A z-score is how many standard deviations a value sits from the mean—useful with normal tables and cross-scale comparisons.
How to use
- Enter value x, mean μ, and standard deviation σ (σ > 0).
- Read z = (x − μ) ÷ σ and the position hint on the page.
Example
Score 110, mean 100, SD 10 → z = 1.0.
For a mean interval from sample stats, see the confidence interval calculator.
Notes
Sample-based μ and σ need careful wording; very small samples may need t-based methods.
Frequently asked questions
How is z-score calculated?
z = (x − mean) ÷ SD. Sign shows above/below mean; magnitude shows distance in SD units.
Why use a z-score?
Compare values on different scales; pair with normal tables. Related: confidence interval.
Must SD be positive?
Yes—SD = 0 means no spread; division is undefined.
Is z = 2 extreme?
Under near-normal data, |z|≈2 is fairly uncommon; |z|>3 is rarer—thresholds vary by field.
Sample mean and SD?
Sample μ and σ are common approximations; wording should reflect estimation.
Can I save my inputs?
Yes. Copy link below the form keeps your current inputs so you can share the scenario or save it for later.