Z-Score Calculator
Calculate z-scores, percentiles and normal probabilities, or the z for a probability like 95%, with this free online z-score calculator and bell curve.
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Part of the toolkit
How to use Z-Score Calculator
- 1Enter the mean and standard deviation (or tap Standard normal)
- 2Choose: value to z-score and percentile, the probability between two values, or a probability to its z (critical value)
- 3Read the result with the shaded area on the bell curve and copy it
Frequently asked questions
How do you calculate a z-score?▾
z = (x − μ) ÷ σ: subtract the mean from the value and divide by the standard deviation. An IQ of 130 with mean 100 and SD 15 has z = 2.0 — the 97.72nd percentile.
How do I convert a z-score to a percentile?▾
The percentile is the area under the normal curve to the left of z: Φ(z). z = 0 is the 50th percentile, z = 1 the 84.13th and z = −1 the 15.87th.
What z-score corresponds to 95% confidence?▾
±1.96 for a two-sided 95% interval (2.5% in each tail). For 90% it's ±1.645 and for 99% ±2.576; a one-sided 95% cutoff is 1.645.
What percentage of data is within 1, 2 and 3 standard deviations?▾
About 68.27%, 95.45% and 99.73% for a normal distribution — the 68–95–99.7 rule.
How accurate are the results?▾
The normal CDF is computed with a series/continued-fraction method accurate to about 12 significant digits, far beyond a printed z-table.
Embed Z-Score Calculator on your website▾
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