Find a z-score from a raw value, or work backward from a z-score to the value it represents.
A z-score expresses how many standard deviations a value sits from the mean: z = (x − mean) / standard deviation. It standardizes values so data measured on different scales — test scores, heights, reaction times — can all be compared on the same footing.
A positive z-score means the value is above the mean; a negative z-score means it's below. The size of the number shows how many standard deviations away it is — a z-score of 0.5 is close to typical, while a z-score of 3 is far from typical in either direction.
Commonly, a z-score with an absolute value greater than 2 or 3 is considered notably unusual in many contexts — these are general guidelines used across statistics, not strict cutoffs that apply identically to every situation.
The Standard Deviation Calculator computes standard deviation FROM a full data set. This tool assumes you already have a mean and standard deviation and uses them to standardize one specific value (or work backward from a z-score to a value).
Worked example: a test score of 85, with a class mean of 75 and standard deviation of 10: z = (85−75)/10 = 1.5 — one and a half standard deviations above average. Working backward, a z-score of 1.5 with that same mean and standard deviation maps back to exactly 85.