Master the LOGNORMDIST Function: Complete Guide to Lognormal Distribution in Excel
=LOGNORMDIST(x, mean, standard_dev)The LOGNORMDIST function is a powerful statistical tool in Excel designed to calculate the cumulative lognormal distribution probability. This function evaluates the probability that a random variable from a lognormal distribution falls below a specified value. The lognormal distribution is particularly valuable in financial analysis, risk assessment, and scientific research where data naturally follows logarithmic patterns rather than normal distributions. Understanding LOGNORMDIST is essential for professionals working with financial modeling, option pricing, and reliability analysis. The function operates on the principle that the logarithm of a variable follows a normal distribution, making it ideal for analyzing phenomena such as stock prices, income distributions, and particle sizes. In Excel versions 2007 and 2010, this function provides critical functionality for advanced statistical computations, though it has been superseded by LOGNORM.DIST in newer versions. Mastering this formula enables you to perform sophisticated probability calculations without manual logarithmic transformations, saving time and reducing computational errors in complex analytical workflows.
Syntax & Parameters
The LOGNORMDIST function syntax is =LOGNORMDIST(x, mean, standard_dev), where each parameter plays a distinct role in the calculation. The first parameter, x, represents the value at which you want to evaluate the lognormal distribution. This must be a positive number, as logarithms of non-positive values are undefined. The x parameter defines the specific point on the distribution curve where probability is being calculated. The second parameter, mean, refers to the mean of the natural logarithm of x values, not the mean of x itself. This is a critical distinction that prevents calculation errors. This represents the average of ln(x) across your dataset or theoretical distribution. The third parameter, standard_dev, denotes the standard deviation of ln(x), measuring how dispersed the logarithmic values are around the mean. Important considerations include ensuring all parameters are numeric values and that standard_dev is positive. The function returns a value between 0 and 1, representing the cumulative probability. When standard_dev equals zero or is negative, Excel returns a #NUM! error. Always verify that your mean and standard deviation values are calculated from logarithmic transformations of your original data to ensure statistical accuracy.
xmeanstandard_devPractical Examples
Stock Price Risk Analysis
=LOGNORMDIST(150, 4.8, 0.35)This formula calculates the cumulative probability for a stock price of $150. The mean 4.8 represents the average of natural logarithms of historical prices, while 0.35 is the standard deviation of those logarithmic values. The result indicates the likelihood of prices staying at or below this threshold.
Equipment Reliability Assessment
=LOGNORMDIST(500, 6.5, 0.8)Since ln(500) ≈ 6.215, this formula determines the cumulative failure probability for the 500-hour mark. The lognormal distribution is ideal for reliability analysis because failure times typically follow this pattern rather than normal distribution.
Income Distribution Analysis
=LOGNORMDIST(30000, 10.2, 0.9)Income distributions are naturally lognormal, making this function ideal for socioeconomic analysis. The formula evaluates the proportion of households earning less than $30,000 based on the logarithmic distribution parameters.
Key Takeaways
- LOGNORMDIST calculates cumulative lognormal distribution probability for values in Excel 2007-2010; use LOGNORM.DIST in newer versions
- All three parameters must be numeric: x must be positive, and mean/standard_dev must be derived from ln(x) transformations
- The function returns values between 0 and 1 representing cumulative probability, not probability density
- Common errors (#NUM!, #VALUE!, #REF!) stem from invalid parameter values or broken cell references; implement validation rules to prevent them
- Combine LOGNORMDIST with other functions for range probabilities, conditional analysis, and sensitivity testing in financial and risk models
Pro Tips
Always validate that your mean and standard deviation are calculated from LN() transformed data before using LOGNORMDIST. Use helper columns to calculate ln(x) for verification.
Impact : Prevents systematic calculation errors that could invalidate entire analyses. This single verification step saves hours of debugging.
Create a data validation rule restricting x values to positive numbers only. Use conditional formatting to highlight invalid inputs in your analysis spreadsheet.
Impact : Reduces #NUM! errors and ensures data quality. Automated validation catches errors before formulas execute, improving workflow efficiency.
For sensitivity analysis, use Data Tables to test multiple x values against your LOGNORMDIST formula. This reveals how probability changes across different thresholds.
Impact : Enables comprehensive risk assessment and scenario planning. One-way or two-way data tables create probability matrices for decision-making.
Document your mean and standard deviation sources clearly. Include the original data range and transformation method in adjacent cells for audit trails and formula transparency.
Impact : Improves spreadsheet maintainability and allows other users to understand your statistical methodology instantly.
