Math
Standard deviation
Calculate population mean, variance and standard deviation for five values.
Calculators / Math / Z-score
Z-score calculator
Standardize an observation using a population mean and standard deviation.
On this page
Z-score1.5
Calculator controls
How to calculate
Standardize an observation using a population mean and standard deviation.
Z-score = (value-mean)/sd
Worked example
Observed value: 85; Population mean: 70; Standard deviation: 10.
Z-score: 1.5 .
Assumptions and limits
The sign indicates whether the observation is above or below the mean. Distribution assumptions matter when converting z-scores to probabilities.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Standardize an observation using a population mean and standard deviation. The displayed figures use the inputs and formula shown on this page.
When this tool is useful
Use the z-score to compare a scenario, check an estimate, or verify a manual calculation.
Understanding your inputs
| Input | What to enter |
|---|---|
| Observed value | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Population mean | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Standard deviation | Enter a number of at least 0.000001 and no more than 1000000000000. |
Frequently asked questions
What should I check before using the z-score result?
The sign indicates whether the observation is above or below the mean. Distribution assumptions matter when converting z-scores to probabilities.
Is this z-score result exact?
It is exact for the stated mathematical model and entered values. Real-world results can differ when rates, timing, fees, definitions or measurement conditions differ.