Finite mean, positive standard deviation, and lower-tail probability strictly between zero and one.
Inverse Normal Distribution Calculator
Enter your values below to get the result first, then scroll for the full explanation and guidance.
Normal quantile
1.95996399Lower-tail probability 0.975
Normal quantile: 1.95996399 (Lower-tail probability 0.975)
The inverse standard-normal approximation is scaled by the entered standard deviation and shifted by the mean.
Inverse normal result
The inverse standard-normal approximation is scaled by the entered standard deviation and shifted by the mean.
Result snapshot
A quick visual read of the values behind this result.
z-score1.95996399
Recommended next checks
- →Enter probability as a decimal strictly between zero and one.
- z-score
- 1.95996399
Try different values to compare results.
Find the normal-distribution quantile for a lower-tail probability, mean, and standard deviation.
Normal quantile
1.95996399Lower-tail probability 0.975
Normal quantile: 1.95996399 (Lower-tail probability 0.975)
The inverse standard-normal approximation is scaled by the entered standard deviation and shifted by the mean.
Inverse normal result
The inverse standard-normal approximation is scaled by the entered standard deviation and shifted by the mean.
Result snapshot
A quick visual read of the values behind this result.
z-score1.95996399
Recommended next checks
- →Enter probability as a decimal strictly between zero and one.
- z-score
- 1.95996399
Try different values to compare results.
Table of Contents
Table of Contents
About Inverse Normal Distribution Calculator
Inverse Normal Distribution Calculator helps you work through the main numbers for this topic quickly with a simple input flow and an instant result.
Use the calculator result as a practical starting point, then review the explanation and assumptions on the page if you want more context.
Calculation method
Apply a standard-normal inverse-CDF approximation, then scale by sigma and add the mean.
Formula explained
Calculation flow
This calculator is structured for fast UK-focused estimates with clear inputs, repeatable logic, and instant results.
Formula
Input values -> calculation engine -> instant result
How the result is built
1Enter the values requested in the form.
2The calculator applies the configured formula logic.
3The result updates instantly with a breakdown.
4Use the output to compare scenarios quickly.
Example
Example verified by the calculator's probability distributions reference cases.
Assumptions
- Finite mean, positive standard deviation, and lower-tail probability strictly between zero and one.
Source basis
- UK-focused calculator flow
- Structured input validation
- Instant result breakdowns
FAQ
Common questions
Trust and notes
Assumptions and important notes
This calculator is designed to give a fast estimate using the method shown on the page. Results are most useful when your inputs are accurate and the tool matches your situation.
Use the result as guidance rather than a final diagnosis or professional decision. If the result could affect health, legal, financial, or compliance decisions, verify it with a qualified source where appropriate.
- Finite mean, positive standard deviation, and lower-tail probability strictly between zero and one.
Method
UK calculator guidance
Last reviewed
April 17, 2026