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Math & Statistics Calculator
Z-Score Calculator
Calculate a z-score from a value, mean and standard deviation, or paste a data set and let the calculator estimate the mean and standard deviation for you.
Calculate z-score and normal percentile
The number you want to standardize.
Ignored when a data set is provided.
Must be greater than zero.
Used only when the data box has values.
Paste numbers separated by commas, spaces or new lines.
How the z-score is calculated
The core formula is z = (x - mean) / standard deviation. A result of 1.5 means the value is 1.5 standard deviations above the mean.
The percentile estimate assumes a normal distribution. For skewed real-world data, use it as a quick reference rather than a guarantee.
When to use it
- Compare test scores that use different scales.
- Standardize measurements before statistical analysis.
- Find how unusual a value is in a normal model.
Z-Score Calculator FAQ
What is a z-score?
A z-score tells how many standard deviations a value is above or below the mean.
What does a positive z-score mean?
A positive z-score means the value is above the mean. A negative z-score means it is below the mean.
Can this calculator find percentile from z-score?
Yes. It estimates the normal distribution percentile and the area above the z-score.
Should I use sample or population standard deviation?
Use sample standard deviation when your numbers are a sample from a larger population. Use population standard deviation when the list is the whole population.