Z-Score Calculator

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Convert any value into a standard z-score using the mean and standard deviation, then read its percentile, the percentage above and the two-tailed p-value. Free and instant.

Must be greater than zero.
Z-score –
Percentile (below) –
Percentage above –
Two-tailed p-value –
Assumes a normal distribution. The z-score is (x − μ) ⁄ σ. The percentile uses an erf approximation of the standard normal CDF and is accurate to a few decimal places.

About Z-Score Calculator

The z-score calculator standardizes any value against a normal distribution: given the value x, the mean μ and the standard deviation σ, it computes z = (x − μ) ⁄ σ — how many standard deviations the value sits above or below the mean.

It then translates that z-score into position: the percentile of values below, the percentage above, and the two-tailed p-value. The percentile comes from an erf-based approximation of the standard normal CDF, accurate to a few decimal places.

Z-scores let you compare results from different scales — test scores, lab measurements, growth data — on one footing, and the p-value output makes the tool a quick companion for hypothesis testing.

How to use Z-Score Calculator

  1. Enter the value x you want to standardize.
  2. Enter the distribution's mean μ.
  3. Enter the standard deviation σ — it must be greater than zero.
  4. Read the z-score, the percentile below, the percentage above and the two-tailed p-value.

Frequently asked questions

The value lies 1.5 standard deviations above the mean. Under a normal distribution that is roughly the 93rd percentile — about 93% of values fall below it.

Yes — negative z-scores mark values below the mean. A z of −2 sits two standard deviations under average, around the 2.3rd percentile.

The probability of seeing a value at least as extreme as yours in either direction: 2 × P(Z > |z|). It is the figure used in two-sided hypothesis tests.

The standard normal CDF is evaluated with an erf approximation accurate to a few decimal places — more than enough for coursework, test-score interpretation and screening analyses.

The z-score itself is just a rescaling and always valid, but the percentile and p-value assume a normal distribution. For strongly skewed data, those probability readings will be off.
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