Online Tool Store
Z-Score Calculator
Calculate a z-score, its percentile, and a plain-language interpretation from a value, mean, and standard deviation. Runs entirely in your browser.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
Z-score
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Percentile
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Interpretation
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How it works
- Enter a value, the distribution's mean, and its standard deviation.
- See the z-score, corresponding percentile, and a plain-language interpretation.
The formula
z = (x − μ) ÷ σ
Percentile = Φ(z) × 100, where Φ is the standard normal cumulative distribution function
FAQ
What is a z-score?
A measure of how many standard deviations a value is from the mean of its distribution — a z-score of 0 means exactly average, positive means above average, negative means below average.
What does the percentile mean?
The percentage of values in a normal distribution that fall below your value — a percentile of 84% means your value is higher than roughly 84% of the distribution, assuming the data is normally distributed.
Does this assume a normal distribution?
Yes — the percentile calculation assumes the underlying data follows a normal (bell-curve) distribution. The z-score itself is valid for any distribution, but the percentile interpretation specifically relies on normality.
Is my data uploaded anywhere?
No — every calculation happens locally in your browser. Nothing is sent to a server.
What happens if I enter 0 for standard deviation?
It's rejected — a standard deviation of zero would mean dividing by zero in the z-score formula, so a positive value is required.
How we compare
| Feature | Online Tool Store | Z-table lookup by hand | Statistics software |
|---|---|---|---|
| Instant percentile, no table needed | ✓ | Look up and interpolate manually | ✓ |
| No install | ✓ | ✓ | Requires dedicated software |
For a quick homework check or a fast percentile lookup, this beats interpolating a printed z-table by hand.