Z-Score Calculator
Enter a value, the mean and the standard deviation to get its z-score — how many standard deviations it sits above or below the mean.
Quick answer: z = (x − μ) ÷ σ. A test score of 85 in a class with mean μ = 70 and standard deviation σ = 10 has z = (85 − 70) ÷ 10 = 1.5 — one and a half standard deviations above the mean.
A z-score (or standard score) rescales a value so it's expressed in standard-deviation units from the mean. It lets you compare values from different distributions on a common footing and is the entry point to reading normal-distribution probability tables.
The formula
z = (x − μ) ÷ σ
x = μ + zσ (to reverse it)
x = μ + zσ (to reverse it)
Worked example
A height of 180 cm in a population with mean 175 cm and σ = 6 cm has z = (180 − 175) ÷ 6 = 0.83 — about 0.83 standard deviations above average.
Frequently asked questions
What is a z-score?
The number of standard deviations a value is from the mean: z = (x − μ)/σ.
What does a negative z-score mean?
The value is below the mean. A z of −2, for instance, is two standard deviations below average.
What z-score is unusual?
A common rule of thumb treats |z| above 2 (or 3) as unusual, since most values in a normal distribution fall within ±2.
How do I turn a z-score into a percentile?
Look up the z in a standard normal table (or use a normal CDF); it gives the proportion of values below that z.
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