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LOGNORM.DIST Function
Summary
The LOGNORM.DIST function calculates the lognormal distribution for a specified value, where the natural logarithm of x follows a normal distribution defined by mean and standard deviation parameters. Essential for statistical analysis of positively skewed data like stock prices, sizes, and durations.
Syntax
LOGNORM.DIST(x, mean, standard_dev, cumulative)Parameters
| Parameter | Type | Required | Description |
|---|---|---|---|
| x | Number |
Yes | Value at which to evaluate the lognormal distribution (must be positive) |
| mean | Number |
Yes | Arithmetic mean of ln(x) - natural log of the value |
| standard_dev | Number |
Yes | Standard deviation of ln(x) - must be positive |
| cumulative | Boolean |
Yes | TRUE for cumulative distribution function (CDF), FALSE for probability density function (PDF) |
Using the LOGNORM.DIST Function
LOGNORM.DIST models data that cannot be negative and often shows right-skewness, such as financial returns, particle sizes, failure times, and biological measurements. Use TRUE for CDF to find probabilities up to a value; use FALSE for PDF to analyze distribution shape.
Common LOGNORM.DIST Examples
Cumulative Distribution Example
=LOGNORM.DIST(4, 3.5, 1.2, TRUE)Returns 0.0391 - probability that a lognormally distributed variable is less than 4 given mean(ln(x))=3.5, sd(ln(x))=1.2
Probability Density Example
=LOGNORM.DIST(4, 3.5, 1.2, FALSE)Returns 0.0176 - probability density at exactly x=4 with same parameters
Stock Price Probability
=LOGNORM.DIST(50, 3.9, 0.3, TRUE)Probability a stock reaches $50 or less when ln(price) mean=3.9, sd=0.3 (~$49.24 median)
Manufacturing Tolerance
=LOGNORM.DIST(10, 2.3, 0.25, TRUE)Fraction of parts measuring 10mm or less in lognormal production process
Frequently Asked Questions
Common Errors and Solutions
#NUM! error
Cause: x ≤ 0 or standard_dev ≤ 0
Solution: Verify x is positive and standard_dev > 0
#VALUE! error
Cause: Non-numeric input
Solution: Check all arguments contain valid numbers or TRUE/FALSE
Unexpected small results
Cause: Parameters create narrow distribution
Solution: Review mean and standard_dev values for realistic ln(x) distribution
Notes
- Equation: LOGNORM.DIST(x,μ,σ,TRUE) = NORM.S.DIST((LN(x)-μ)/σ)
- PDF (FALSE) gives distribution shape, CDF (TRUE) gives cumulative probability
- Parameters describe NORMAL distribution of LN(X), not X itself
- Excel 2010+ only - use LOGNORMDIST for compatibility with Excel 2007
Compatibility
Available in: Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Excel for Microsoft 365, Excel for the web
Not available in: Excel 2007, Excel 2003, Earlier versions
Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2010+