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Inverse Normal Distribution Calculator — result sheet
Find the normal-distribution value at a chosen cumulative percentile from a mean and standard deviation.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: z = Φ⁻¹(p); x = μ + zσ, where p is the cumulative probability and Φ is the standard-normal CDF.
An inverse normal calculation answers the reverse question: given a cumulative percentile, what value marks that point in a normal model? The page reports both the standardized z quantile and the value in the visitor's original unit, with tail probabilities kept visible for checking.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Mean μ — minimum -1000000000000; maximum 1000000000000
- Standard deviation σ — minimum 1.0E-6; maximum 1000000000000
- Cumulative percentile — %; minimum 1.0E-6; maximum 99.999999
Worked example
| Input | Value |
|---|---|
| Mean μ | 100 |
| Standard deviation σ | 15 |
| Cumulative percentile | 95 |
The 95th percentile is approximately 124.6728, with z approximately 1.64485.
Assumptions and limits
- The modeled variable follows a normal distribution with the entered mean and positive standard deviation.
- The percentile is cumulative from the lower tail and is entered as a percentage between zero and 100.
- The inverse is evaluated numerically, so the result is an approximation within ordinary floating-point precision.
- A normal model does not prove that an observed dataset is normal or remove sampling uncertainty.
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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