Useful Combinations
Confidence Interval Calculation
=LOGNORMDIST(upper_bound, mean, std_dev) - LOGNORMDIST(lower_bound, mean, std_dev)Calculate the probability of a value falling within a specific range by subtracting the cumulative probability at the lower bound from the upper bound. This combination determines confidence intervals for lognormal distributions, essential for risk assessment.
Conditional Probability Analysis
=LOGNORMDIST(value1, mean, std_dev) / LOGNORMDIST(value2, mean, std_dev)Determine conditional probabilities by dividing cumulative distributions. Useful for analyzing the probability of outcomes given that another condition has occurred, common in financial scenario analysis.
Inverse Probability Lookup with LOGINV
=LOGINV(LOGNORMDIST(x, mean, std_dev), mean, std_dev)Combine LOGNORMDIST with LOGINV to verify calculations or create bidirectional lookups. This validates that your probability calculations are consistent with inverse distribution functions.
Common Errors
Cause: The standard_dev parameter is zero, negative, or the x value is zero or negative. Lognormal distribution requires positive values for all parameters.
Solution: Verify that x > 0, standard_dev > 0, and both mean and standard_dev are derived from ln(x) calculations. Use IF statements to validate inputs: =IF(AND(x>0,standard_dev>0),LOGNORMDIST(x,mean,standard_dev),"Invalid input")
Cause: One or more parameters contain non-numeric values, text strings, or cell references that cannot be converted to numbers.
Solution: Check that all three parameters reference numeric cells or values. Remove any text formatting or ensure proper data type conversion. Use VALUE() function if needed: =LOGNORMDIST(VALUE(x_text),mean,standard_dev)
Cause: Cell references in the formula are broken, pointing to deleted rows/columns, or referencing invalid ranges.
Solution: Verify all cell references are correct and cells haven't been deleted. Use absolute references for fixed parameters: =LOGNORMDIST(x,$B$5,$B$6) to prevent reference errors when copying formulas.
Troubleshooting Checklist
- 1.Verify x parameter is positive (x > 0); lognormal distribution requires positive values only
- 2.Confirm standard_dev is positive and non-zero; negative or zero values trigger #NUM! errors
- 3.Check that mean and standard_dev are calculated from LN(x) transformation, not raw data values
- 4.Ensure all three parameters reference numeric cells with proper data types; text values cause #VALUE! errors
- 5.Validate cell references haven't been deleted or moved; use absolute references ($B$5) for fixed parameters
- 6.Test with known values from statistical tables to verify formula accuracy and parameter correctness
Edge Cases
x value equals the mean (when converted to lognormal scale)
Behavior: LOGNORMDIST returns approximately 0.5, representing the median of the distribution where cumulative probability is exactly 50%
Solution: This is expected behavior; the result correctly indicates the probability equals the distribution's midpoint
This property is useful for identifying median values in lognormal distributions
Very large x values (e.g., x = 1,000,000) with small standard deviation
Behavior: Function returns values very close to 1.0 (approaching certainty), potentially displaying as 0.9999999 or 1
Solution: Use TEXT function to format output: =TEXT(LOGNORMDIST(x,mean,std_dev),"0.00000000") for precise display
This represents extreme tail probability; verify your parameters reflect intended statistical model
Very small x values (e.g., x = 0.001) with large standard deviation
Behavior: Function returns values very close to 0, potentially displaying as 0.0000001 or showing as 0
Solution: Increase decimal places or use scientific notation for display: =TEXT(LOGNORMDIST(x,mean,std_dev),"0.00E+00")
Represents extreme lower tail; ensure your data range and parameters align with analytical objectives
Limitations
- •LOGNORMDIST is deprecated in Excel 2013 and later versions; Microsoft recommends LOGNORM.DIST for new spreadsheets, limiting long-term maintainability
- •Function cannot handle negative x values or zero values, restricting analysis to positive-only datasets; data transformation may be required for some applications
- •Returns cumulative probability only; cannot directly calculate probability density function (PDF) values, requiring alternative functions or manual calculations for density analysis
- •Requires precise calculation of logarithmic mean and standard deviation; errors in LN() transformation propagate through results, making data validation critical for accuracy
Alternatives
Compatibility
✓ Excel
Since 2007
=LOGNORMDIST(x, mean, standard_dev) - Available in Excel 2007, 2010. Deprecated in Excel 2013+ (use LOGNORM.DIST instead)✗Google Sheets
Not available
✓LibreOffice
=LOGNORMDIST(x, mean, standard_dev) - Supported in LibreOffice Calc with identical syntax and behavior to Excel