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Z-Score Calculator
Calculate z-scores, raw scores, and probabilities for normal distribution analysis
Z-Score Calculator
Calculate
Z-Score from Raw Score
Raw Score from Z-Score
Z-Score from Percentile
Mean (μ)
Standard Deviation (σ)
Raw Score (X)
Calculate
Common Standardized Tests
IQ Test
μ = 100, σ = 15
SAT (Total)
μ = 1500, σ = 300
ACT Composite
μ = 21, σ = 5
GRE Verbal
μ = 150, σ = 7
GMAT Total
μ = 550, σ = 100
Results
Enter values and click Calculate to see results
Z-Score Interpretation
Common Z-Scores
Z = 0: 50th percentile
Z = 1: 84.1th percentile
Z = 2: 97.7th percentile
Z = -1: 15.9th percentile
Empirical Rule
68% within 1 SD (|Z| ≤ 1)
95% within 2 SD (|Z| ≤ 2)
99.7% within 3 SD (|Z| ≤ 3)
Interpretation
Z > 0: Above average
Z < 0: Below average
|Z| > 2: Unusual value
|Z| > 3: Very unusual value
Tips
Enter the dimensions in the same unit for consistency.
Results update automatically as you type.
Use the unit selector to convert between different measurement systems.