How far is a pellet still dangerous??

Depends on what you consider dangerous. For arguments sake let's say a daisy BB gun is dangerous up to 10 yards (would break the skin). Beyond that it would sting like a SOB, but would only really do any damage if it hit you in the eye. I'm guessing the muzzle energy is ~2 fpe on a Daisy.

My .22 Marauder is ~32 fpe at the muzzle (~890 fps with 18.1 JSBs). That works out to the following (using Chairgun app): ~15fpe @ 100 yards; ~7fpe @ 200 yards; ~3.6fpe @ 300 yards; ~2fpe @ 400 yards. So the Marauder has the muzzle power of the Daisy at 400 yards.
 
I have always treated my airguns in the same manner as my firearms. Shoot in a safe direction with a proper backstop. I do use chairgun to check what distance the pellet is below 1fpe as I consider that to be "safe". Realistically any amount of energy should be considered dangerous, but I can sleep with below 1fpe.

So, use chairgun or a similar ballistics program to check what distance that particular airgun is producing whatever fpe you deem safe.
 
Define dangerous?

You can get shot in the head by a low powered BB, it bump off, yet die of internal bleeding to the brain.

As children using airguns we shot each other, always below the neck, with pellet impacts up to about 8ftIb. They hurt, which was part of the fun, and sometimes broke the skin but nobody had to go to hospital.

Apple fights were another matter, with a few people having trips to hospital after getting hit on the head. 

The fact is that it will probably be the case that throughout the World, if you shoot a pellet and it hits someone you'll probably have committed a criminal offence (for starters).
 
I think it's safe to consider that a projectile is dangerous even at 400 yards. At 200 yards a 12 fpe airgun has penetrated cardboard easily. Higher fpe guns will probably do a lot more damage. Reason being GRAVITY. You can shoot a pellet high and the force of gravity can still make it dangerous enough to penetrate skin. For the love of all things sacred, let's assume that pellets or bb's are not toys. 
 
Until it stops it is dangerous. The horizontal(x) and vertical(y) motions are independent of each other. Yes, it will slow down from air resistance, but not much. If you're assuming a perfectly horizontal shot from a given height you can simply drop a pellet from that height and measure how long it takes to hit the ground. Then multiply that time by the fps of the pellet and you'll know how far it will travel in that time. 

|> > ———
| ----- |
| ------ Y
| ------ |
->— > ———

|-----------x--------------|

Assuming 'Y' is 1m you can calculate the speed to drop distance 'Y' pretty easily. A 25 grain pellet is about 1.6g or .0016kg. Plug the numbers in here and it will tell you the 'splat' time: http://www.angio.net/personal/climb/speed. It will be about .5sec. So a 25grain pellet launched at 900fps horizontally at 1m elevation will travel about 450 ft before hitting the ground. Probably a little less because of wind resistance. 
900ft/1sec * .5sec = 450ft

If you shoot at an angle things get trickier, but not much. 

 
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The RWS Operator Manual lists the danger zones as being out to 650 yards. Depending on which model you shoot, the distance is listed somewhat shorter. I had a similar discussion with some other Team 5 members concerning whether they would stand and be shot at by a .44 magnum at 850 yards.When I repeatedly knocked down a hit reactive target at that distance with my Super Blackhawk 7.5" barreled .44 magnum, the discussion ended.Long story short...If you don't know what is behind your target, don't shoot.

 
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"ztirffritz"Until it stops it is dangerous. The horizontal(x) and vertical(y) motions are independent of each other. Yes, it will slow down from air resistance, but not much. If you're assuming a perfectly horizontal shot from a given height you can simply drop a pellet from that height and measure how long it takes to hit the ground. Then multiply that time by the fps of the pellet and you'll know how far it will travel in that time. 


Even though I liked your physics lesson ( just finished up the class and we were talking about this exact topic of vectors) I disagree with your statement about pellets not being slowed down much by air resistance. Light bjects traveling at high speeds are heavily effected by air resistance that is why there is a significant loss in power at farther ranges. If the pellet always maintained a similar horizontal velocity it would impact with the same force as when it left the muzzle. 



 
It does slow down. But I guess I didn't word that well. My point is it will hit the ground long before it has a chance to slow down much. Wind resistance is a function of cross sectional surface area and velocity. A 1/4" diameter pellet doesn't offer much resistance, even at 900fps. Even if it loses 50% of its velocity, it's still going 450 fps. That's faster than just about every CO2 pellet handgun, and those can still kill a squirrel or rat at close range with 400fps or less velocities. If you aim it up in the air at 45° you'll get much longer distances, more time in flight, and more time to slow down from air resistance but it will still be incredibly dangerous.
 
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You could easily have a pellet with the same mass as those feathers, but you can clearly see the effects that drag has on the feathers. It isn't mass, but the surface area resisting the air that is important. You start to get into fluid dynamics behind the pellet and you'll drive yourself crazy. Turbulence behind the object will create a pressure differential that creates counter intuitive results. It's similar to debris in the bed of a truck getting blown forward into the cab through the back window, even though the truck is moving at 50mph. People much much smarter than you or I have spent decades trying to quantify fluid dynamics and they're still learning new stuff all the time. There are computer models that will handle some of it, but empirical testing in wind tunnels or fluid chambers is still the go-to method for quite a bit of our knowledge.
 
Just for the sake of argument, let's say the threshold for "safe" is as fast as a person can throw a pellet. That seems like a standard that would probably sound reasonable to anybody you're trying to convince.

A major league pitcher can throw a baseball around 130 fps. If that's the standard, a 14.3gr Crosman Premier leaving the muzzle at 950 fps won't be "safe" until it travels about 400 yards.