Z-score Calculator
Calculate Z-scores, percentiles, and probabilities for normal distribution
Calculate What?
Choose what to calculate
Input Values
Enter known values
The actual observed value
Average of the dataset
Measure of data spread
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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