Download your PDF
Inverse Standard Normal (z Quantile) result sheet — free, supported by sponsors. Your download button appears in 20 seconds.
This free download is supported by sponsors — continuing in
20
Your file is generated in your browser when you choose Download — nothing is uploaded. If this calculator returns enough numeric data, the export also includes its best-fit chart alongside the readable table.
WorldCalculate result export
Inverse Standard Normal (z Quantile) — result sheet
Finds the z-score with a given left-tail area under the standard normal curve.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Acklam rational approximation for Φ⁻¹(area).
Inverts the standard normal CDF via the Acklam approximation (accurate to ~1e-9). Use it for critical values and percentiles.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Left-tail area — Strictly between 0 and 1; 0 and 1 are invalid.; minimum 0; maximum 1
Worked example
| Input | Value |
|---|---|
| Left-tail area | 0.975 |
z ≈ 1.9600.
Assumptions and limits
- Standard normal (mean 0, sd 1); rescale other normals separately.
- Area is a left-tail probability strictly inside (0, 1).
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.
No saved result was found. Please run the calculation first, then choose Download again.