Z-Score Calculator

Calculate z-scores, percentiles, and statistical interpretations. Convert raw scores to standard scores.

Calculation Type:

Value (x):

Mean (μ):

Standard Deviation (σ):

About Z-Scores

A z-score measures how many standard deviations a value is from the mean
Positive z-scores indicate values above the mean
Negative z-scores indicate values below the mean
Z-scores follow a standard normal distribution
Useful for comparing values from different distributions

Interpretation Guide

|z| < 1: Within 1 standard deviation (68% of data)
|z| < 2: Within 2 standard deviations (95% of data)
|z| < 3: Within 3 standard deviations (99.7% of data)
|z| ≥ 3: Beyond 3 standard deviations (potential outlier)

Formula

z = (x - μ) / σ

x = individual value
μ = population mean
σ = population standard deviation