Z-Score Calculator
Calculate the Z-score and corresponding percentile using z = (x−μ)/σ.
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Quick Tip
Enter the value (x) you want to place.
About This Tool
Why use Z-Score Calculator?
A z-score says how many standard deviations a value sits from the mean: z = (x − μ) ÷ σ. A z of +1.5 means the value is one and a half standard deviations above average. This calculator returns the z-score, the percentile, the probability below the value and the percentage above it.
Percentiles come from the normal distribution, so they are meaningful when your data is roughly bell-shaped. Under that assumption about 68% of values fall within ±1σ, 95% within ±1.96σ and 99.7% within ±3σ. The probability here is computed with a standard numerical approximation of the normal curve, accurate to several decimal places.
Key Benefits
Z-score and percentile together
No normal table lookup needed — the cumulative probability is calculated for you.
Both tails reported
The probability below and the percentage above are both shown, which covers either phrasing of a question.
Standardises different scales
Z-scores let you compare results from tests or measurements that use completely different units.
How to use Z-Score Calculator
- 1
Enter the value (x) you want to place.
- 2
Enter the mean (μ) and standard deviation (σ) of the distribution.
- 3
Read the z-score: positive is above the mean, negative is below.
- 4
Use the percentile and the percentage above to answer "how unusual is this?".
Best use cases
See what percentile a test score falls into.
Compare performance across two exams with different means and spreads.
Flag outliers in quality control, where |z| above 3 is unusual.
Find the tail probability for a hypothesis test.
Z-Score Calculator FAQs
What is a good or normal z-score?
A z-score near 0 is typical. Around 68% of values sit between −1 and +1, and 95% between −1.96 and +1.96. Beyond ±3 is rare, about 0.3% of values.
What does a negative z-score mean?
The value is below the mean. A z of −2 is two standard deviations below average, which is roughly the 2.3rd percentile.
How do I convert a z-score back to a value?
Multiply by the standard deviation and add the mean: x = μ + zσ. With μ = 100 and σ = 15, a z of 1.5 is 122.5.
Do percentiles require a normal distribution?
Yes. The z-score itself works for any data, but converting it to a percentile assumes the values follow a normal curve. For strongly skewed data, the percentile shown is only an approximation.
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