The only way I've seen to determine how effective an attack might be is through using VATS. When you've selected a target, you will see their current health. Part of that health bar will be darkened or blinking. (Don't have the game in front of me now, so I'm not certain which.) This indicates how much damage your attack would do if successful.

I haven't particularly noticed whether distance is a factor for calculating damage of precision weapons like sniper rifles, or how such an effect might scale. However, VATS does appear to take into account the body part selected (head-shots do substantially greater damage, of course) and whether or not you're going to get a sneak attack bonus. Other factors, like applicable perks and other bonuses, are probably included in the calculation as well.

I'm also not sure what happens with targets at extreme distances. I do believe it's possible for a target to be out of VATS range, while still actually being within weapons range for a skillful player shooting manually. (I believe I did encounter this once, but chose to maneuver closer instead of trying my luck.) But I am not sure whether a "successful" attack under such conditions would actually do any damage, or if that damage would be substantially reduced.

I'd suggest playtesting it a bit when you have some time.

The only way I've seen to determine how effective an attack might be is through using VATS. When you've selected a target, you will see their current health. Part of that health bar will be darkened or blinking. (Don't have the game in front of me now, so I'm not certain which.) This indicates how much damage your attack would do if successful. It appears to take into account things like bonuses for head-shots and sneak attacks, so I expect range is factored in as well.

Unless a weapon has some sort of special feature on it (such as a range-finding scope; I haven't completed the game yet, so I'm not sure whether or not these might exist), or someone makes an appropriate mod for your platform, VATS is probably the best you can do. After using VATS with certain weapons for awhile, you might be able to make reasonably accurate guesses by yourself. But that's about it.