In the military science of ballistics, Circular Error Probability or circular error probable (CEP) is a simple measure of a weapon system's precision. It is defined as the radius of a circle into which a missile, bomb, or projectile will land at least half the time.
For example, an ICBM warhead with a CEP of 100 meters will impact within 100 meters of the target point in at least 50 percent of all attempts.
The impact of munitions near the target tends to be bivariate 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 percent 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 meaningful 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 percent of rounds land inside the circle, then 50 percent land outside it! Generally, if CEP is n meters 50 percent of rounds land within n meters of the target, 43 percent between n and twice that distance and 7 percent between two and three times that distance. If misses were exactly normally distributed as in this theory, then the proportion of rounds that land farther than three times the CEP from the target is less than 0.2%. With precision-guided munitions, the number of 'close misses' is higher.
