NORM.INV Function (LibreOffice Calc)

NORM.INV answers a percentile question for a normally distributed quantity: what value has a specified proportion of observations at or below it? Suppose the average weight of an egg is 63 grams, the population standard deviation is 5 grams, and the weights follow a normal distribution. The 90th-percentile weight is approximately 69.41 grams, meaning the model predicts about 90% of weights at or below that threshold. This does not mean 90% of eggs weigh exactly 69.41 grams, nor does it establish that real measurements are normally distributed.

For a normal variable with mean μ and positive standard deviation σ, the mathematical relationship is

NORM.INV(p; mean; stdev) = mean + stdev * standard_normal_quantile(p)
0 < p < 1; stdev > 0

where Φ is the cumulative distribution function of the standard normal distribution. NORM.S.INV(p) supplies the standard-normal quantile Φ⁻¹(p). The percentile function is the inverse of the cumulative distribution, not the inverse of a probability-density curve. The result has the same units as the mean and standard deviation.

Official definition and example: LibreOffice Calc Help — Statistical Functions Part Four, NORM.INV, consulted 2026-10-13. Mathematical input limits are also specified for the equivalent legacy NORMINV in OASIS OpenDocument 1.4 OpenFormula, §6.18.53, consulted 2026-10-13.

=NORM.INV(Number; Mean; StDev)

There are no optional arguments or defaults. The third argument is the population distribution’s assumed standard deviation, not a choice between sample and population standard-deviation functions. When estimating parameters from samples, assess uncertainty separately.

These formulas use the English function names, dot decimal separator, and semicolon argument separator used in the native-tested Calc locale. Another locale can display translated function names, comma decimals or different separators; adapt the formula to your installation instead of changing the mathematical meaning. Calc’s function language and separators can be configured. LibreOffice Calc Guide 26.2 — Setting Up and Customizing LibreOffice, consulted 2026-10-13.

Enter this in any empty cell:

=NORM.INV(0.9;63;5)

Expected result: 69.4077578277 (approximately 69.41). This is LibreOffice Help’s own example, also verified by native Calc calculation in the saved historical test workbook. For a threshold rounded to two decimal places, format the result cell to two decimals; keep the underlying unrounded value for later computations.

Build a reusable percentile calculator

Enter these labels and numbers on an empty sheet:

Use TRUE() for a cumulative probability check. With FALSE() the related NORM.DIST returns probability density, which is not the percentile probability and generally will not equal 0.9. The forward cumulative relationship is documented in LibreOffice Help — NORM.DIST (same statistical function reference), consulted 2026-10-13. The back-check was also performed natively in this review.

All values below were independently calculated with Python’s standard-library normal quantile implementation and compared against recalculated Calc results; the displayed decimals are rounded for readability.

When using a threshold in whole units (for example, inventory), choose the appropriate business rule for rounding. For a high-service-level stocking target, rounding up with ROUNDUP may be suitable, but note that a normal-demand approximation is not by itself a complete inventory model. For a two-sided central interval with tail probability α/2 at each end, use NORM.INV(α/2; μ; σ) and NORM.INV(1-α/2; μ; σ).

Suppose process measurements are modeled with mean 50 and standard deviation 2. A central 95% range leaves 2.5% of model probability in each tail:

=NORM.INV(0.025;50;2)   → 46.0800720309
=NORM.INV(0.975;50;2)   → 53.9199279691

For a central 99% range, replace 0.025 and 0.975 by 0.005 and 0.995. These are distribution ranges for individual observations under the normal model, not 95% confidence intervals for an unknown population mean. For a confidence interval, you need a standard error and an applicable inferential procedure; do not substitute the spread of individual observations for sampling uncertainty.

Use NORM.S.INV to expose the underlying z-score

An exactly equivalent expression is:

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

Its result matches the official egg-weight example within normal floating-point precision. This identity is useful when explaining a threshold to readers who are more familiar with z-scores. For an observed value x, STANDARDIZE gives (x-μ)/σ; avoid treating that forward z-score transformation as a replacement for finding a percentile threshold.

