Normal Distribution & Z-Score Calculator
Compute z-scores and normal distribution probabilities P(X < x), P(X > x) and P(x₁ < X < x₂) for any mean and standard deviation.
How to use the Normal Distribution & Z-Score Calculator
- Enter or select: Mean μ, Standard deviation σ, x (or x₁).
- Fill in what you know of: x₂ (optional, for between) — leave the unknown empty.
- The results (z-score, P(X < x), P(X > x), P(x₁ < X < x₂), Percentile, Density f(x)) are calculated instantly as you type.
- Use “Copy link” to share the calculation with the same input values.
Formula
- z = (x − μ)/σ
- Φ(z) = ½[1 + erf(z/√2)]