Math & Statistics

Z-Score Calculator

Calculate the z-score and percentile for any value.

Enter a value, the mean, and the standard deviation of a normally distributed data set to calculate its z-score and approximate percentile rank.

Enter a valid number.
Enter a valid number.
Enter a valid standard deviation greater than 0.

Z-Score

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Approximate Percentile

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How to Use This Tool

  1. Enter your value, the data set's mean, and its standard deviation.
  2. Click Calculate to see the z-score and approximate percentile.

The Z-Score Formula

z = (x − μ) ÷ σ

Where x is your value, μ (mu) is the mean, and σ (sigma) is the standard deviation. The z-score tells you how many standard deviations your value is from the mean.

Interpreting Z-Scores

From Z-Score to Percentile

Assuming a normal (bell-curve) distribution, a z-score can be converted to a percentile using the cumulative distribution function — this calculator uses a well-established polynomial approximation of that function to give an accurate percentile estimate.

Common Applications

Frequently Asked Questions

What does a negative z-score mean?

A negative z-score means your value is below the mean — the more negative, the further below average it is, in units of standard deviation.

Does this work for any data distribution?

The percentile conversion assumes a normal (bell-curve) distribution. The z-score itself can be calculated for any distribution, but the percentile interpretation is only accurate when the underlying data is approximately normally distributed.

This calculator is provided for general informational and estimation purposes only. Results should not be treated as professional financial, tax, legal, medical, or engineering advice. Always verify critical calculations with a qualified professional or official source before making decisions.