📐 Z-Score Calculator

Updated: 2026-07-11

Free online Z-score calculator. Enter a value, mean, and standard deviation to compute the Z-score. Supports normal distribution probability lookup. Pure frontend, no data upload.

How to Use

  1. Enter Parameters
    Enter the value X, mean μ, and standard deviation σ.
  2. Calculate
    Click Calculate to get the Z-score.
  3. View Probability
    View Z-score, normal distribution probabilities, and percentile.

FAQ

What is a Z-score?

A Z-score (standard score) indicates how many standard deviations a data point is from the mean. Formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. Positive Z means above mean, negative means below.

What are Z-scores used for?

Z-scores are used for data standardization, comparing data on different scales, identifying outliers, and calculating normal distribution probabilities. Examples: comparing test scores across subjects, detecting anomalies, assessing investment risk.

How to interpret Z-scores?

Z=0 means at the mean; Z=1 means 1 standard deviation above (about 84.13 percentile); Z=-1 means 1 below (about 15.87 percentile); |Z|>2 is typically considered an outlier.

Does this tool support normal distribution probability?

Yes. The tool uses the error function (erf) approximation to calculate cumulative normal distribution probabilities, giving P(Xx), and percentile rank.

Is my data uploaded to a server?

No. All calculations happen locally in your browser. Data is never uploaded to any server.