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Normal Distribution CDF Area & Percentile Calculator

P(X ≤ x) from μ and σ via z-score standardisation.

Calculates the cumulative area under the normal curve (P(X ≤ x)) and the percentile rank for a value x given mean μ and standard deviation σ.

Priya Venkatesan By Priya Venkatesan
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

z = (x−μ)/σ; P(X≤x) ≈ Φ(z) via rational approximation

In depth

Calculates the cumulative area under the normal curve (P(X ≤ x)) and the percentile rank for a value x given mean μ and standard deviation σ.