What's the difference between LOGNORM.DIST and NORM.DIST?

NORM.DIST calculates normal (Gaussian) distribution probabilities, while LOGNORM.DIST calculates lognormal distribution probabilities. The key difference is that LOGNORM.DIST works with the logarithm of values, making it suitable for positive-only data like prices and income. Use NORM.DIST for data that can be negative (like temperature changes), and LOGNORM.DIST for data that must be positive (like prices and time durations).

How do I calculate the mean and standard_dev parameters from my dataset?

First, calculate the natural logarithm of each data point using LN() function. Then calculate the mean of these log values using AVERAGE() and the standard deviation using STDEV() or STDEV.S(). For example: Mean = AVERAGE(LN(data_range)) and Standard_Dev = STDEV(LN(data_range)). These transformed values become your mean and standard_dev parameters.

When should I use cumulative TRUE versus FALSE?

Use cumulative=TRUE when you need the probability that a value is less than or equal to x (cumulative probability). This is useful for risk assessment and threshold analysis. Use cumulative=FALSE when you need the probability density at a specific point, which is useful for understanding the distribution shape and identifying peak probability areas. For most business applications, cumulative=TRUE is more intuitive.

Can LOGNORM.DIST handle negative values?

No, LOGNORM.DIST cannot handle negative x values and will return a #NUM! error. The lognormal distribution is specifically designed for positive values only. If your data contains negative values, you may need to transform it (add a constant to shift all values positive) or use a different distribution like NORM.DIST that handles negative values.

How is LOGNORM.DIST related to LOGNORM.INV?

LOGNORM.INV is the inverse function of LOGNORM.DIST. While LOGNORM.DIST takes a value and returns a probability, LOGNORM.INV takes a probability and returns the corresponding value. Together they enable two-way analysis: LOGNORM.DIST answers 'what's the probability of this value?' while LOGNORM.INV answers 'what value corresponds to this probability?' Use them together for comprehensive probability analysis.

Complete Guide to LOGNORM.DIST: Excel's Lognormal Distribution Function

Advanced

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

The LOGNORM.DIST function is a powerful statistical tool in Excel that calculates the lognormal distribution probability. This function is essential for financial analysts, risk managers, and data scientists who need to model phenomena that follow a lognormal distribution pattern. The lognormal distribution is particularly valuable in real-world applications because many natural and financial variables—such as stock prices, income distributions, and product lifespans—exhibit lognormal characteristics rather than normal distribution. Understanding LOGNORM.DIST enables professionals to perform sophisticated probability analysis and create accurate predictive models. Unlike the normal distribution which can produce negative values, the lognormal distribution only generates positive values, making it ideal for modeling quantities that cannot be negative. Whether you're analyzing investment returns, assessing operational risks, or conducting quality control studies, LOGNORM.DIST provides the mathematical foundation for informed decision-making and strategic planning. This comprehensive guide will walk you through the syntax, parameters, practical examples, and advanced techniques for leveraging LOGNORM.DIST in your Excel workflows. You'll learn how to interpret results, avoid common pitfalls, and combine this function with other Excel tools for maximum analytical power.

Syntax & Parameters

The LOGNORM.DIST function follows the syntax: =LOGNORM.DIST(x, mean, standard_dev, cumulative). Each parameter plays a critical role in the calculation. The 'x' parameter represents the value at which you want to evaluate the lognormal distribution—this must be a positive number. The 'mean' parameter is the mean of the natural logarithm of x, not the mean of x itself; this distinction is crucial for accurate calculations. The 'standard_dev' parameter represents the standard deviation of ln(x), and it must be greater than zero to produce valid results. The 'cumulative' parameter is a logical value that determines the function's output type. When set to TRUE, the function returns the cumulative distribution function (CDF), which represents the probability that a random variable is less than or equal to x. When set to FALSE, it returns the probability density function (PDF), which represents the probability density at the specific value x. Understanding this distinction is essential: use TRUE when you need cumulative probabilities for decision thresholds, and FALSE when analyzing probability density at specific points. Remember that all parameters must be numerical values, and x must always be positive. The mean and standard_dev can be calculated from your dataset using LN() and STDEV() functions respectively.

x

Value to evaluate

mean

Mean of ln(x)

standard_dev

Standard deviation of ln(x)

cumulative

TRUE for cumulative, FALSE for density

Practical Examples

Financial Risk Assessment: Stock Price Analysis

=LOGNORM.DIST(150, 4.8, 0.35, TRUE)

This formula calculates the cumulative probability that the stock price stays at or below $150. The mean (4.8) and standard deviation (0.35) represent the natural logarithm parameters of historical price movements. Setting cumulative to TRUE returns a probability between 0 and 1, helping the manager understand risk exposure.

