Z-Score Calculator
Standardize a value with mean and std dev.
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Formula
z = (x − μ) ÷ σ
Z-score counts how many standard deviations x lies from the mean. Under normality, maps to tail probabilities via the normal CDF.
Worked example
85 with μ=75 and σ=10 gives z = 1 — about 84th percentile.
Where this can give the wrong answer
- σ must be positive.
- Skewed data makes z less meaningful for tail claims.
- Sample vs population σ affects z slightly.
FAQ
- Estimate from sample SD and note you are approximating.