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- A z-score tells you how many standard deviations a value is from the mean.
- z = (x − μ) ÷ σ.
- The calculator also gives the percentile, left and right tail areas and the two-tailed p-value.
- Works backwards too: enter a percentile to get its z-score.
How to use the z-score calculator
Choose what you have
A raw score with the mean and standard deviation, a z-score, or a percentile.
Enter the values
For a test score of 85 with mean 70 and SD 10, type 85, 70 and 10.
Read the z-score and percentile
The z-score appears with the share of values below it.
Use the probabilities
Left area, right area, the area between −z and z, and the two-tailed p-value are all shown.
How z-scores are calculated
Z-score formula
z = (x − μ) ÷ σ
x = μ + z × σ (to go back to a raw score)
μ is the mean and σ the standard deviation. A positive z is above the mean, a negative z is below it.
Probabilities come from the standard normal distribution. The area to the left of z, written Φ(z), is the percentile. The area to the right is 1 − Φ(z).
Example 1: a test score
Score 85, class mean 70, standard deviation 10.
- z (85 − 70) ÷ 10 = 1.5
- Percentile 93.32%
- Area to the right 6.68%
The student scored better than about 93% of the class, assuming scores are roughly normal.
Example 2: critical values
Common z-scores used for confidence intervals and tests.
- 90% confidence (two-tailed) z = 1.645
- 95% confidence (two-tailed) z = 1.96
- 99% confidence (two-tailed) z = 2.576
For a one-sided 95% test, the critical value is 1.645, which is the 95th percentile.
| z | Area left P(Z<z) | Area right P(Z>z) | Between −z and z |
|---|---|---|---|
| 0.0 | 0.5000 | 0.5000 | 0.0000 |
| 0.1 | 0.5398 | 0.4602 | 0.0797 |
| 0.2 | 0.5793 | 0.4207 | 0.1585 |
| 0.3 | 0.6179 | 0.3821 | 0.2358 |
| 0.4 | 0.6554 | 0.3446 | 0.3108 |
| 0.5 | 0.6915 | 0.3085 | 0.3829 |
| 0.6 | 0.7257 | 0.2743 | 0.4515 |
| 0.7 | 0.7580 | 0.2420 | 0.5161 |
| 0.8 | 0.7881 | 0.2119 | 0.5763 |
| 0.9 | 0.8159 | 0.1841 | 0.6319 |
| 1.0 | 0.8413 | 0.1587 | 0.6827 |
| 1.1 | 0.8643 | 0.1357 | 0.7287 |
| 1.2 | 0.8849 | 0.1151 | 0.7699 |
| 1.3 | 0.9032 | 0.0968 | 0.8064 |
| 1.4 | 0.9192 | 0.0808 | 0.8385 |
| 1.5 | 0.9332 | 0.0668 | 0.8664 |
| 1.6 | 0.9452 | 0.0548 | 0.8904 |
| 1.7 | 0.9554 | 0.0446 | 0.9109 |
| 1.8 | 0.9641 | 0.0359 | 0.9281 |
| 1.9 | 0.9713 | 0.0287 | 0.9426 |
| 2.0 | 0.9772 | 0.0228 | 0.9545 |
| 2.1 | 0.9821 | 0.0179 | 0.9643 |
| 2.2 | 0.9861 | 0.0139 | 0.9722 |
| 2.3 | 0.9893 | 0.0107 | 0.9786 |
| 2.4 | 0.9918 | 0.0082 | 0.9836 |
| 2.5 | 0.9938 | 0.0062 | 0.9876 |
| 2.6 | 0.9953 | 0.0047 | 0.9907 |
| 2.7 | 0.9965 | 0.0035 | 0.9931 |
| 2.8 | 0.9974 | 0.0026 | 0.9949 |
| 2.9 | 0.9981 | 0.0019 | 0.9963 |
| 3.0 | 0.9987 | 0.0013 | 0.9973 |
For a negative z, use the same row and swap the left and right columns.
Where a z-score calculator helps
Statistics classes
Find z-scores, percentiles and p-values without looking up a printed table.
Test scores
Compare results from different tests by putting them on the same scale.
Quality control
See how unusual a measurement is compared with the normal range.
Research and A/B tests
Turn a test statistic into a p-value.
Find the mean and standard deviation of your data first with the standard deviation calculator or the average calculator. To spot outliers using quartiles instead, use the upper and lower fence calculator.
Z-score calculator FAQ
What is a z-score?
It is the number of standard deviations a value sits above or below the mean. A z-score of 2 means two standard deviations above average.
How do I calculate a z-score?
Subtract the mean from the value and divide by the standard deviation: z = (x − μ) ÷ σ.
What is a good z-score?
It depends on context. Above 0 is above average. Values beyond ±2 are unusual, and beyond ±3 are rare in a normal distribution.
How do I turn a z-score into a percentile?
Find the area to the left of z under the normal curve. The calculator does this for you, for example z = 1.5 is the 93.32nd percentile.
What z-score is the 95th percentile?
About 1.645. The 97.5th percentile is about 1.96.
Does this work for any data?
The percentile and probabilities assume the data is roughly normally distributed. The z-score itself can be calculated for any data.