Product Reliability: Equipment Lifespan Distribution

=LOGNORM.DIST(5000, 8.2, 0.6, FALSE)

This formula returns the probability density function value at 5,000 hours. Setting cumulative to FALSE provides the density value rather than cumulative probability. This helps the company understand the likelihood concentration at specific failure points for maintenance scheduling.

Income Distribution Analysis: Economic Research

=1-LOGNORM.DIST(35000, 10.5, 0.8, TRUE)

This formula calculates the probability of income exceeding $35,000 by subtracting the cumulative probability from 1. The lognormal distribution accurately models income since incomes are positive-skewed and cannot be negative. This helps policymakers understand income inequality.

Key Takeaways

LOGNORM.DIST calculates lognormal distribution probabilities for positive-only data like prices, income, and product lifespans
The mean and standard_dev parameters must be calculated from log-transformed data using LN(), not from raw data
Use cumulative=TRUE for probability analysis and cumulative=FALSE for probability density analysis at specific points
Always ensure x is positive and standard_dev is greater than zero to avoid #NUM! errors
Combine LOGNORM.DIST with LOGNORM.INV, IF statements, and visualization tools for comprehensive statistical analysis and reporting

Pro Tips

Always verify that your mean and standard_dev parameters are calculated from LN-transformed data, not raw data. Many errors stem from using raw data statistics instead of log-transformed statistics.

Impact : Prevents calculation errors and ensures accurate probability results. This single step eliminates 80% of LOGNORM.DIST implementation mistakes.

Use data validation rules to ensure x values are always positive before passing them to LOGNORM.DIST. Create a helper column with =IF(x>0, x, NA()) to catch invalid inputs.

Impact : Prevents #NUM! errors and creates more robust, maintainable spreadsheets that handle edge cases gracefully.

Create a reference table with LOGNORM.DIST calculations at different percentiles (10th, 25th, 50th, 75th, 90th) for quick visual analysis and reporting without recalculating each time.

Impact : Saves calculation time in large models and provides stakeholders with standardized reporting formats for consistent decision-making.

Combine LOGNORM.DIST with CHART functions to visualize the probability distribution curve, making it easier to communicate statistical findings to non-technical stakeholders.

Impact : Enhances data communication and helps stakeholders understand probability concepts intuitively through visual representation.

Useful Combinations

Confidence Interval Calculation

=LOGNORM.INV(0.975, mean, std_dev) - LOGNORM.INV(0.025, mean, std_dev)

Combines LOGNORM.INV with subtraction to calculate a 95% confidence interval width. This shows the range within which 95% of values fall, essential for risk management and quality control decisions.

Conditional Probability Analysis

=(LOGNORM.DIST(upper, mean, std_dev, TRUE) - LOGNORM.DIST(lower, mean, std_dev, TRUE))

Calculates the probability that a value falls between two boundaries by subtracting cumulative probabilities. Useful for defining acceptable ranges in manufacturing or financial thresholds.

Dynamic Risk Assessment with IF Statements

=IF(LOGNORM.DIST(value, mean, std_dev, TRUE) > 0.9, "High Risk", IF(LOGNORM.DIST(value, mean, std_dev, TRUE) > 0.5, "Medium Risk", "Low Risk"))

Combines LOGNORM.DIST with nested IF statements to create automated risk classification based on probability thresholds, enabling quick decision-making in dashboards.

Common Errors

#NUM!

Cause: This error occurs when x is negative or zero, when standard_dev is less than or equal to zero, or when parameters are outside acceptable ranges. The lognormal distribution requires strictly positive x values and standard deviation.

Solution: Verify that x is positive using IF statements: =IF(x>0, LOGNORM.DIST(x, mean, standard_dev, cumulative), "Invalid input"). Check that standard_dev is calculated correctly using STDEV() on log-transformed data.

#VALUE!

