Z-Score Calculator
See how far a value sits from the mean in standard-deviation units.
Z-Score Calculator
Standardize one observation against a mean and standard deviation.
Z-score
1
The value is 1 standard deviations above the mean.
A z-score alone does not show whether the data are normally distributed or determine a probability.
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What This Calculator Does
Calculate a z-score from an observed value, a mean, and a standard deviation. The result expresses the observation’s signed distance from the mean in standard-deviation units.
How It Works
Subtract the mean from the observed value, then divide by the standard deviation: z = (x − μ) / σ. A positive result is above the mean, a negative result is below it, and zero is exactly at the mean. The standard deviation must be greater than zero.
Example
If a score is 85, the mean is 80, and the standard deviation is 5, then z = (85 − 80) / 5 = 1. The score is one standard deviation above the mean.
Formula
z = (x − μ) / σx is the observation, μ the mean, and σ the standard deviation.
Reading the Results
Z-score
The signed number of standard deviations between the observation and the mean.
Frequently Asked Questions
What does a z-score of 1 mean?
It means the observation is one standard deviation above the mean. A z-score of −2 means it is two standard deviations below the mean.
Can a z-score be negative?
Yes. Values below the mean produce negative z-scores; values above the mean produce positive z-scores.
Does a z-score tell me a probability?
Not by itself. Converting a z-score to a probability requires an appropriate distribution model; this calculator only standardizes the value.