Z-Score Calculator
How many standard deviations a value sits above or below the mean.
- Z-score2.0000
Inputs used
- Value (x)130
- Mean100
- Standard deviation15
About this calculator
A z-score standardizes a value: z = (x − mean) ÷ standard deviation. It answers "how unusual is this?" on a universal scale — z = 2 means two standard deviations above the mean, z = −1.5 means one and a half below.
For roughly normal data, the 68–95–99.7 rule gives instant context: about 68% of values fall within one standard deviation of the mean, 95% within two, 99.7% within three. A z-score beyond ±2 is uncommon; beyond ±3 is rare.
Z-scores make different scales comparable: an IQ of 130 (mean 100, SD 15) and a height of 6'4" are both z = 2 — equally far from typical, in their own distributions.
Frequently asked questions
What is the formula for a z-score?
A z-score is the value minus the mean, divided by the standard deviation: z = (x − mean) ÷ SD. An IQ of 130 with a mean of 100 and SD of 15 gives (130 − 100) ÷ 15 = 2.
What does a z-score of 2 mean?
The value sits two standard deviations above the mean. Under the 68–95–99.7 rule for normal data, about 95% of values fall within two standard deviations, so a z of 2 is at the upper edge of the typical range.
Can a z-score be negative?
Yes — a negative z-score means the value is below the mean. A z of −1.5, for example, is one and a half standard deviations below average; the sign shows direction and the magnitude shows distance.
What is considered an unusual z-score?
For roughly normal data, a z-score beyond ±2 is uncommon (outside about 95% of values) and beyond ±3 is rare (outside about 99.7%). The larger the magnitude, the more of an outlier the value is.
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Results are informational only — not financial, medical or legal advice.