Normal Distribution Cdf Calculator

Normal Distribution CDF

The cumulative distribution function (CDF) of a normal N(μ, σ) gives the probability that X ≤ x.

Standard Relation

Φ(z) = ½ [1 + erf(z/√2)] where z = (x − μ)/σ.

Example

For μ=0, σ=1, x=1 → z=1 → Φ(1) ≈ 0.8413.

FAQs

Two-tailed probabilities?
Use symmetry: P(|Z| ≥ z) = 2[1 − Φ(z)].

Nonstandard μ, σ?
Standardize via z = (x − μ)/σ.