NORM.S.INV Function (LibreOffice Calc)

NORM.S.INV turns a cumulative probability into the corresponding z-score on the standard normal distribution. The standard normal distribution has mean 0 and standard deviation 1. Its z-score measures how many standard deviations a cutoff lies above or below the mean. For example, the one-sided 95th percentile is approximately +1.64485, so a standard normal random variable is at or below that z-score with probability 0.95.

NORM.S.INV is a quantile function, not a calculation of the normal curve’s height and not a direct measure of an empirical dataset. It inverts the cumulative standard normal distribution Φ:

z = inverse_standard_normal_CDF(p), for 0 < p < 1

The sign of a result has meaning: p below 0.5 gives a negative z-score, p equal to 0.5 gives zero, and p above 0.5 gives a positive z-score. This symmetry is useful when building two-sided cutoffs: NORM.S.INV(1-p) = -NORM.S.INV(p) to floating-point precision.

Official description: LibreOffice Help, Statistical Functions Part Five — NORM.S.INV, checked 2026-10-13. The older LEGACY.NORMSINV function is also specified in OASIS OpenDocument 1.4 OpenFormula, §6.18.55, checked 2026-10-13.

=NORM.S.INV(Number)

One required argument, no optional arguments and no default. The function assumes μ=0 and σ=1; there are no mean or standard-deviation parameters. For a normal distribution with another mean and standard deviation, use NORM.INV(p;mean;stdev) instead.

The examples use English-language Calc function names, decimal points, and semicolon separators from the tested environment. If your locale uses commas for decimals or translated function names, adjust what you type and confirm your Calc formula settings. LibreOffice Calc Guide 26.2 — Setting Up and Customizing, checked 2026-10-13.

=NORM.S.INV(0.95)

Native-tested result: 1.64485362695147 (roughly 1.645). This cutoff leaves 95% of a standard normal distribution to the left and 5% to the right. It is not the cutoff for a central 95% interval, which places 2.5% in each tail and needs a larger positive value.

The official LibreOffice Help example also reproduces as:

=NORM.S.INV(0.908789)

Result: approximately 1.333334673. This matches the LibreOffice Help example after rounding; the native stored result was approximately 1.33333467304411. Official example, checked 2026-10-13.

In a blank Calc sheet enter these values, formulas and descriptions:

These quantities are probabilities of a continuous model, not observed frequencies in any particular finite sample. The saved historical ODS workbook includes closely related numerical assertions and independent Python-standard-library expected values; this exact prose table has also been checked against the recorded results, rounded as shown.

Verify a quantile with the forward cumulative function

The inverse result can be checked using NORM.S.DIST with TRUE() for cumulative evaluation:

=NORM.S.DIST(NORM.S.INV(0.975);TRUE())

Expected result: approximately 0.975. The round-trip relation was tested natively across multiple probabilities in this review. Do not use FALSE() in the check: that selects the probability density at the z-score, not the probability to its left. The forward function’s syntax is documented in the relevant LibreOffice Help statistical functions; check 2026-10-13.

For a one-sided upper-tail α=0.05 cutoff:

=NORM.S.INV(1-0.05)       → 1.64485362695147

For a two-sided central 95% normal interval, place α/2 in each tail:

=NORM.S.INV(1-0.05/2)     → 1.95996398454005
=NORM.S.INV(0.05/2)       → -1.95996398454005

This distinction is especially important when checking critical values for a z-test. A value of 1.96 is a familiar rounded presentation for a two-sided 5% normal threshold, but formulas should use the full computed precision unless a particular rounding policy is required.

Advanced example: illustrative confidence interval for a known standard error

Suppose an estimate equals 100 and its known standard error is 4. Under an applicable normal approximation, the 95% margin based on a two-sided normal critical value is:

=NORM.S.INV(1-0.05/2)*4

Expected margin: approximately 7.8398559382. The interval endpoints are:

=100-NORM.S.INV(1-0.05/2)*4     → 92.1601440618
=100+NORM.S.INV(1-0.05/2)*4     → 107.8398559382

This is a normal-based illustrative interval. It is justified only when the estimator and standard error meet the method’s assumptions; the function alone cannot determine whether those assumptions hold. For estimated variances in small samples, a t-based interval may be needed instead. LibreOffice’s CONFIDENCE.NORM addresses a related normal approximation but is a separate function.

