Z-Score (Standardized Score) Calculator
Enter a value, the mean, and the standard deviation of its distribution to calculate the z-score and percentile.
Last updated: September 5, 2026
Frequently asked questions
How do I calculate a standardized score (z-score)?
Subtract the mean from your value, then divide by the standard deviation: z = (x − mean) / SD. A score of 85 with a mean of 75 and standard deviation of 10 gives z = (85−75)/10 = 1.0, meaning the score is exactly 1 standard deviation above average.
What does a z-score of 0 mean?
A z-score of 0 means the value is exactly equal to the mean - neither above nor below average. Positive z-scores are above the mean, negative z-scores are below it.
How is percentile calculated from a z-score?
Using the standard normal cumulative distribution function, which gives the proportion of a normal distribution falling below a given z-score - a z-score of 1.0 corresponds to about the 84th percentile, meaning roughly 84% of values in a normal distribution fall below that point.
How do you calculate percentile in general?
Enter your value, the distribution's mean, and its standard deviation above - this calculator converts that into a z-score, then into a percentile using the normal distribution. That's the standard method for calculating percentile when you know a distribution's mean and spread.
What does a negative z-score mean?
It means the value is below the mean - a z-score of -1.5 indicates the value sits 1.5 standard deviations below average, corresponding to a low percentile (around the 7th percentile).
What's the z-score and percentile for a value exactly equal to the mean?
The z-score is 0, and the percentile is 50% - a value equal to the mean sits at the exact center of a normal distribution, with half the data above and half below.
Is a 'standard score' the same thing as a 'z-score'?
Yes - 'standard score' and 'z-score' are interchangeable terms for the same calculation: how many standard deviations a value is from the mean.