Normal Distribution Calculator
Find probabilities, z-scores, and x-values for any normal distribution with step-by-step solutions.
- Find probability — enter μ, σ, and x to get P(X ≤ x) and P(X ≥ x)
- Find z-score — convert any value to its z-score
- Find x from z — convert a z-score back to its original value
Given μ, σ, and x — find P(X ≤ x) and P(X ≥ x)
Formulas Used
Z-score
Value from z-score
Empirical rule
How to Use This Calculator
- Select a mode — find probability, z-score, or x-value
- Enter your values — mean (μ), standard deviation (σ), and your target value
- See the result with a complete step-by-step breakdown
Quick Reference
| Percentile | Z-Score | P(X ≤ x) |
|---|---|---|
| 1st | -2.326 | 0.01 |
| 5th | -1.645 | 0.05 |
| 10th | -1.282 | 0.10 |
| 25th | -0.674 | 0.25 |
| 50th | 0.000 | 0.50 |
| 75th | 0.674 | 0.75 |
| 90th | 1.282 | 0.90 |
| 95th | 1.645 | 0.95 |
| 99th | 2.326 | 0.99 |
Related
- The Normal Distribution — properties, empirical rule, and worked examples
- Z-Scores — how to calculate and interpret standard scores