Normal CDF Calculator

P(Z ≤ z) for standard normal.

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Formula

Φ(z) = ∫_{−∞}^{z} φ(t) dt

Uses Abramowitz & Stegun rational approximation for the standard normal cumulative distribution.

Worked example

Φ(1.96) ≈ 0.975 — the familiar two-tailed 95% critical value.

Where this can give the wrong answer

  • Approximation error tiny for |z| < 6.
  • Assumes exact normality of data.
  • Heavy tails in finance violate normality.

FAQ

For |z|=1.96, two-tailed p ≈ 0.05.