Cause: This error occurs when any parameter is text, contains non-numeric characters, or when cumulative parameter is not a logical value (TRUE/FALSE). Excel cannot perform calculations on text strings.

Solution: Ensure all parameters are numeric: convert text to numbers using VALUE() function. Verify cumulative is either TRUE or FALSE, not "true" or "false" as text. Use =LOGNORM.DIST(VALUE(x_text), VALUE(mean_text), VALUE(std_text), TRUE).

#REF!

Cause: This error occurs when referenced cells have been deleted or when cell references are broken due to worksheet modifications or file corruption.

Solution: Verify all cell references exist and contain valid data. Use absolute references ($A$1) for parameters that shouldn't change. Check the formula bar to confirm references are correct. Rebuild the formula if references are corrupted.

Troubleshooting Checklist

1.Verify that x parameter is a positive number greater than zero; negative or zero values cause #NUM! errors
2.Confirm that mean and standard_dev are calculated from LN-transformed data using AVERAGE(LN(range)) and STDEV(LN(range))
3.Check that standard_dev is greater than zero; zero or negative standard deviation values return #NUM! errors
4.Ensure cumulative parameter is a logical value (TRUE or FALSE), not text; text values cause #VALUE! errors
5.Validate that all cell references are correct and haven't been deleted; broken references cause #REF! errors
6.Test the formula with known values first before applying to large datasets to verify parameters are correct

Edge Cases

x equals 0 or negative values

Behavior: Returns #NUM! error because lognormal distribution is undefined for non-positive values

Solution: Implement input validation: =IF(x<=0, NA(), LOGNORM.DIST(x, mean, standard_dev, cumulative))

The lognormal distribution's mathematical definition requires x > 0; this is a fundamental constraint, not a bug

Very large x values (e.g., 10^15) combined with large mean

Behavior: May return very small probability values close to 1 (for cumulative) or very small density values, potentially showing as 1 or 0 due to rounding

Solution: Use LOGNORM.INV for inverse calculations instead; consider logarithmic scaling for visualization

This is expected behavior in extreme cases; verify results make business sense before using in critical decisions

Standard deviation very close to zero (e.g., 0.0001)

Behavior: Creates an extremely narrow, peaked distribution where probability concentrates around a single value

Solution: Verify data quality and calculation of standard deviation; very small std_dev suggests insufficient data variability

While mathematically valid, extremely small standard deviations usually indicate data quality issues or calculation errors

Limitations

•LOGNORM.DIST cannot handle negative or zero x values, limiting its use to strictly positive data; data requiring transformation or alternative distributions must use different functions
•The function requires accurate calculation of mean and standard_dev from log-transformed data; incorrect parameter calculation is the most common source of errors and produces misleading results
•LOGNORM.DIST provides point probabilities only; it cannot automatically fit distribution parameters from raw data—you must calculate these separately using statistical methods
•The function has limited visualization capabilities within Excel; creating clear distribution graphs requires additional charting work, and complex statistical testing requires external tools or manual calculation

Alternatives

LOGNORM.INV Function

Provides the inverse calculation—returns the value corresponding to a given probability rather than the probability for a given value.

When: Use when you need to find confidence intervals, percentiles, or value thresholds based on probability targets in lognormal distributions.

Manual Calculation with NORM.DIST and LN

Offers more granular control and transparency by calculating lognormal distribution through normal distribution of log-transformed values.

When: Use when you need to understand the underlying mathematics, create custom variations, or when LOGNORM.DIST is unavailable in legacy Excel versions.

Probability Distribution Analysis Tools

Third-party statistical software like R, Python (SciPy), or SPSS provide more advanced distribution fitting and hypothesis testing capabilities.

When: Use for large-scale statistical research, distribution fitting validation, or when you need multiple distribution comparisons beyond Excel's capabilities.

Compatibility

✓ Excel

Since 2010

=LOGNORM.DIST(x, mean, standard_dev, cumulative) - Fully supported in Excel 2010, 2013, 2016, 2019, and 365

✓Google Sheets

=LOGNORM.DIST(x, mean, standard_dev, cumulative) - Identical syntax and functionality

Google Sheets provides full compatibility with Excel's LOGNORM.DIST function, making spreadsheet migration seamless

✓LibreOffice

=LOGNORM.DIST(x, mean, standard_dev, cumulative) - Available in LibreOffice Calc with identical syntax

Frequently Asked Questions

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