This tool will convert percentiles to Z score or vice-versa and is based upon standard tables of Z-scores between -4.00 and 4.00, which corresponds to 0.003% to 99.997%. 

This tool applies ONLY to normally distributed (Gaussian) data sets.

In simple terms, the z-score is the number of standard deviations the data item falls above (+ z-score) or below (- z-score) the mean for the data set.

The formula is: Z Score = (x-µ)/delta;

x = the actual data item you want the Z score for

µ = the mean of the data set (or population)

delta = the standard deviation of the data set