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Zoho Sheet LOGNORMDIST: Lognormal Cumulative Probabilities

Statistical Intermediate Zoho Sheet

Learn how to calculate lognormal cumulative probabilities in Zoho Sheet with LOGNORMDIST, using practical examples, model checks, and error guidance.

Verification status: See the evidence and test scope described in this guide. How formula examples are checked

Quick answer: =LOGNORMDIST(10;2;0.5) asks for the probability that a positive lognormally distributed random variable is 10 or less, assuming the natural logarithm of that variable follows a normal distribution with mean 2 and standard deviation 0.5. An independent SciPy calculation gives 0.727467038316 (about 72.75%). The formula’s name and three-argument order are confirmed by Zoho’s published reference; this numerical result was not executed in Zoho Sheet. [Z-LND, M1]

Availability and version history

  • Introduced: The original introduction version and date are not established by the checked sources.
  • Availability: Currently documented in Zoho Sheet’s rolling web-service help; no numbered release or retirement endpoint is established.
  • Scope: English-language web-service documentation. Mobile and offline-client parity is outside the verified scope.
  • Checked: October 14, 2026, against the official LOGNORMDIST reference. Documentation check; not a new native test.

Exact Zoho syntax and arguments

LOGNORMDIST(x; μ; σ)
Position Required argument Data and meaning Example
1 x Positive numeric point at which to evaluate the cumulative probability 10
2 μ Numeric mean of the natural-log-transformed random variable, not the arithmetic mean of the original measurements 2
3 σ Positive numeric standard deviation of those natural-log-transformed values 0.5

All three arguments are required in the public Zoho syntax. The help article does not document a fourth cumulative or mode argument, nor an optional default. Use semicolons as printed in the English official examples; Zoho’s spreadsheet locale settings can affect decimal/number formats, so confirm how an imported workbook displays numbers rather than silently changing decimal punctuation. [Z-LND, Z-LOCALE]

What is returned? A cumulative distribution function (CDF), a number in [0,1] representing P(X ≤ x) under the specified model. It is not a lognormal probability density. The distinction matters: the density has a different numerical value and does not itself express the probability of a continuous random variable equalling exactly x. [Z-LND, M1]

Reproducible worksheet: six distinct cases

Enter the following independent model inputs in A through C. Put =LOGNORMDIST(A2;B2;C2) in D2 and fill down to D7. The last column shows independently computed expectations to 12 decimal places; numbers may be rounded differently by the worksheet’s display format. [M1]

Row A: x B: log mean μ C: log SD σ D: formula Independent expected CDF
2 1 0 1 =LOGNORMDIST(A2;B2;C2) 0.500000000000
3 1.648721270700128 0 1 =LOGNORMDIST(A3;B3;C3) 0.691462461274
4 10 2 0.5 =LOGNORMDIST(A4;B4;C4) 0.727467038316
5 20 2 0.5 =LOGNORMDIST(A5;B5;C5) 0.976785080434
6 0.5 0 1 =LOGNORMDIST(A6;B6;C6) 0.244108595786
7 25.947598893 4.2 1.8 =LOGNORMDIST(A7;B7;C7) ≈ 0.300000000000

Row 7 recreates the input corresponding to a Zoho-published LOGINV example: Zoho lists illustrative arguments 0.3, 4.2 and 1.8 and a referenced-cell example producing approximately 25.947598893; those values agree mathematically. Feeding that value into the mathematical forward CDF returns approximately 0.3. This cross-reference is official-example research plus an independent model, not a claimed native cross-function test. [Z-LNI, M1]

A compact direct-formula check is =LOGNORMDIST(1;0;1). Under the mathematical model, the median is EXP(0)=1, so the result is 0.5. For the same parameters, values below 1 have CDF below 0.5 and values above 1 have CDF above 0.5. [M1]

Why the logarithmic parameters matter

Let Y = LN(X). The model assumption is Y ∼ Normal(μ, σ²), hence the cumulative lognormal probability is

P(X ≤ x) = Φ((LN(x) - μ) / σ), for x > 0 and σ > 0.

Here Φ means the standard normal CDF. Zoho separately documents NORMSDIST(z) and NORMDIST(x; mean; sd; mode) with a cumulative mode, so a conceptual worksheet cross-check is:

= NORMSDIST((LN(A4)-B4)/C4)

This is a mathematical equivalent for valid inputs; no equality within a specific Zoho build, account, or rounding configuration was measured. Do not mistake μ=2 for a raw-data mean of 2: when μ=2, σ=0.5, the lognormal median is EXP(2)≈7.3891, while the model mean is EXP(2+0.5^2/2)≈8.3729. [Z-NORMSDIST, Z-NORMDIST, M1]

Worked application: order-completion times

Suppose a planning team models a positive order-completion time in days with an illustrative lognormal median of 8 days and log-scale SD 0.6. Put 8 in B2 and 0.6 in B3. The corresponding log mean is =LN(B2) (approximately 2.07944154168). Put a delivery target of 12 days in B4. Then:

