LOGNORM.INV in Excel: Find Positive Cutoffs From Lognormal Probabilities

=LOGNORM.INV(probability, mean, standard_dev)

All three arguments are required. probability is a lower-tail probability strictly between zero and one. mean and standard_dev describe LN(X), with standard_dev positive. The returned cutoff is on the original positive X scale.

Mathematically, the cutoff is EXP(mean + standard_dev*z), where z is the standard normal quantile for probability. The exponential transformation makes all finite theoretical cutoffs positive and makes equal changes on the log scale multiplicative on the original scale.

This inverts the cumulative lognormal distribution, not its density. To check a cutoff x, use LOGNORM.DIST(x,mean,standard_dev,TRUE).

Put 0.039084 in A2, 3.5 in A3 and 1.2 in A4. Enter =LOGNORM.INV(A2,A3,A4) in B2.

The independent target is 4.0000252187, matching the source’s rounded 4.0000252. This is not exactly four because A2 is a rounded probability. The more precise cumulative probability at four is approximately 0.0390835557068.

For a mathematical round trip, use =LOGNORM.INV(LOGNORM.DIST(4,3.5,1.2,TRUE),3.5,1.2). Its target is four. Actual floating-point agreement and native error displays were not captured, so use an appropriate tolerance rather than promising exact bitwise identity.

For log mean zero and log standard deviation one, enter 0.05, 0.50, 0.95 in D2:D4. In E2 enter =LOGNORM.INV(D2,0,1) and fill down.

Independent cutoffs are 0.1930408167, 1, and 5.1802516022. The median is one, but the upper and lower percentile distances from one are not symmetric. The logarithms of the endpoints are symmetric around zero.

The 5th-to-95th-percentile interval contains 90%, not 95%, of the specified continuous distribution. Both outer tails contain 5%. Label the desired central coverage before selecting endpoint probabilities.

If the intended upper-tail probability is 5%, use =LOGNORM.INV(1-0.05,0,1), giving the 95th-percentile cutoff above. Using 0.05 directly instead returns the low cutoff 0.1930408167.

The cutoff is a model percentile rather than a guarantee for future observations. A probability model and estimated parameters require separate justification; the inverse function does not establish either from the supplied numbers.

Adding LN(10) to the log mean multiplies every original-scale quantile by ten while leaving log standard deviation unchanged. Thus =LOGNORM.INV(0.95,LN(10),1) has independent target 51.80251602.

This is useful for checking a consistent unit conversion. It is not equivalent to multiplying the log mean by ten. Similarly, changing the log standard deviation affects quantiles through an exponential, rather than by an additive shift on the original scale.

At probability 0.5 the result is EXP(mean), regardless of a valid positive standard deviation. For log mean 3.5 the median is approximately 33.11545196. It should not be confused with the original-scale arithmetic mean, which also depends on the variance of the logarithms.

Microsoft documents #VALUE! for nonnumeric arguments, #NUM! for probability≤0 or probability≥1, and #NUM! for standard_dev≤0. Enter 95% or 0.95, not 95. The input is a probability, while the output is a positive measurement cutoff.

The mathematical lower limit approaches zero as probability approaches zero, but the Excel reference still excludes a literal zero probability. Likewise, probability one has no finite theoretical lognormal cutoff. Do not substitute endpoints simply to avoid a tiny decimal.

Inspect the original-scale versus log-scale distinction first when a result seems implausible. Base-ten logs, raw-data means or incompatible units can produce a valid-looking but wrong model. Extreme exponential overflow, numerical tail precision and native platform differences were not tested here.

• Current documentation: the dedicated Microsoft reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Introduced: Microsoft’s alphabetical catalog marks LOGNORM.INV 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.INV 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.