Z-score Calculator

Calculate Z-scores, percentiles, and probabilities for normal distribution

Results

Z-score
1.0000
Percentile
84.13%
Probability
0.8413
Interpretation
Average (Normal Range)
Formula
Z = (X - μ) / σ

About Z-scores

A Z-score (standard score) measures how many standard deviations a value is from the mean. It standardizes different datasets for comparison and is fundamental in statistics and probability theory.

Interpretation Guide

  • Z > 3: Very High (Exceptional) (99.9%+)
  • Z = 2 to 3: High (Above Average) (95-99.9%)
  • Z = 1 to 2: Above Average (84-95%)
  • Z = -1 to 1: Average (Normal Range) (16-84%)
  • Z = -2 to -1: Below Average (5-16%)
  • Z = -3 to -2: Low (Below Average) (0.1-5%)
  • Z < -3: Very Low (Exceptional) (<0.1%)

Common Uses

  • Standardized test scores (SAT, IQ tests)
  • Comparing performance across different metrics
  • Quality control and outlier detection
  • Research and data analysis in social sciences