Z-score Calculator
Adjust the inputs below. Results update as you type.
How it works
Z = (x − μ) / σ. A z-score tells how many standard deviations a value is from the mean. Z=0: at the mean. Z=1: one SD above (84th percentile). Z=−1: one SD below (16th percentile). Z=1.96: 97.5th percentile (used in 95% CIs). Assumes a normal distribution—z-scores have less meaning for skewed distributions. Used for outlier detection, standardizing test scores, and quality control.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
Z = (x − μ) ÷ σ: how many standard deviations a value sits from the mean. It converts any normal value to a standard scale.
Worked example
A test score of 85 with mean 70 and SD 10 has z = (85 − 70) ÷ 10 = 1.5, meaning 1.5 SD above average (about the 93rd percentile).
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
What is a z-score?+
A standardized value showing how far a data point is from the mean in standard deviations. Positive is above the mean, negative below.
How does z relate to percentile?+
On a normal distribution, z = 0 is the 50th percentile, z = 1 about the 84th, and z = 2 about the 97.7th.
Why standardize values?+
Z-scores let you compare measurements from different scales or distributions on a common standard footing.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.