adjustment also depends on whether the scope was at the midpoint of the adjustment range when you started.
After you make coarse adjustments to get within an inch or two, you can make smaller adjustments until you are sighted in well enough for your intended purpose. You may want to finish by shooting another five shot group just to be sure that group is small and centered.
Most of the time it is not difficult to sight in a new scope, but there are some problems which can occur. I do not want to make you nervous by focusing on rare problems. But to have good general knowledge about scopes, you should be aware of how to resolve some potential issues. For most of you, this section will provide background knowledge that you will not need to use.
5.1 If the rifle will not group
As I mentioned at the beginning, it is very important to test that your rifle groups acceptably. Shooting a good group demonstrates that everything is working correctly. If you find that the rifle will not group, there are many possible causes. Some of the potential issues are: the scope, the mount, the shooter, the rifle and the ammunition. But the most common causes are the mount and the shooter.
To find and fix the problem, you need to change one component at a time and see if the groups improve. The most common cause of poor groups with a newly mounted scope is the mounting hardware, but let's talk first about problems with the shooter.
Shooting good groups is not easy. It takes practice to shoot good groups, especially with a high powered rifle. If your rifle will not group well, and you do not have much experience shooting groups, then you should have an experienced shooter shoot the rifle. And you should not be embarrassed to ask for this help. There is nothing wrong if you do not excel at a skill that you have not had a chance to practice much. You will have more chances to practice after the rifle is sighted in. Having someone else shoot the rifle is also a pretty easy test since it does not require changing any components. If the rifle groups well for another shooter, then there is no mechanical problem.
Now, lets talk about the most common source of mechanical problems, which is the scope mount. Very often the mount loosens up a little within the first few rounds of shooting. Sometimes it loosens enough that you can feel a wobble. But even if the mount feels tight, it may still be the problem. The mount may seem tight, but still allow the scope to shift during recoil. You should check all the mounting screws. If any of the screws are loose, then tighten them and shoot another group.
If the groups are poor, and no screws are loose, then the mount is still a likely culprit. You should remove the scope and remount it with extra care. This process is described later in this article.
I rarely see problems that are not resolved by remounting the scope. But it is possible for the scope, the rifle, or even the ammunition to be defective. If you suspect this is the issue, you need to test different components to narrow down the problem. For example, you could put a different scope on the rifle, or you could put the new scope on a different rifle. You could also try shooting the rifle with iron sights. But overall, problems with newly installed scope mounts are fairly common, and mechanical issues with the other components are quite rare. So you should not worry about these issues unless you encounter them.
5.2 If you run out of adjustment
If the scope starts out very far off target, then you may not be able to adjust far enough to get it zeroed. For example, if the first shots are 2 feet off at 25 yards, then that is equal to 8 feet off at 100 yards. Many scopes do not have that much adjustment. If the scope is way off, then you can try to zero it. But you should be prepared to stop if you find that the adjustment turret does not want to turn any further.
If the scope is very far off, it is possible that something is wrong with the mounts or the scope, but most of the time this issue is resolved by removing the scope and then remounting it with extra care. Remounting the scope is described in the next section.
If you have carefully remounted the scope, and it is still very far off, then ask a professional for help. You could talk to a gun store or a gunsmith. It is possible that some part of the mount is defective or is not the right part for your rifle.
5.3 Remounting a scope with extra care
To resolve certain problems with a newly mounted scope, I recommend that you remove the scope and mounts, and then remount them with extra attention and care. Often when I tell someone how to remount a scope, he responds "I mounted this scope myself, and I exactly followed all of those steps the first time." I always believe that it was done carefully the first time, but I have still seen problems resolved by doing it again. I don't know why the second time is the charm, but sometimes it is.
The first step to carefully remounting a scope is to take everything apart. Take the scope and rings off the mount, and remove the mount from the receiver. If the mount is very firmly attached to the receiver, you might choose to leave it in place and just inspect it carefully, but it is better to take everything apart.
