Inverse Normal Calculator
Calculate inverse normal using your data.
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What this tool does
Calculate inverse normal using your data. Finds the value below which the entered percentage of a normal distribution falls (a quantile). Accuracy is about 1 part in 10⁹ for the z value.
How to use the Inverse Normal Calculator
- Enter or select percentile — area to the left (%).
- Enter or select mean (μ).
- Enter or select standard deviation (σ).
- Read the calculated result; change any measurement to compare alternatives.
Formula
z = Φ⁻¹(percentile) by the Acklam rational approximation; x = μ + zσ
- pct
- Percentile — area to the left (%)
- mu
- Mean (μ)
- sigma
- Standard deviation (σ)
Finds the value below which the entered percentage of a normal distribution falls (a quantile). Accuracy is about 1 part in 10⁹ for the z value.
Worked example
For inverse normal calculator, the following measurements illustrate the exact method: Percentile — area to the left (%): 95; Mean (μ): 100; Standard deviation (σ): 15.
Inputs
- Percentile — area to the left (%)95
- Mean (μ)100
- Standard deviation (σ)15
Result
- Value x at the percentile124.67
- Z-score1.64
Results explained
- Value x at the percentile
- Value x at the percentile from the formula above. Finds the value below which the entered percentage of a normal distribution falls (a quantile). Accuracy is about 1 part in 10⁹ for the z value.
- Z-score
- Z-score from the formula above. Finds the value below which the entered percentage of a normal distribution falls (a quantile). Accuracy is about 1 part in 10⁹ for the z value.
Frequently asked questions
z = Φ⁻¹(percentile) by the Acklam rational approximation; x = μ + zσ
Finds the value below which the entered percentage of a normal distribution falls (a quantile). Accuracy is about 1 part in 10⁹ for the z value.
Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.
No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.
No. Every calculation, including the distribution algorithms, runs entirely in your browser.