Z-Score Calculator | Normal Distribution & Percentiles
Calculate Z-scores, solve for raw scores, and find the area under the normal distribution curve (left, right, two-tailed, or interval regions).
Standard Z-Score
1.5
Solved Raw Value (x)
1.5
Dynamic Shaded Bell Curve Plot
Normal Distribution Area Metrics
Left-Tailed P(Z < z₀)
93.3193%
Percentile: 93
Right-Tailed P(Z > z₀)
6.6807%
Upper tail significance
Two-Tailed Out (Outside)
13.3614%
Extreme regions
Two-Tailed In (Inside)
86.6386%
Central coverage
Z-Score Workings Steps
1. Formula: Z = (x - μ) / σ
2. Z = (1.5 - 0) / 1 = 1.5000
3. Standard Normal probability areas derived:
4. - P(Z < 1.50) = 93.3193%
5. - P(Z > 1.50) = 6.6807%
6. - Two-tailed outside extremes: P(|Z| > |1.50|) = 13.3614%
7. - Two-tailed central inside: P(-|1.50| < Z < |1.50|) = 86.6386%