Now inspect all of the parts, including the screws, very carefully. You might use a magnifying glass. You want to look for any burrs, lumps, or manufacturing imperfections which might cause parts to sit unevenly. You also want to look for any wear marks showing where parts did not mate well. When you examine the screws, pay particular attention to the mating surfaces of the screw heads. Usually, you will not find anything during this inspection process, but it is still important to complete these steps carefully. If you do find any defects, you may be able to dress the area with stones or sandpaper, or the part may need to be replaced.
After you are confident that all the parts are fine, then pay careful attention that everything stays correctly aligned while you reassemble each component. It is very important to tension the screws evenly. When you attach the mounts to the receiver, you want to get all of the screws just barely snug before you tighten any of them. Then you want to tighten them a little at a time in an alternating pattern like you would use for lug nuts on a tire. Make sure that tightening the screws does not pull anything out of alignment. Then follow the same process to tighten the screws on the rings.
As I mentioned at the beginning, it is likely that all of this is the same procedure that was used the first time the scope was mounted, but doing it again may still resolve issues.
In a magazine article, a sidebar is a separate standalone section that goes in its own block or column. The format of this blog does not support sidebars. But the sections below would be sidebars to this article if the format supported it. These sections are not critical for getting your scope sighted in, but they do contain useful information about related topics.
6.1 Basics of mounting a scope
Some of you may never have mounted a scope on a rifle. You may be reading this article in preparation for mounting your scope, or you may have had a scope mounted by someone else. This section will not provide a complete tutorial on mounting scopes, but it will give an overview of some important points. If you are deciding whether you should mount a scope yourself or have someone else do it, then this section will give you an idea of what is involved.
First, I want to say that mounting a scope is not difficult. It is something that anyone who has some experience with hand tools can do. However, it is also a service that is offered by almost every gunsmith, and if you are unsure of your ability, you should not hesitate to contact a professional. While serious problems are unlikely, it is possible to damage either the rifle or the scope if proper care is not taken.
Below is a list of important points about mounting a scope. This list is not intended to be a full tutorial.
- Most scope mounts only require simple tools. Often Allen wrenches are the only tools required. In some cases, you may need Torx wrenches or standard screwdrivers. If you use screwdrivers, make sure that they fit properly so you do not damage the screw heads.
- You need to have a good feel for the amount of tension to use with small screws. The screws need to be tight enough to hold firmly, but not so tight that they break or strip.
- Some gunsmiths use a torque wrench to set a precise tension on the mount screws. A torque wrench is nice to have, but is not required if you have a good feel for the screws.
- Be aware that when you tighten screws, the threads can "relax" after a little while. You should go back after about an hour and check that the screws are still tight.
- Pay special attention if you are putting screws into aluminum. Aluminum is much softer than the steel screws, so use care not to strip the threads.
- It is often necessary to use a chemical thread locker like Loctite to get the screws to stay tight.
- When attaching the mount to the receiver, you need to be especially careful not to strip the threads in the receiver or break off screws in the receiver. You do not want to damage the receiver of the gun.
- When putting screws into the receiver, you need to check that the screws do not extend through the receiver in a way that could bind the action.
- Do not over tighten the screws on the scope rings, it is possible to crush the scope tube and damage it. These screws need to be tight, but not too tight.
- It is important to tighten all of the screws evenly so that everything remains square and pressure is even throughout the mount. You should tighten the screws in a criss-cross pattern like you were tightening the lugs nuts on a tire.
- Be aware of the amount of eye relief you want when you are positioning the scope. Eye relief is explained in the next section.
- It is important to keep the reticle level. You want to make sure that when the rifle is perfectly vertical, that the horizontal line of the reticle is perfectly level. This step can be tricky. As you are tightening the rings, check that the reticle looks exactly right.
Despite this long list of concerns, mounting a scope is not difficult. I expect some people reading these points will feel that this is an easy job. Other people will review the list and decide to have someone else do it. Each group of people will be making the right decision.
I recently discussed mounting a scope with the owner of a new rifle. He said "I'm ready to mount my scope, but sometimes I have a knack for breaking the heads off screws." I told him to have a professional mount his scope. I think he already wanted to have a gunsmith do it, but he still wanted to hear it from me. So I gave him the answer that he already knew was the right one for him.
