Z-Score Calculator
Use your own numbers after reviewing the formula and worked example.
Quick answer
A z-score measures how many standard deviations a value lies above or below the mean.
Formula or method
Keep units, percentages and time periods consistent. The formula is useful as a transparent check on the calculator result and helps explain why changing one input changes the answer.
Step-by-step
- Subtract the mean from the observed value.
- Divide by the standard deviation.
- Keep the sign.
- Interpret the magnitude as standard deviations from the mean.
Worked example
If x=85, mean=75 and standard deviation=5, z=(85−75)/5=2.
How to interpret the result
Positive z-scores are above the mean; negative scores are below it. Probability interpretations require an appropriate distribution model.
When the answer is used for a purchase, loan, payroll decision, construction order, school grade, health estimate or other real-world choice, verify the assumptions that matter in that context. Accurate arithmetic still depends on accurate inputs.
Common mistakes
- Using variance instead of standard deviation.
- Dropping the negative sign.
- Assuming all data are normally distributed.
Frequently asked questions
What does z=0 mean?
The value equals the mean.
What does negative z mean?
The value is below the mean.
Can z exceed 3?
Yes.