What Is a Z-Score?
A z-score measures how many standard deviations a value is from the mean of a data set. It standardizes values from different distributions so they can be compared on a common scale, and it's the basis for finding percentiles in a normal distribution.
How to Use the Z-Score Calculator
- Enter your value (x).
- Enter the mean of the data set.
- Enter the standard deviation.
- View the z-score, percentile, and associated probabilities.
Z-Score Formula
Worked Example
z = (85 − 75) / 10 = 1.00
A z-score of 1.00 means the score is exactly 1 standard deviation above the mean.
This corresponds to approximately the 84th percentile in a normal distribution.
Understanding Your Results
A positive z-score means the value is above the mean; a negative z-score means it's below. The percentile shows the approximate percentage of values in a normal distribution that fall below your value — assuming the underlying data is normally distributed.
Common Uses for Z-Scores
- Standardized test scores (comparing performance across different tests or score scales).
- Quality control (identifying values that deviate significantly from the norm).
- Statistics and research (hypothesis testing, comparing across normal distributions).
Common Mistakes to Avoid
- Applying z-scores and their percentile interpretation to data that isn't approximately normally distributed.
- Confusing population standard deviation with sample standard deviation when calculating z-scores.
- Misreading the sign — a negative z-score means below average, not an error.
Frequently Asked Questions
A z-score of 0 means the value is exactly equal to the mean of the data set.
In a normal distribution, a z-score of 1.00 corresponds to approximately the 84th percentile, meaning about 84% of values fall below it.
Yes — a negative z-score means the value is below the mean. For example, a z-score of −1 means the value is one standard deviation below average.
It standardizes values so they can be compared across different distributions or scales, and it's used to find percentiles and probabilities in a normal distribution.
The z-score itself can be calculated for any distribution, but the percentile and probability interpretations assume the data is approximately normally distributed.