Circular error probable

In the military science of ballistics, circular error probable is a simple measure of a weapon system's precision.

The impact of munitions near the target tends to be normally distributed around the aim point, with most reasonably close, progressively fewer and fewer further away, and very few indeed at long distance.

A mathematician might characterise this pattern by its standard deviation, but a more intuitive method is to state the radius of a circle within which 50% of rounds will land. That radius is the circular error probable, commonly abbreviated to CEP.

For most weapons, the CEP increases with range, so it should either be stated for a particular range, or as an angle.

In the case of munitions which strike at a shallow angle to the Earth's surface, the pattern will become elongated into an ellipse. This can be thought of as the ellipse formed by the plane of the Earth's surface intersecting a cone of error. In this case, the CEP is usually given as what it would be if the rounds impacted the surface vertically, and it must be remembered that at shallow trajectories it will be elongated.

It should be noted that the concept of CEP is only strictly meaninglful if misses are roughly normally distributed. This is generally not true for precision-guided munitions.

Another important thing to remember about CEP is that if 50% of rounds land inside the circle, then 50% land outside it!