NORM.S.INV in Excel: Normal Quantiles and Critical Values

=NORM.S.INV(probability)

The single argument is a left-tail cumulative probability. A value of 0.95 means 95% of the assumed standard-normal population lies below the requested score. It does not mean 95% lies symmetrically within ±that score.

Microsoft documents #NUM! for probability≤0 or probability≥1, and #VALUE! for nonnumeric input. The mathematical extreme quantiles at probabilities 0 and 1 are not finite z-scores.

=NORM.S.INV(0.5)
=NORM.S.INV(0.025)
=NORM.S.INV(0.975)

Expected results are 0, -1.959963985 and 1.959963985. The median is zero, and complementary probabilities have opposite quantiles.

Enter 0.1, 0.25, 0.5, 0.75 and 0.9 in A2:A6 and fill down =NORM.S.INV(A2). Expected results are -1.281551566, -0.674489750, 0, 0.674489750 and 1.281551566. The resulting scores increase with the probabilities.

=NORM.S.INV(0.95)
=NORM.S.INV(1-0.05/2)

Expected results are 1.644853627 and 1.959963985. The first leaves 5% in the upper tail. The second leaves 2.5% in each tail when used symmetrically with its negative.

A central 95% interval therefore uses approximately ±1.96 under the standard-normal model. Using ±1.645 instead gives about 90% central coverage. Write down which tail or interval is intended before choosing the probability argument.

Assume a fictional normal model has mean 100 and standard deviation 15. Its 90th-percentile measurement is:

=100+15*NORM.S.INV(0.9)

Expected result: 119.223273483. The inverse function supplies the standardized score; multiplying by the positive scale and adding the mean returns original units.

The parameter values and normal-model assumption must come from the analysis. This formula neither estimates them from raw data nor guarantees that an observed dataset has the assumed distribution.

For an illustrative sample mean 50, known population standard deviation 10 and sample size 100, a 95% normal-model margin is:

=NORM.S.INV(1-0.05/2)*10/SQRT(100)

Expected margin: 1.959963985, giving endpoints about 48.040036015 and 51.959963985 when subtracted from and added to 50.

This example explicitly assumes an appropriate sampling model and known population standard deviation. Replacing that scale with an estimated sample standard deviation can require a different distribution. NORM.S.INV does not choose between a z-based and t-based method or validate independence.

=NORM.S.DIST(NORM.S.INV(0.9),TRUE)
=NORM.S.DIST(NORM.S.INV(0.025),TRUE)

Expected results are approximately 0.9 and 0.025. Treat the comparison as numerical, with a tolerance appropriate to the application, rather than promising exact equality for every binary floating-point value.

Microsoft describes an iterative search and dependence on the cumulative calculation’s precision. These examples do not establish accuracy in extreme tails or every supported Excel build.

• Inputs 0, 1, -0.1 and 1.1 have documented #NUM! expectations.
• Enter 95% or 0.95, not 95, when a 95th percentile is intended.
• A negative output for probability below 0.5 is expected; it is a score below the mean.
• If the desired input is an upper-tail probability alpha, the corresponding upper score uses 1−alpha.
• If a confidence level is central, divide the excluded probability between two tails before taking the upper inverse.

Do not clip invalid probabilities silently to tiny positive numbers: that invents a finite threshold with a different meaning. Blank handling, text coercion, platform-specific convergence and native extreme-tail behavior remain unverified.

• Current documentation: the dedicated Microsoft reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Introduced: Microsoft’s alphabetical function catalog marks NORM.S.INV as introduced in Excel 2010. The exact first build and platform-specific introduction dates are not established here.
• Last functioning version: unknown; a current help listing is not a last-working-build test.
• Evidence checked: October 15, 2026. Official documentation was freshly retrieved; examples below were independently calculated. No native Excel, Mac or web-client execution was performed.

• Microsoft NORM.S.INV reference.
• Microsoft function catalog and introduction-marker explanation.
• Editorial testing standards.

Examples use English function names and comma separators. Expected numbers are rounded independent mathematical calculations; documented error expectations are labeled as such. They are not captured Excel output. All illustrative data and policies are fictional.