Convert a z critical value to real-world units

For mean 63 g and standard deviation 5 g, the 90th percentile threshold can be expressed as:

=63+5*NORM.S.INV(0.9)

Expected: 69.4077578277 grams, matching =NORM.INV(0.9;63;5) to numerical precision. For any normally modeled quantity, mean + standard_deviation * z maps from standard-normal units back into the original measurement units. Do not interpret this as proof that the raw observations truly follow a normal model.

Input checks you can paste into a sheet

If the probability is in cell A2, this guards the mathematical domain:

=IF(OR(A2<=0;A2>=1);NA();NORM.S.INV(A2))

The saved Calc test validated a corresponding constant-input guard for a valid probability; its invalid branch was not separately executed. Invalid values produce a deliberately visible #N/A; the output is not a valid quantile. For strict worksheets, also configure Data ▸ Validity to constrain probability input to numeric values between 0 and 1, exclusive. Quoted numeric text may be converted automatically in some cases, so spreadsheet entry constraints are preferable to relying solely on computed errors.

For a finite inverse-standard-normal quantile, the cumulative probability must satisfy 0 < p < 1. Endpoints correspond to infinite limiting quantiles, not valid finite results. The exact error labels below are observed for Calc 25.2.3.2 on Linux, October 13, 2026, and must not be assumed identical in other releases or spreadsheet applications.

Extra diagnostic observations were not counted as passes of numerical assertions. A different function or implementation can return a different error message for the same mathematically invalid input; prioritize domain validation over hardcoding error-string comparisons.

The official LibreOffice Help page states that NORM.S.INV was introduced in LibreOffice 4.3, and that its dotted naming is documented with COM.MICROSOFT.NORM.S.INV namespace information, rather than being part of the OpenDocument 1.3 OpenFormula function list. The newer OpenDocument 1.4 OpenFormula specification documents an older standard-normal inverse as LEGACY.NORMSINV; LibreOffice Help also documents NORMSINV as a legacy undotted spelling. These names are useful for understanding imported or older spreadsheet formulas, but support should be checked in the target application.

Although equivalent legacy functionality and inverse relationships were tested in this Calc environment, no Microsoft Excel, OpenOffice, Google Sheets, mobile, or cross-OS execution occurred. An ODS or XLSX document may require different namespaces or formula-name translations on import; this guide makes no untested cross-application round-trip promise.

The current online Help page is titled for a newer LibreOffice release than the tested Calc 25.2.3.2 desktop build. Documentation statements are clearly distinguished from native results and independent math.

• NORM.INV — inverse quantile with specified mean and standard deviation.
• NORM.S.DIST — standard-normal cumulative probability and density (back-check a z quantile).
• NORM.DIST — cumulative probability and density for other normal distributions.
• STANDARDIZE — transform an observation into a z-score.
• CONFIDENCE.NORM — normal-based confidence margin.

1. LibreOffice Help — Statistical Functions Part Five: NORM.S.INV, NORMSINV, NORM.S.DIST, checked 2026-10-13. Supports syntax, z-quantile definition, LibreOffice 4.3 availability, official example and namespace information.
2. LibreOffice Help — Statistical Functions Part Four: NORM.INV, NORMINV, checked 2026-10-13. Supports converting z to real-world percentile units.
3. OASIS OpenDocument 1.4 OpenFormula §6.18.55 — LEGACY.NORMSINV, checked 2026-10-13. Supports legacy standard-normal quantile syntax and probability domain; it does not alone standardize the dotted Calc spelling.
4. LibreOffice Calc Guide 26.2, Setting Up and Customizing, checked 2026-10-13. Supports formula language/locale discussion.
5. First-party test evidence, 2026-10-13: the immutable review ZIP contains native/test_native.py, the recalculated native/NORM_INV_NORM_S_INV_native.ods and native/native_results.json. Both companion guides together have 81 of 81 independent native numerical assertions passed, plus 25 separate diagnostic observations. Independent expected numbers were computed with Python’s statistics.NormalDist.inv_cdf, not inferred from cached spreadsheet results.