How to use the Z-Score Calculator
- Choose what you want to find.
- Enter the mean and standard deviation.
- Enter your value(s) or z-score and read the results.
What does this tool do?
A z-score tells you how many standard deviations a value sits above or below the mean. An IQ of 130 with mean 100 and SD 15 has z = 2, which is about the 97.7th percentile.
For normally distributed data, the z-score converts directly into a probability using the standard normal distribution — no z-table needed.
Why use it?
- Percentile and tail probabilities at once.
- Works in both directions.
- Probability between two values.
The formula
z = (x − μ) ÷ σ
x = μ + zσ
Accuracy and limits
- Percentiles assume the data are normally distributed. For skewed data, z-scores still measure distance from the mean but the percentiles won't be exact.
Privacy
The calculation happens instantly in your browser. The numbers you enter are not sent to our servers or saved. There's no account to create and nothing to install.
Frequently asked questions
What's a “good” z-score?
It depends on context. Around 95% of normal data falls within z = ±1.96, so values beyond that are often called unusual.
Last reviewed by the M2Toolkit team.