# Dictionary:Rms positional error

The circle whose radius is the square root of the mean of the sum of the squares of the distances of measured positions from a point. If the uncertainties in *x* and *y* directions are equal and normal (that is, a Rayleigh distribution), the probability of a measurement lying within the rms positional-error circle is 41 percent. Called **one-sigma circle** because this radius is equal to the standard deviation when taken about the mean of the observations. Compare *CEP*.