What is a z-score calculator?
A z-score converts a raw value to a standardized distance from the mean. Positive scores are above the mean, negative scores are below it, and zero is exactly at the mean.
Use this page for a transparent calculation, then compare the result with the Standard Deviation Calculator when a different view of the same data would be useful.
How does this z-score calculator work?
The calculator subtracts the mean from the raw score and divides by the positive standard deviation. It also applies the standard normal cumulative distribution to estimate a percentile.
Before interpreting spread or position, it can help to check the center with the Average Calculator. Every tool states its assumptions so results can be reproduced.
How to use this calculator
- Enter the requested numbers in the labeled fields.
- Review unit, sample, confidence, or test choices when shown.
- Select Calculate Z-Score.
- Read the main result, supporting facts, and method note.
- Use Copy, Download, or Print when you need to keep the result; select Reset to start over.
If you edit any input after calculating, the old result is marked stale and hidden until you calculate again.
How should you interpret the result?
A z-score of 1.5 means the value is 1.5 standard deviations above the mean. The percentile is meaningful only when a normal distribution is a reasonable model.
For another useful perspective, open the Percentile Calculator; it answers a related question without changing the values you entered here.
Assumptions and limitations
A z-score describes relative position, not practical importance. Extreme values and skewed or heavy-tailed data can make a normal-percentile interpretation misleading.
Consider the Confidence Interval Calculator for a complementary summary and the Probability Calculator when your question involves another statistical property. No single statistic describes every important feature of a data set.
Frequently asked questions
Sources and methodology
The formulas and cautions on this page are documented so the calculation can be checked against authoritative statistical guidance.