Find how many standard deviations a value is from the mean
Enter your data set, then type a value (x) to get its z-score — the number of standard deviations it sits above or below the mean. The calculator derives the mean and standard deviation from your data and shows both the sample and population z-score.
z = (x − mean) ÷ standard deviation, using the mean and SD of your data.
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A z-score (or standard score) tells you how far a value lies from the mean, measured in standard deviations. A z-score of 0 means the value equals the mean; +1 means one standard deviation above the mean; −2 means two standard deviations below it. Standardizing values this way lets you compare measurements from different scales on a common footing.
The z-score is z = (x − μ) ÷ σ, where x is the value, μ is the mean and σ is the standard deviation. When your numbers are a complete population, use the population standard deviation; when they are a sample, use the sample standard deviation. This calculator reports both so you can pick the one that matches your situation.
For roughly bell-shaped (normal) data, about 68% of values fall within ±1 standard deviation of the mean, 95% within ±2, and 99.7% within ±3. So a z-score beyond about ±2 is relatively unusual, and beyond ±3 is rare. Note that z-scores describe position, not probability, unless the data is approximately normal.
Subtract the mean from your value and divide by the standard deviation: z = (x − mean) / SD. This calculator computes the mean and SD from your data automatically.
Use the population SD when your data is the entire group of interest, and the sample SD when it is a sample from a larger population. Both z-scores are shown above.
There is no universally "good" value — it depends on context. For normal data, most values fall between −2 and +2; scores beyond ±3 are uncommon.