6.2 Eye relief
Eye relief is the distance from your eye to the lens of the scope. When you look through a scope, the eye relief needs to be correct for you to see a good visual picture. If your eye is the wrong distance from the lens, then you will not see a full round view through the scope. You may see a black ring around the entire field of view, or you may see black on just one side. If you move your head closer or further from the scope, then the picture will improve.
Different scopes need different amounts of eye relief, and the required eye relief should be documented in the manual. Also, some scopes have a very narrow range of eye relief, while others are more forgiving. On variable power scopes, the eye relief may be less forgiving at high magnification.
Different shooters will have different head positions when they hold a rifle. And each shooter may vary his head position depending on whether he is standing, kneeling or prone. So the ideal mounting location for a scope can be different for different people.
Most scope mounts have some flexibility about exactly how far forward to mount the scope. If you are mounting a scope for yourself, make sure the eye relief is right before you fully tighten the rings. If you are using a scope that was mounted for someone else, and you need to place your head in an awkward position to see a good picture, then you might need to move the scope.
6.3 Point of aim vs. point of impact
At most distances, where you put the crosshairs is not exactly where the bullet will hit. This difference exists because a bullet always travels in an arc, and the line of sight is a straight line. Also, since the scope is above the barrel, the line of sight through the scope starts out above the path of the bullet.
Let's use an AR15 with 5.56 rounds as an example. On an AR15 the center of the optic is about 2.5" above the bore. If you zero in an AR15 at 50 yards, then the barrel is actually pointed slightly upwards relative to the scope so that the bullet will rise 2.5" in 50 yards. That means that at distances less than 50 yards the bullet will hit below the spot where you put the crosshairs. Then after 50 yards the bullet will continue rising until it is more than 1" high at 100 yards and more than 2" high at 150 yards. Then the bullet will reach the top of its arc and begin to come back down. Somewhere around 200 yards the bullet will cross the line of sight and will again be exactly zeroed with the crosshairs. Then at longer distances the bullet will hit below the crosshairs.
So based on the arc of the bullet, it will only hit exactly at the crosshairs at two specific distances. This general principle holds true for all firearms. The exact distances will vary according to the type and velocity of the bullet and the height of the scope, but point of impact will still vary from point of aim at most distances.
So now that you have a brief understanding about point of aim, you might ask "What distance should I sight my rifle at?" and "How can I determine where my rifle will hit at 50 yards if it is sighted for 100 yards?"
The answer to "What distance should I sight my rifle at?" is that it depends on the rifle and your intended use for it. A extremely simplified answer is that many rifles have a useful trajectory if they are sighted about 2" high at 100 yards. But that is an oversimplified answer that does not apply to all situations. A complete examination of this question is beyond the scope of this article. In fact, there are entire articles about how to zero rifles for different purposes. But the important point here is that after following the methods in this article, you will have an easy time changing your zero distance if you want to. You will just need to move your scope up or down a few clicks, and then shoot a group to see that everything looks right.
As for understanding where your rifle will hit at different distances, you can use a ballistic calculator to understand the flight path of the rounds you will be using. But after you get an estimate from the ballistic calculator, you will need to shoot some rounds at different distances to determine exactly how your rifle behaves. There is a link to an online ballistic calculator in the further reading section.
7 Further reading
The links below provide more information that you may find helpful. Note that I have no association with any of the articles or authors below.
7.1 Article about sighting in a hunting rifle
As you would expect, there are other articles about sighting in a rifle. If you have time for more reading, then another article with different perspective may offer further insight. Here is an article by Chuck Hawks about sighting in hunting rifles.
7.2 Article about bore sighting a rifle
This article by Chuck Hawks gives a brief summary about how to visually bore sight a rifle.
7.3 Article about zeroing an AR15
This article from Ammoland is about how to zero an AR15. It discusses how to choose the distance to zero your sight, and it also has illustrations of the arc of a bullet's flight path. While this article is focused on the AR15, the illustrations and principles apply to any firearm.
7.4 Hornady ballistics calculator
Hornady provides an online ballistics calculator. You enter characteristics of your ammunition, and the height of your optic, and the ballistics calculator prints a table of the trajectory.