Convert any raw value into a standardised Z-score using the mean and standard deviation — with the corresponding percentile, probability, and a normal curve showing exactly where the value sits.
Enter your values on the left, then press Calculate.
A Z-score expresses how many standard deviations a value is from the mean. A z of +1 means one SD above the mean (84th percentile in a normal distribution). A z of -2 means two SDs below (2.3rd percentile). It standardises any value to a comparable scale.
Z-scores let you compare values from completely different distributions on equal terms — for example, a candidate scoring 75 in one test and 80 in another. The Z-score tells you which performance was actually better relative to its peer group.
Six Sigma uses Z-scores directly: the Sigma Level is just the Z-score above which 99.99966% of process output falls. A 6σ process produces only 3.4 defects per million opportunities — that's z = 4.5 (long-term) or z = 6 (short-term).