Circular Error Probable - Conversion Between CEP, RMS, 2DRMS, and R95

Conversion Between CEP, RMS, 2DRMS, and R95

While 50% is a very common definition for CEP, the circle dimension can be defined for percentages. Approximate formulas are available to convert the distributions along the two axes into the equivalent circle radius for the specified percentage.

Accuracy Measure Probability (%)
Root mean square (RMS) 63 to 68
Circular error probability (CEP) 50
Twice the distance root mean square (2DRMS) 95 to 98
95% radius (R95) 95
From/to CEP RMS R95 2DRMS
CEP - 1.2 2.1 2.4
RMS 0.83 - 1.7 2.0
R95 0.48 0.59 - 1.2
2DRMS 0.42 0.5 0.83 -

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