Normal Distribution Calculator

Calculate probabilities, PDF, CDF, and z-scores for the normal distribution

Distribution Parameters

Probability Density Function

PDF Formula f(x) = (1 / (σ√(2π))) · e^(-(x-μ)² / (2σ²))

Cumulative Distribution Function

CDF Formula F(x) = 0.5 · [1 + erf((x-μ) / (σ√2))]

Point Analysis

Z-Score — z = (x - μ) / σ
PDF Value f(x) — Probability density
CDF Value F(x) — P(X ≤ x)
Percentile — % below this value

Probability Range

P(Lower ≤ X ≤ Upper) — F(upper) - F(lower)

Standard Normal Percentiles

Percentile Z-Score X Value

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