B5: =LOGNORMDIST(B4;LN(B2);B3)
B6: =1-B5

An independent lognormal model gives B5 ≈ 0.750408302396 and B6 ≈ 0.249591697604. Under the assumptions, around 75.04% of modeled completions occur by 12 days and 24.96% later. This is not a guarantee about real orders: missing cases, weekends, changing staffing and biased sampling can invalidate the distribution choice. The model describes a hypothetical probability, not a measured service-level agreement. [M1]

To evaluate multiple service targets, enter 8, 12, 15 and 30 in A2:A5 of a new sheet; hold the median 8 in $D$2, log SD 0.6 in $D$3, and use =LOGNORMDIST(A2;LN($D$2);$D$3). At 15 days, the independent CDF is 0.852607220682; at 30 days, 0.986200031725. Use absolute references for fixed parameters to avoid accidental changes while filling down. [M1]

Advanced use: interval probability, median and diagnostics

For a continuous lognormal model, the probability of falling between two positive values L and U, with 0<L≤U, is F(U)-F(L):

=LOGNORMDIST(20;2;0.5)-LOGNORMDIST(10;2;0.5)

The independent expected probability is 0.249318042119. A difference of two CDFs is an interval probability; neither individual CDF is the probability of an exact individual value. For lower endpoints at or below zero, the theoretical CDF is zero, but Zoho documents #NUM! for x≤0—so do not pass zero directly and assume the mathematical boundary convention is implemented. Explicitly set the lower probability to 0 in your own logic if the business domain truly excludes nonpositive values. [Z-LND, M1]

Parameter estimation should be performed on LN(X) values only when original observations are positive. If the raw observations are x1…xn, an illustrative model-building route is to create helper values =LN(A2) etc., calculate their sample mean and sample standard deviation with functions supported by the sheet, and validate the distribution fit. A lognormal assumption is not established by observing a right-skewed histogram. If zeros or negative values occur, examine the source process rather than deleting those observations merely to force a lognormal formula. [M1]

LOGINV is the inverse-partner function. For strictly interior probability p, LOGINV(p;μ;σ) supplies a threshold whose lognormal CDF is p. When creating a dashboard, store p in a separate cell; use =LOGINV(0.9;LN(8);0.6) to estimate a mathematical 90th-percentile time of 17.259668530947 days. See the independent LOGINV guide for the inverse calculation and cautions. [Z-LNI, M1]

Errors, boundaries and troubleshooting

Situation Evidence and action
#NUM! at x≤0 Explicitly documented by Zoho. For a strictly positive-variable model, check the incoming data or formula references; don’t assume a call at zero will return 0. [Z-LND]
#NUM! at σ≤0 Explicitly documented by Zoho. The log-scale SD must be positive. For all-identical measurements, a limiting distribution requires separate reasoning, not a zero-SD call. [Z-LND]
#VALUE! Zoho’s general function error table cites bad argument data types. Check whether imports contain text like "10 days" rather than a number. [Z-LND]
#NAME! Check spelling LOGNORMDIST, semicolon-separated three-argument form from Zoho’s English reference, and invalid named ranges. LOGNORM.DIST is an Excel name—not independently confirmed here as a Zoho alias. [Z-LND, MS-LND]
#REF! Investigate deleted or moved references. A missing reference is not evidence that the distribution function is absent. [Z-LND]
#N/A! Zoho’s generic table discusses failed lookups, not a special LOGNORMDIST numerical rule; investigate the actual input/source before assigning a function-specific meaning. [Z-LND]
CDF appears 0 or 1 Extreme tails and display rounding may explain apparent endpoints. Inspect number formatting and input scaling; do not infer exact certainty from a rounded display. [M1]
Results look unexpectedly small Verify μ and σ describe LN(data), not the original observations; if the input uses base-10 logs, refit using natural logs. [M1]

For a reproducible model, use numeric, finite parameters with x>0 and σ>0, and avoid passing complex/array inputs unless separately confirmed in the target Zoho environment. Zoho does not give a first-supported product release or a web-versus-mobile execution matrix on this individual help page; no such version/platform guarantee is made by this guide. [Z-LND]

Compatibility: Zoho versus Excel

Zoho’s documented LOGNORMDIST(x;μ;σ) is a three-argument cumulative function. Microsoft documents legacy Excel LOGNORMDIST(x,mean,standard_dev) with the same CDF concept, and modern Excel LOGNORM.DIST(x,mean,standard_dev,cumulative) with an additional required boolean allowing either a CDF or a density. Do not mechanically paste the four-argument modern Excel formula into Zoho. These are comparisons of published references, not cross-application execution tests. Function spellings with dots must not create extra Zoho pages or aliases without official Zoho evidence. [Z-LND, MS-LEGACY, MS-LND]

Native validation: Check parsing, numerical outputs, boundary responses and locale behavior in your own Zoho account before operational use.