LOGNORM.INV Formula: Calculate Inverse Lognormal Distribution Values
=LOGNORM.INV(probability, mean, standard_dev)The LOGNORM.INV function is a powerful statistical tool in Excel that calculates the inverse of the lognormal cumulative distribution function. This advanced formula is essential for professionals working with statistical modeling, risk analysis, and financial forecasting. The lognormal distribution is particularly useful when analyzing data that cannot be negative, such as stock prices, product lifespans, and income distributions. Understanding LOGNORM.INV requires familiarity with probability theory and statistical concepts. The function takes a probability value and returns the corresponding x-value from a lognormal distribution defined by a specific mean and standard deviation. This is invaluable for determining thresholds, confidence intervals, and predictive values in complex statistical analyses. Whether you're conducting financial risk assessments, quality control analysis, or academic research, LOGNORM.INV provides precise calculations that would otherwise require complex manual computation or specialized statistical software. Mastering this formula elevates your Excel proficiency and enables sophisticated data-driven decision-making.
Syntax & Parameters
The LOGNORM.INV function syntax is straightforward but requires precise parameter inputs: =LOGNORM.INV(probability, mean, standard_dev). The first parameter, probability, must be a value between 0 and 1 (exclusive), representing the cumulative probability for which you seek the corresponding value. This is typically expressed as a decimal (0.95 for 95%) rather than a percentage. The mean parameter represents the mean of the natural logarithm of x values, not the mean of x itself. This distinction is critical—you must calculate or know the mean of ln(x) from your dataset. Similarly, standard_dev represents the standard deviation of ln(x), not of the original x values. These parameters define the shape and position of your lognormal distribution curve. Practical tips: Always validate that your probability argument falls strictly between 0 and 1; values of exactly 0 or 1 will produce errors. Ensure your standard_dev is positive; negative or zero values will trigger #NUM! errors. When working with real datasets, use AVERAGE(LN(range)) and STDEV(LN(range)) to calculate the correct mean and standard deviation parameters from your data's natural logarithm values.
probabilitymeanstandard_devPractical Examples
Financial Risk Analysis: Stock Price Valuation
=LOGNORM.INV(0.95, 4.5, 0.3)This formula calculates the stock price value at the 95th percentile of the lognormal distribution. The result represents the price level below which 95% of predicted outcomes should fall, useful for risk management and option pricing strategies.
Product Lifespan Prediction: Warranty Analysis
=LOGNORM.INV(0.5, 6.2, 0.4)Using 0.5 as the probability gives the median value of the distribution. This helps determine typical product lifespan for warranty period planning and inventory management decisions.
Environmental Data: Pollution Concentration Thresholds
=LOGNORM.INV(0.90, 2.1, 0.5)This calculates the pollution concentration level that should not be exceeded more than 10% of the time, critical for environmental compliance reporting and setting safe exposure limits.
Key Takeaways
- LOGNORM.INV calculates the inverse of the lognormal cumulative distribution function, finding x-values for given probabilities in lognormal distributions
- Parameters must be the mean and standard deviation of LN(x), not of x itself—use AVERAGE(LN(range)) and STDEV(LN(range)) to calculate them correctly
- Probability argument must be strictly between 0 and 1 (exclusive); values of 0 or 1 produce #NUM! errors
- LOGNORM.INV is ideal for financial risk analysis, product lifespan prediction, and environmental threshold determination where data follows lognormal distributions
- For Excel 2007 and earlier, use the legacy LOGINV function with identical syntax and results
Pro Tips
Use named ranges for your mean and standard deviation calculations to create self-documenting formulas. For example, define 'ln_mean' as =AVERAGE(LN(dataset)) and 'ln_stdev' as =STDEV(LN(dataset)), then write =LOGNORM.INV(0.95, ln_mean, ln_stdev).
Impact : Dramatically improves formula readability, reduces errors, and makes maintenance easier when sharing workbooks with colleagues.
Create a lookup table with multiple probability values (0.1, 0.25, 0.5, 0.75, 0.9) and their corresponding LOGNORM.INV results for quick reference and visualization. This helps identify distribution patterns and validate calculations.
Impact : Enables faster decision-making and provides visual confirmation that your distribution parameters are reasonable for your business context.
Always validate your mean and standard deviation parameters by comparing LOGNORM.INV(0.5, mean, stdev) results with the actual median of your dataset. Significant discrepancies indicate incorrect parameter calculations.
Impact : Catches parameter errors early, preventing cascading mistakes in dependent analyses and ensuring statistical validity of results.
Combine LOGNORM.INV with data validation dropdown menus to allow users to select probability levels (Low Risk/Medium Risk/High Risk) that trigger corresponding calculations without exposing complex formulas.
Impact : Makes advanced statistical analysis accessible to non-technical users and reduces formula complexity in shared business intelligence dashboards.
