Z Z-Score Calculator

Calculate the z-score (standard score) of a value and find its corresponding percentile in a normal distribution.

Values

Your Result

Z-Score
1.00
Percentile
Interpretation
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How the Z-Score Calculator Works

A z-score tells you how many standard deviations a value is from the mean of its distribution. Z-scores are used to compare values from different normal distributions and to find percentile ranks.

Formula

z = (x − μ) / σ
Percentile = Φ(z) × 100, where Φ is the standard normal cumulative distribution function

Frequently Asked Questions

What does a negative z-score mean?

A negative z-score means the value is below the mean. A positive z-score means it's above the mean. A z-score of 0 means the value equals the mean.

How is percentile related to z-score?

The percentile shows the percentage of values in a normal distribution that fall below your value. For example, a z-score of 0 corresponds to the 50th percentile.

How accurate is the percentile calculation?

This calculator uses a well-known polynomial approximation of the standard normal cumulative distribution function, accurate to about 7 decimal places — more than enough precision for practical use.

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