LOGNORMDIST Function (OpenOffice Calc)

• Introduced: First release not established. The OpenOffice.org 3.3 function appendix documents this name; historical presence does not prove introduction.
• Supported in: Apache OpenOffice 4.1.16. No final supported release has been established.
• Scope: Desktop Calc. Current argument defaults are stated for the cited release, not inferred for every older version.
• Checked: October 14, 2026. Official documentation/source and independent mathematics checked; Apache OpenOffice Calc was not run for this guide.

A positive variable X is lognormally distributed when LN(X) is normally distributed. Mean and StDev describe that logarithm, not the arithmetic mean and standard deviation of X itself. Confusing the two scales changes the model even when the formula calculates successfully. Official reference.

For x>0, the CDF is Φ((LN(x)−μ)/σ). The density is exp(−z²/2)/(xσ√(2π)), where z=(LN(x)−μ)/σ. Density has inverse-measurement units and is not the probability of one exact outcome. The model’s median is exp(μ), while its arithmetic mean is exp(μ+σ²/2).

=LOGNORMDIST(Number [; Mean [; StDev [; Cumulative]]])

Only Number is required. The release evaluator accepts one through four arguments: omitted Mean defaults to 0, omitted StDev to 1, and omitted Cumulative to true. Supply Mean and StDev when specifying the final selector. Use Cumulative=1 for the CDF or 0 for density.

Number is the value x at which the model is evaluated, not an input probability. StDev must be positive. The wiki retains an older three-argument CDF-oriented description. The pinned 4.1.16 implementation already supports the optional parameters and fourth density/CDF selector shown here.

Enter each formula in a separate cell. These independently calculated values are rounded to twelve decimal places.

Put x=2 in A2, log-mean 0 in B2 and log-SD 1 in C2. In D2 use =LOGNORMDIST(A2;B2;C2;1), expected 0.755891404214. The result is the modeled fraction at or below two measurement units. Change the last argument to 0 for density, approximately 0.156874019279 per unit.

Keep the parameters labeled as log-scale values. For this model the median is 1, but the arithmetic mean is exp(0.5), approximately 1.648721270700. Entering that arithmetic mean into B2 would describe a different lognormal distribution.

If an arithmetic mean m>0 and arithmetic SD s>0 are the intended model inputs, the corresponding log parameters are σ=SQRT(LN(1+s²/m²)) and μ=LN(m)−σ²/2. These relationships concern a lognormal model, not an arbitrary transformation that makes every dataset lognormal.

For m=10 and s=5, put 10 in H2 and 5 in I2. In J2 enter =SQRT(LN(1+(I2/H2)^2)), approximately 0.472380727077. In K2 use =LN(H2)-J2^2/2, approximately 2.191013317337. Then =LOGNORMDIST(10;K2;J2;1) is approximately 0.593357521603.

For cumulative mode the current evaluator returns zero when x≤0. Density mode instead rejects x≤0 as an invalid argument. A nonpositive StDev is invalid in either mode. Do not transfer an error rule from another spreadsheet solely because it uses the same function name.

For an inverse check, =LOGNORMDIST(LOGINV(0.9;0;1);0;1;1) should recover approximately 0.9. Retain the unrounded inner result. Extreme probabilities, nonnumeric coercion and imported locale settings need separate checks; an ordinary-range round trip is not a comprehensive precision test.

• LOGNORMDIST documentation
• Apache OpenOffice 4.1.16 evaluator and argument contract