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The term point blank range is of French origin. The center of a target was once a small white spot and the French for white is blanc, and aim is point. The term therefore means "aim at the center of the target."

The term originated with the techniques used to aim muzzleloading cannon. The barrels of the cannon tapered down from breech to muzzle, so that when the top of the cannon was held horizontal, the bore actually sat at an elevated angle. In addition, the firing of the gun caused the muzzle to elevate slightly due to recoil, and this would result in an upward movement by the shot even in a cylindrical cannon. This caused the shot to rise above the natural line of sight very soon after leaving the muzzle, and later dropping below the line of sight due to the curved trajectory of the shot.

By firing a given projectile and charge in the cannon, the distance at which the shot fell below the bottom of the bore could be measured. This distance was considered the point blank range. Any target within the point blank range required the gun to be depressed; any target beyond the point blank range required the gun to be elevated, up to the angle of greatest range, which happens somewhat before 45 degrees of elevation.

The point blank range varies significantly with not only the ballistics of the gun, but also its shape, as it is shape that determines the natural line of sight on which point blank range is based. Various cannon of the 19th century had point blank ranges from 250 yards (12 lb howitzer, 0.595 lb (0.270 kg) powder charge) to nearly 1075 yards (30 lb carronade, solid shot, 3.53 lb (1.60 kg) powder charge).
Small arms and maximum point blank range

Small arms are often sighted-in so that the sight line and bullet path are within a certain acceptable margin out to the longest possible range, called the maximum point blank range. The range of distance inside the maximum point blank range is greatly dependent on the external ballistics of the cartridge in question; high velocity rounds have long point blank ranges, while slow rounds have much shorter point blank ranges. Other factors in the point blank range are the target size (which determines how far above and below the line of sight the trajectory may deviate), the height of the sights, and an acceptable drop before a shot is ineffective.
Maximum point blank range for hunting

A large target, like the vitals area of a deer, allows a deviation of a few inches (as much as 10 cm) while still ensuring a quickly disabling hit. A varmint such as a prairie dog requires a much smaller deviation, less than an inch (about 2 cm). The height of the sights has two effects on point blank range. If the sights are lower than the allowable deviation, then point blank range starts at the muzzle, and any difference between the sight height and the allowable deviation is lost distance that could have been in point blank range. Higher sights, up to the maximum allowable deviation, push the maximum point blank range further from the gun. Sights that are higher than the maximum allowable deviation push the start of the point blank range out from the gun; this is quite common on varmint rifles, where close shots are never made, as it places the point blank range out to the expected range of the targets.
Maximum point blank range for military use

This sight setting for maximum point blank range is also referred to in the military as Battle Zero. Soldiers are instructed to fire at any target within this range by simply placing the sights on the center of mass of the enemy target. Any errors in range estimation are tactically irrelevant as a well-aimed shot will hit the torso of the enemy soldier. The current trend for elevated sights and higher velocity cartridges in assault rifles is in part due to a desire to extend the maximum point blank range, which makes the rifle easier to use.
Calculating point-blank range

A projectile falls due to gravity once it leaves a weapon barrel. All objects at the same geographic location fall with the same acceleration, denoted g, roughly 9.8 m/s² (32 ft/s²). Velocity is a vector; the vertical component of any projectile's velocity can be treated separately from the horizontal component. If the barrel is horizontal and at height h above the ground, then Newton's Equations of Motion can be used to show that the range is approximately \scriptstyle v \sqrt\frac{2h}{g}, where v is the muzzle velocity. This calculated range is reduced by air resistance. The air resistance depends on at least the frontal area of the projectile, the drag coefficient, air density and obviously the speed of the projectile -- making the problem a differential equation.