Which gun shoots the farthest, a pistol, shotgun or rifle? Please help me understand the order of which shoots the farthest, and why. 
I, of course, appreciate your help.
You seem to have brought out some of the loonies. My jaw has dropped at some of the totally wrong answers here.
I am a ballistics technician. We study the flight of bullets in air. Remember holding your hand out while the car is going fast? Hold it open and your hand is slapped backwards by the air. Hold it flat and streamlined - it just kinda sits there? And how the same thing happens in water?
Bullets have the same problem going through air. A typical rifle bullet has a point - this helps it cut through the air. When anyting moves faster than 1100fps it creats a vacuum behind it that wants to pull the bullet to a stop (drag). A typical bullet travels at 2800fps to 3800fps from a rifle. Some bullets have less drag that others - you see these used in long range shooting.
Bullets from a modern barrel are given a spin. This does not make it go faster. It allows gravity to effect the bullet more evenly. A rifle bullet traveling at 3600fps gets to the target 4 times faster than a pistol bullet traveling at 900fps. The pistol bullet drops more because gravity has had more time to pull it toward the ground. Since pistol bullets are always slower than rifle bullets - the rifle will go much further. And since rifle bullets are more streamline than a pistol bullet - that will go much, much further than a pistol bullet.
Shot guns fire balls of lead. Ball are not at all steamlined what-so-ever. The shot might start out going faster than a pistol bullet - but at 25 yards the shot has slowed down to pistol speed and by 50 yards the shat is way behind the pistol bullet.
There are always exceptions in firearms. There are people who make great big huge pistols that have equal power to some rifles - so the statement that all rifles are faster than all pistols isn't perfect - just 99.9999% - but- there is no shortage of people online that want to make that .00001% stand out all the time.
Bottom line - it's all laws of physics. The power of a projectile going forwards can never exceed the power of the firearm going backwards (recoil). The gun with the most recoil and streamlined bullet is the one that goes the farthest - or - could have the most power.
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