Contact
12 programs
Explore the site

LOGINV in Apple Numbers: Lognormal percentiles and inverse CDF

Statistical Intermediate Apple Numbers

Get the positive lognormal threshold for a target cumulative probability in Apple Numbers.

Verification status: Official documentation referenced; example outcomes independently reasoned or arithmetically checked where stated. Not executed in Apple Numbers. How formula examples are checked

Quick answer: =LOGINV(0.78,1.7,2.2) returns about 29.9289150377259 in Apple’s official example. This is the positive x at which the corresponding lognormal distribution has accumulated 78% probability. It does not mean 78% of observations exceed x, nor does it use the original-scale arithmetic mean or standard deviation. [A1, A2, C1]

Why use LOGINV?

LOGINV translates a target percentile into a positive value for a lognormally modelled quantity such as service duration, a multiplicative forecast outcome, or a positively skewed measurement. For a fixed log-scale mean and SD, a 90th-percentile result means an estimated 90% of values are at or below that cutoff under the model. It does not inspect or rank the existing table’s observations; use a ranking function if you need an empirical percentile. [A1, C1]

Apple’s exact syntax, types, order and defaults

=LOGINV(probability, mean, stdev)
Position Apple argument Type Required Bound / definition / default
1 probability Number value Yes Strictly 0 < probability < 1; no default. Use 0.90, not 90.
2 mean Number value Yes Arithmetic mean of the natural logarithm LN(X), not the mean of raw X; no default.
3 stdev Number value Yes Population SD of LN(X), strictly >0; no default.

All three arguments appear in Apple’s signature without an optional marker; the source does not give omitted defaults. The return is a positive original-scale threshold, not a probability. If the logarithm of X is normal with mean μ and SD σ, LOGINV(p,μ,σ) = EXP(μ + σ × Φ⁻¹(p)) mathematically. In Apple’s function catalogue the normal quantile counterpart is NORMINV and the forward lognormal CDF is LOGNORMDIST. [A1, A2, C1]

Reproducible Numbers worksheet: delivery-time percentiles

Name a Numbers table DeliveryModel. Set B1 Target probability, C1 Log mean, D1 Log population SD, E1 Estimated threshold. Enter the following B–D numbers, then put the row-2 formula in E2 and fill down through E6. Interpret the resulting thresholds as minutes for this hypothetical lognormal time model; times are numeric and unitless inside the formulas. [A5, C1]

Row B: target p C: μ D: σ E: formula Expected threshold
2 0.1 1 0.5 =LOGINV(B2,C2,D2) 1.4322178935
3 0.25 1 0.5 =LOGINV(B3,C3,D3) 1.94013027892
4 0.5 1 0.5 =LOGINV(B4,C4,D4) 2.71828182846
5 0.75 1 0.5 =LOGINV(B5,C5,D5) 3.80853604483
6 0.9 1 0.5 =LOGINV(B6,C6,D6) 5.15917035562

The median (p=0.5) is 2.71828182846 minutes; the 90th percentile is about 5.15917035562 minutes. The distance between the 75th and 90th percentiles is larger than between the 10th and 25th percentiles because the original-scale lognormal distribution is right-skewed. This shape is a mathematical characteristic of the model, not a property established by a sample of deliveries. [C1]

Apple’s example and independent check

=LOGINV(0.78,1.7,2.2)

Apple gives 29.9289150377259. Independent calculation uses z=Φ⁻¹(0.78) then EXP(1.7 + 2.2×z) to give 29.9289150377259 (rounding agrees with Apple). This check is performed using SciPy’s lognormal quantile formula, not the Numbers app. [A1, C1]

Advanced use: model checks and decisions

Check the inverse against the forward CDF

=LOGNORMDIST(LOGINV(0.9,1,0.5),1,0.5)

Mathematically expected 0.9 up to floating-point rounding, because LOGINV returns the x where the forward CDF equals p. This is a valuable review check but not proof of native Numbers numerical stability. Do not exchange the parameters: p is always first in LOGINV while x is first in LOGNORMDIST. [A2, C1]

Three delivery planning cutoffs

Use a common μ=1, σ=0.5: =LOGINV(0.1,1,0.5) → 1.4322178935; =LOGINV(0.5,1,0.5) → 2.71828182846; =LOGINV(0.9,1,0.5) → 5.15917035562. The first and last are not symmetric around the median in original units, though the corresponding standard-normal z-scores have equal and opposite magnitudes. [C1]

Hold parameter cells fixed when comparing many percentiles

Put log mean 1 in C2 and log SD 0.5 in D2. With target probability in B3 (say 0.75), use:

=LOGINV(B3,$C$2,$D$2)

