Z Score Calculator
Calculate the standard score (z-score) for a value using the population mean and standard deviation.
How to Use the Z Score Calculator
Enter a value, population or sample mean, and standard deviation to calculate how many standard deviations the value lies from the mean.
Practical Example
If x = 85, mean = 70 and standard deviation = 10, the z-score is 1.5.
Factors That Affect the Result
The observed value, mean, standard deviation and whether the data model is appropriate affect interpretation.
Frequently Asked Questions
What does a positive z-score mean?
The value is above the mean.
What does z = 0 mean?
The value equals the mean.
Can standard deviation be zero?
A z-score is undefined when standard deviation is zero.
Interpreting a Z Score
A z score describes how far a value is from the mean in units of standard deviation. The formula is z = (x − mean) ÷ standard deviation. A z score of 0 means the value equals the mean, a positive score is above the mean, and a negative score is below it. For example, if a test has a mean of 70 and standard deviation of 10, a score of 85 has z = 1.5, meaning it is 1.5 standard deviations above the mean. Z scores are useful for standardizing values measured on different scales and for working with normal-distribution probabilities. The interpretation depends on the quality and distribution of the underlying data, and the standard deviation must be greater than zero. A large absolute z score indicates distance from the mean but does not by itself prove that a value is erroneous or abnormal.