Circular Error Probable

The Circular Error Probable ( CEP short, in German: Kreis error probability or scattering radius ) are at a circular normal distribution, the radius of a circle within which 50 percent of all measured values ​​lie. CEP is used as a measure of the accuracy of the system.


Common applications for the indication of the CEP especially in description of the hit accuracy of a weapon system with unguided munitions. Also, when specifying the accuracy of systems avionics navigation and one speaks of the CEP.

The enclosed percent value is written as an index to indicate CEP (eg: CEP for 20%: ). If no index is specified, the CEP is meant for 50 % of all values ​​.

Mathematical derivation

An approximation under the assumption of normally distributed strikes with maximum hit density at the origin of the coordinate system is obtained by the following double integral:

Here, the probability that impact is within a circle with the radius. is the variance -covariance matrix of the random vector of the coordinates of the impact.

Spherical Error Probable

In a three-dimensional analysis of the accuracy of a system (for example, satellite navigation systems ) is the value of the radius of a sphere within which are the measurement results with a probability of 50 percent, as Spherical Error Probable (SEP ) refers.