LOGNORM.DIST in Excel: Use Log-Scale Parameters for Positive Data

=LOGNORM.DIST(x, mean, standard_dev, cumulative)

All four arguments are required. x is a positive value in the original measurement scale. mean is the mean of the natural logarithm of that variable. standard_dev is the positive standard deviation of that natural logarithm. cumulative selects the lower-tail probability with TRUE or density with FALSE.

If Y=LN(X) is normal with mean μ and standard deviation σ, then X is lognormal. Its cumulative probability is the standard normal cumulative value at (LN(x)-μ)/σ. Natural logarithms are essential: base-ten log parameters are not interchangeable with these inputs.

The density is the standard normal density at that transformed value divided by x*σ. That extra x factor is why simply substituting LN(x) into a normal density does not produce the original-scale lognormal density.

Enter 4 in A2, 3.5 in A3 and 1.2 in A4. In B2 enter =LOGNORM.DIST(A2,A3,A4,TRUE). In B3 use the same arguments with FALSE.

Independent results are 0.03908355571 and 0.01761759668. About 3.9084% of the specified distribution is at or below four. The second number is a density height, not the probability of exactly four.

Microsoft displays rounded outputs 0.0390836 and 0.0176176. Keep the calculated cell values if they are used downstream. Rounding a probability before an inverse calculation changes the recovered cutoff.

Use mean 0 and standard deviation 1. Then =LOGNORM.DIST(1,0,1,TRUE) has independent result 0.5, because LN(1)=0 is the center of the underlying normal distribution.

At x=2, =LOGNORM.DIST(2,0,1,TRUE) targets 0.7558914042. At x=0.5 the cumulative probability is approximately 0.2441085958. The interval from 0.5 through 2 therefore has probability 0.5117828084.

Those endpoints are symmetric on the log scale, because their logarithms have opposite signs. They are not equally spaced around one on the original scale.

For log parameters μ=3.5 and σ=1.2, the original-scale median is EXP(3.5), independently 33.11545196. The arithmetic mean is EXP(3.5+1.2^2/2), independently 68.03348429.

Neither summary is the supplied log mean 3.5. A positive, right-skewed distribution can have a mean substantially above its median. If a dataset provides an arithmetic mean and standard deviation of raw X, do not insert those numbers as log parameters without an explicitly justified conversion or log-scale estimation procedure.

This guide illustrates a chosen distribution; it does not estimate parameters from observations or establish that a lognormal fit is appropriate.

For positive bounds L<U, use =LOGNORM.DIST(U,mean,standard_dev,TRUE)-LOGNORM.DIST(L,mean,standard_dev,TRUE). It returns the probability between the bounds under the continuous model.

For an upper tail above U, subtract the cumulative result from one. Do not use FALSE to request the upper tail. For μ=0, σ=1 and U=2, the independent upper-tail target is 0.2441085958.

When a theoretical interval begins at zero, its lower probability is mathematically zero. Use only the upper cumulative value rather than calling LOGNORM.DIST at zero, which the documented input rules reject.

Microsoft documents #VALUE! for nonnumeric arguments and #NUM! for x≤0 or standard_dev≤0. Use an explicit TRUE/FALSE cumulative flag as shown. Additional text/logical coercion details were not native-tested.

Check that logarithms are natural and taken from the same original units used for x. Changing original units shifts log means, so a parameter set fitted to one unit cannot be reused blindly with another. Density and probability also have different units.

Very extreme tails can suffer rounding or subtraction loss. The independent examples verify ordinary parameter values; they do not establish numerical accuracy or error display for a particular Excel build.

• Current documentation: the dedicated Microsoft reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Introduced: Microsoft’s alphabetical catalog marks LOGNORM.DIST as introduced in Excel 2010. Exact first build and platform-specific introduction dates remain unverified.
• Last functioning version: unknown; a current help listing is not a last-working-build test.
• Evidence checked: October 15, 2026. Official documentation was freshly retrieved; examples were independently calculated. No native Excel, Mac or web-client execution was performed.

• Microsoft LOGNORM.DIST reference.
• Microsoft function catalog and introduction-marker explanation.
• Editorial testing standards.

Examples use English function names and comma separators. Expected numbers are rounded independent mathematical calculations; documented error expectations are labeled as such. They are not captured Excel output. All illustrative data and policies are fictional.