NORMSINV Function (LibreOffice Calc)

• Introduced: First release not established. This name is documented in the LibreOffice 3.3 function appendix; that establishes historical presence, not introduction.
• Supported in: LibreOffice 26.8.1.1. The NORMSDIST/NORMSINV spellings are retained legacy functions, not proven retired functions.
• Scope: Desktop Calc. These examples use English function names, semicolon separators and decimal points.
• Checked: October 14, 2026. Official source/documentation and independent mathematical examples checked; LibreOffice Calc was not run for this guide.

NORMSINV maps a left-tail cumulative probability to a standard-normal z-score. It reverses NORMSDIST and is equivalent to NORMINV(p;0;1). The result is measured in standard-deviation units; it is not itself a probability. Official reference.

Probabilities below 0.5 produce negative scores, 0.5 produces zero, and probabilities above 0.5 produce positive scores. Mathematically z=√2×erf⁻¹(2p−1). The inverse is not the reciprocal 1/NORMSDIST(p).

=NORMSINV(Probability)

The single argument is required. Use an interior probability 0<p<1 for a finite result. Enter 0.975 or 97.5%, not 97.5, when requesting the 97.5th percentile. The percentage format changes how a value is shown; it does not convert an already stored 97.5 to 0.975.

The release evaluator rejects probabilities outside [0,1]. At exactly 0 and 1 it takes a separate no-value error path. These endpoints correspond to unbounded normal cutoffs, so they must not be treated as ordinary finite z-scores. This statement follows the source; the application’s visible error token was not tested.

Enter each formula in a separate cell. Expected mathematical values below are rounded to twelve decimal places.

For an upper one-sided 5% tail, put 0.95 in A2 and use =NORMSINV(A2). The expected result is 1.644853626951. Supplying 0.05 instead requests the lower 5% cutoff, approximately −1.644853626951.

For a central 95% interval, place 0.025 and 0.975 in A3:A4 and fill =NORMSINV(A3) down. The expected cutoffs are approximately −1.959963984540 and 1.959963984540. Each omitted tail contains 2.5%. Decide which tails the question concerns before choosing probabilities.

Suppose a model has mean 10 and SD 2. The 90th percentile is =10+2*NORMSINV(0.9), approximately 12.563103131089. In a worksheet, put p in A2, mean in B2 and SD in C2, then use =B2+C2*NORMSINV(A2) in D2.

This equals =NORMINV(A2;B2;C2) for valid inputs. Require C2>0 so the affine transformation represents a valid normal model. The resulting D2 has measurement units, whereas the intermediate z-score is dimensionless.

To check the inverse separately, put =NORMSINV(0.975) in F2 and =NORMSDIST(F2) in G2. G2 should recover approximately 0.975. Use the full stored F2 rather than typing 1.96; the rounded cutoff has a slightly different cumulative probability.

Tail quantiles are sensitive to small probability changes near 0 or 1. Preserve the original probability and avoid rounding it before inversion. A cell displayed as 100% can still contain an interior probability; replacing that cell reference with the literal 1 is a meaningful change.

These cutoffs describe an assumed distribution. They are not a complete hypothesis test or confidence-interval procedure by themselves. A numerical round trip checks calculation consistency, not whether the model and chosen tail answer the underlying question. Coercion, locales and extreme probabilities require their own installed-application checks when relevant.

• NORMSINV function documentation
• LibreOffice 26.8.1.1 argument handling and calculation