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Normal CDF (Area Below z) — result sheet
Cumulative standard-normal probability for a z-score, accurate to about 1e-7.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Phi(z) via the Abramowitz-Stegun 7.1.26 rational approximation.
Phi(z) is the area under the standard normal curve left of z. Tails beyond |z|=8 are numerically 0 or 1 and are reported as exact bounds.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- z-score — Standard deviations from the mean.; minimum -8; maximum 8
Worked example
| Input | Value |
|---|---|
| z-score | 1 |
0.8413 (about 84.13% of values fall below z = 1).
Assumptions and limits
- Standard normal (mean 0, sd 1); standardize first with the z-score tool.
- Approximation error below 1e-7.
- Inputs limited to |z| <= 8.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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