Protect a production calculator from invalid inputs

If probability is in B2, mean in B3, and standard deviation in B4, use:

=IF(OR(B2<=0;B2>=1;B4<=0);NA();NORM.INV(B2;B3;B4))

The check guards the two mathematical domain restrictions. Its use of NA() deliberately makes an invalid numeric domain conspicuous to downstream calculations; change the failure behavior if your sheet uses an explicit data-validation message. An equivalent constant-input guard was tested on valid inputs in Calc; invalid branches were not separately saved as executions. it is not a comprehensive type checker, because numeric-looking text can be implicitly converted and some cell types need separate checks. For strict data entry, consider adding Calc’s Data ▸ Validity restrictions to the probability and standard-deviation input cells.

0 < Number < 1 and StDev > 0 are mathematical validity requirements for an ordinary finite inverse-normal quantile. Do not confuse the error label returned by one release with a guaranteed cross-version contract. The following observations were made in native Calc 25.2.3.2 (Linux), 2026-10-13:

These are observations, not independent claims about LibreOffice 26.8 or every platform. The listed error observations remain version-specific. Misleading conclusions can arise if the normal distribution is a poor model (for example, strongly skewed or bounded data): a valid number is not proof of a valid statistical assumption.

LibreOffice Help states NORM.INV has been available since LibreOffice 4.3 and documents the dotted name with COM.MICROSOFT.NORM.INV namespace information and explicitly says the dotted function is not part of the OpenDocument 1.3 OpenFormula standard. The OASIS OpenDocument 1.4 OpenFormula specification documents the older undotted NORMINV as an inverse-normal function, including the probability and standard-deviation constraints. These are distinct spellings for the same mathematical operation in relevant Calc contexts, not evidence that every application handles both names identically. Do not infer that a dotted-name formula saved through XLSX or ODS will round-trip identically on every version without a cross-application opening test.

This review executed the dotted name and related legacy identity natively in Calc 25.2.3.2 on Linux. It did not execute Microsoft Excel, OpenOffice, mobile spreadsheet apps, or LibreOffice 26.8. Locale and formula compatibility statements not backed by that native environment are documentation checks only, not platform-test results. The Help website was consulted on October 13, 2026 and may describe a newer release than the tested desktop build.

• NORM.S.INV — standard-normal inverse quantile: the underlying z-score when μ=0, σ=1.
• NORM.DIST — normal cumulative probability and density: convert a threshold back to a probability.
• NORM.S.DIST — standard-normal cumulative probability and density: check standard z-score tails.
• STANDARDIZE — convert measurements to z-scores: forward transformation given mean and standard deviation.
• CONFIDENCE.NORM — normal-based confidence-margin calculation: a related but different inferential task.

1. LibreOffice Calc Help, Statistical Functions Part Four — NORM.INV and NORMINV. Supports the function meaning, exact syntax, official 69.4077578277 example, legacy name, LibreOffice 4.3 introduction and namespace note.
2. LibreOffice Calc Help, Statistical Functions Part Five — NORM.S.INV. Supports the z-quantile counterpart and inverse-normal naming.
3. OASIS OpenDocument 1.4 OpenFormula, Part 4, §6.18.53 NORMINV. Supports legacy standardized syntax and domain; does not itself prove the dotted implementation is standardized.
4. LibreOffice Calc Guide 26.2, Setting Up and Customizing. Documents formula-language and locale settings.
5. First-party native validation, 2026-10-13: packaged native/test_native.py, recalculated native/NORM_INV_NORM_S_INV_native.ods, and native/native_results.json document execution and observed output separately from official Help or independent Python calculations. Across the two companion reviews there were 81 independent numerical assertions passed (81/81) and 25 additional diagnostic observations. All native claims are limited to LibreOffice 25.2.3.2 on Linux.