Z-Score Calculator
z = (x − μ) / σ — how many standard deviations a value is above or below the mean.
Result
z-score
1.5000
1.50 σ above the mean.
- Difference (x − μ)15.0000
- σ10.0000
- Approximate percentile93.32%
Step-by-step
- z = (85 − 70) / 10 = 15.0000 / 10 = 1.5000.
- |z| = 1.50 → about 93.3% of a normal distribution lies at or below this value.
How to use this calculator
- Enter the value, mean, and standard deviation.
- Read the z-score and approximate percentile.
About this calculator
A z-score expresses how many standard deviations a value is from the mean. Positive = above the mean; negative = below. z=1 means one σ above; z=−2 means two σ below. For a normally distributed dataset, z translates directly to a percentile via the normal CDF.
Frequently asked
|z| > 2 is unusual (~5% chance for normal data). |z| > 3 is rare (~0.3%).
Related calculators
T-Score Calculator
t = (x̄ − μ₀) / (s/√n) — for testing a sample mean against a hypothesized population mean.
Standard Deviation Calculator
Compute sample (n−1) and population (n) standard deviation from a list of numbers.
Mean (Average) Calculator
Compute the arithmetic mean of a list of numbers.
Percentile Calculator
Find the value at the kth percentile in a dataset (linear interpolation).
Variance Calculator
Sample (n−1) and population (n) variance — the square of standard deviation.
Interquartile Range (IQR) Calculator
IQR = Q3 − Q1 — the middle 50% spread, robust to outliers.