Z-Score Calculator
Convert between raw data values and standard z-scores.
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Select a mode: "Value to Z-Score" converts a raw data point into a standardized score, or "Z-Score to Value" does the reverse. Enter the mean and standard deviation of your distribution, then the value or z-score. Results update instantly.
A z-score tells you how many standard deviations a value is from the mean. Positive z-scores are above the mean, negative z-scores are below it.
About Z-Scores
The z-score formula is z = (x - mean) / standard deviation. Z-scores standardize different distributions onto the same scale, making comparisons possible. A z-score of 1.96 corresponds to the 97.5th percentile in a standard normal distribution, which is why it appears in 95% confidence intervals. Z-scores are used in hypothesis testing, quality control, and comparing test scores across different exams.
Frequently Asked Questions
What does a z-score of 0 mean?
A z-score of 0 means the value is exactly at the mean. Positive z-scores are above the mean, and negative z-scores are below it.
What z-score is considered unusual?
In many fields, a z-score beyond +/- 2 is considered unusual (roughly the top or bottom 2.5%). Beyond +/- 3 is very rare (0.13%). These thresholds are commonly used in outlier detection and hypothesis testing.
Can z-scores be used for non-normal distributions?
You can always compute a z-score for any distribution. However, the percentile interpretation (e.g., z=1.96 is the 97.5th percentile) only applies to normal distributions. For non-normal data, use Chebyshev's inequality for a weaker but universal bound.