Copy down to keep the distribution model fixed. Without $ signs, copied formulas will shift C2/D2 and could change the model unexpectedly. Apple’s reference documentation supports relative and locked references. [A5]

Price or time tail budgeting from a model

If an organization wants 95% of modeled completion times not to exceed the planned limit, use:

=LOGINV(0.95,1,0.5)

Independently expected 6.1868545882. Whether 95% actual service performance meets this target requires empirical verification; an inverse CDF cannot validate the model’s real-world fit. [C1]

Locale spelling and formatting

The English reference uses LOGINV with commas separating arguments and decimal points within numeric literals. The corresponding Apple Portuguese-Brazil function identifier is INVLOG, with localized argument separators (semicolons) and decimal commas, e.g. =INVLOG(0,78; 1,7; 2,2) for the same mathematical inputs. It is a translation of the same canonical function, not another English article slug. Check the installed Functions Browser when sharing formulas across languages and software versions. [A3]

Numbers-specific references and formula entry

Build each example as a Numbers table, not an assumed Excel worksheet: enter row-1 headings, type the numeric values in the listed cells, enter each formula beginning with =, and fill down only where instructed. B2 addresses a cell in the current table; copied relative references change by row. A locked reference such as $C$2 keeps a shared parameter fixed. Apple documents that a sheet can contain multiple named tables; if the source is in another table named Model, select the actual cell in the Formula Editor or use a table-qualified reference such as Model::B2. Do not assume a single global sheet grid. [A5]

For LOGINV and GAMMAINV, keep probability inputs as numeric values strictly between 0 and 1, not 90 for a 90% target. You may format cumulative probability results as Percent, but formatting does not alter a mathematical value. The LOGNORMDIST and GAMMADIST first arguments are observation thresholds, not probabilities. Keep parameters numeric and do not append units inside formula input cells. If copied formulas point to the wrong table or a moving shared parameter, inspect the reference tokens in Numbers. [A5]

Errors, input limits and troubleshooting

Apple’s individual function help specifies permitted argument domains; it does not document a stable displayed error token for every invalid input, device, locale, or cell-type conversion. Consequently the following are predicted invalid inputs or user misunderstandings, not observed Numbers errors. No #... token or screenshot is invented. [A1, A4]

Input or result Problem Action
=LOGINV(0,1,0.5) or =LOGINV(1,1,0.5) Endpoints excluded by Apple’s probability domain. Use probability strictly between 0 and 1; treat endpoints as limiting mathematical cases, not valid formula examples.
=LOGINV(90,1,0.5) Percent was entered as 90, outside the probability domain. Enter 0.9 or a numeric cell formatted as 90%.
=LOGINV(0.8,1,0) or SD negative Apple requires strictly positive log-scale population SD. Correct dispersion parameter.
Output appears very large when σ increases Lognormal percentile is measured in original units and varies exponentially. Check that μ and σ are the parameters of LN(X), not raw X.
Negative output expected A lognormal percentile cannot be negative. Revisit the distribution assumption rather than negating the result.
=LOGINV(0.8,1) A required third argument is missing; no default documented. Supply positive population SD.
Imported labels or empty parameters Function’s arguments must be numeric. Replace text with valid numbers and check references.
Percentile values compare differently across locales Decimal comma and argument punctuation changed. Use the locale-appropriate function name and separators.

Compatibility, support and evidence boundaries

The function’s English signature and examples are from Apple Formulas and Functions Help 15.4, inspected 2026-10-13 UTC. Apple also documents formula editing and references for Numbers; the Help navigation covers Apple’s iWork formula ecosystem, but the existence of a current documentation article is not proof of native execution on Mac, iPad, iPhone, iCloud, or older versions. Apple publishes app release documentation, which must not be read as evidence that this particular function debuted in that release. Its earliest supported Numbers version was not independently established. [A1, A4, A5, A6]

Do not transfer Excel, Google Sheets or other spreadsheet engines’ default arguments, error codes, statistical parameter definitions, locale punctuation, or precision guarantees to Numbers. Finite-precision corner cases, text/blank coercion, large-parameter stability, and exact error messages require native confirmation. These guides were checked against documentation and by independent numerical computation only; there was no Apple Numbers execution, import/export test, screenshot or historical-platform regression test. Intermediate expected results below are rounded for readability; a Numbers cell’s number format may show fewer digits. [A1, C1]

  • LOGINV — exact Apple syntax, domains and official numeric example. [A1]
  • LOGNORMDIST — forward cumulative probability for the inverse result. [A2]
  • LN — transform an original-scale positive observation to logarithmic units. [A2]
  • EXP — back-transform a log-scale statistic. [A2]
  • NORMINV — related normal rather than lognormal quantile; use only with correctly transformed parameters. [C1]

Claim-level official references and validation sources