Z-score calculator
Calculator
The calculator needs JavaScript. The tables below give the same numbers for common cases.
How it is worked out
- z = (x − μ) ÷ σ = (85 − 70) ÷ 10 = 1.5.
- The area below z under the standard normal curve is about 0.9332 (about 93.32%).
| Inputs | Answer |
|---|---|
| Value: 85; Mean: 70; Standard deviation: 10 | A value of 85 is 1.5 standard deviations from the mean. |
| Value: 60; Mean: 70; Standard deviation: 10 | A value of 60 is -1 standard deviations from the mean. |
| Value: 1.96; Mean: 0; Standard deviation: 1 | A value of 1.96 is 1.96 standard deviations from the mean. |
How to use it
A z-score tells you how many standard deviations a value lies above or below the mean: z = (x − μ) ÷ σ. A z-score of 1.5 means the value is one and a half standard deviations above the mean.
The calculator also gives the area under the standard normal curve below z, which is the percentile if the data is roughly normally distributed. The percentile uses a numerical approximation accurate to about four decimals.
Frequently asked questions
How do I calculate a z-score?
Subtract the mean from the value and divide by the standard deviation: (85 − 70) ÷ 10 = 1.5.
What does a z-score of 0 mean?
The value equals the mean.
Is a z-score of 2 unusual?
In a normal distribution about 95% of values lie within 2 standard deviations of the mean, so beyond 2 is relatively uncommon.
Method: standard arithmetic shown step by step; no outside data is used. Checked 2026-11-12.
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General information only. Results are plain arithmetic on the numbers you enter; check anything important (money, health, school work) against your own records or the official source.