Useful Combinations
Confidence Interval Calculation
=LOGNORM.INV(0.975, mean, stdev) - LOGNORM.INV(0.025, mean, stdev)Calculates the 95% confidence interval width by finding the difference between the 97.5th and 2.5th percentiles. Useful for establishing upper and lower bounds for statistical estimates in quality control and research applications.
Percentile Ranking System
=IF(LOGNORM.INV(0.5, mean, stdev)>value, PERCENTRANK(range, value)*100, 100-PERCENTRANK(range, value)*100)Combines LOGNORM.INV with PERCENTRANK to categorize values relative to the median of a lognormal distribution. Enables sophisticated ranking systems for performance evaluation or risk stratification.
Dynamic Threshold Adjustment
=LOGNORM.INV(probability_cell, AVERAGE(LN(data_range)), STDEV(LN(data_range)))Creates a dynamic formula that recalculates thresholds automatically when underlying data changes. The probability input is a cell reference allowing real-time adjustments to confidence levels without formula modification.
Common Errors
Cause: Probability argument is ≤0 or ≥1, or standard_dev is ≤0. Example: =LOGNORM.INV(1.5, 4.5, 0.3) or =LOGNORM.INV(0.5, 4.5, -0.2)
Solution: Verify probability is strictly between 0 and 1 (e.g., 0.95 not 1.5). Confirm standard_dev is positive. Use validation formulas like =IF(AND(prob>0,prob<1,stdev>0),LOGNORM.INV(...),"Invalid parameters")
Cause: Non-numeric values passed as arguments. Example: =LOGNORM.INV("95%", 4.5, 0.3) or =LOGNORM.INV(0.5, "mean", 0.3)
Solution: Ensure all parameters are numeric values. Convert percentage text to decimals using VALUE() function if needed. Check that cell references contain numbers, not text formatted as numbers.
Cause: Cell references in the formula point to deleted cells or invalid ranges. Example: =LOGNORM.INV(A1, B1, C1) where columns have been deleted.
Solution: Verify all referenced cells exist and contain valid data. Use absolute references ($A$1) for consistency. Reconstruct the formula with correct cell addresses if ranges were moved or deleted.
Troubleshooting Checklist
- 1.Verify probability argument is a decimal between 0 and 1 (exclusive), not a percentage or value outside this range
- 2.Confirm mean parameter is calculated from LN(data), not from raw data values using =AVERAGE(LN(range))
- 3.Ensure standard_dev parameter is positive and calculated from LN(data) using =STDEV(LN(range)) or =STDEV.S(LN(range))
- 4.Check that all cell references exist and contain numeric values; look for deleted columns or text-formatted numbers
- 5.Test the formula with known probability values (0.5 for median) to validate parameter accuracy before using critical calculations
- 6.Verify Excel version is 2010 or later; use LOGINV function for Excel 2007 compatibility
Edge Cases
Probability value extremely close to 0 (e.g., 0.00001)
Behavior: Returns very small x-values approaching zero, representing the lower tail of the distribution. Results become increasingly sensitive to parameter precision.
Solution: Use high-precision decimal values and verify parameters are accurate. Consider rounding results appropriately for business interpretation.
Extreme probability values may produce results that are theoretically valid but practically meaningless; validate against business context.
Probability value extremely close to 1 (e.g., 0.99999)
Behavior: Returns very large x-values, representing the upper tail of the distribution. May produce unexpectedly large numbers depending on standard deviation.
Solution: Verify that large results align with your expected data range. Check standard deviation isn't inflated, causing unrealistic tail values.
Lognormal distributions have long right tails; extreme probabilities naturally produce large values that may exceed typical data ranges.
Mean parameter is negative (representing ln(x) values from very small x)
Behavior: Formula executes successfully and returns valid results; negative means are mathematically valid for lognormal distributions representing small-valued data.
Solution: Ensure negative means are intentional and represent your actual data distribution. Verify with LOGNORM.DIST that the relationship is correct.
Negative means occur naturally when analyzing data with small values (e.g., probabilities, concentrations <1); this is not an error condition.
Limitations
- •LOGNORM.INV only works with lognormal distributions; it cannot be used for other distribution types without mathematical transformation, limiting its applicability to datasets that actually follow lognormal patterns
- •The function requires accurate calculation of mean and standard deviation from LN(data); errors in these parameter calculations propagate directly into results, and there is no built-in validation to detect incorrect parameters
- •Extreme probability values (very close to 0 or 1) produce results in the distribution tails where precision decreases and numerical instability may occur, limiting reliability for very high confidence intervals
- •LOGNORM.INV assumes continuous data and may produce misleading results with discrete datasets; it also requires all underlying data values to be positive (since ln(negative) is undefined), restricting its use to positive-valued phenomena
Alternatives
Provides flexibility to manually control the transformation. Formula: =EXP(NORM.INV(probability, mean, standard_dev)). Allows for custom variations and deeper understanding of the underlying mathematics.
When: When you need to customize the calculation, perform intermediate calculations, or work with transformed data in specialized analyses.
Compatibility
✓ Excel
Since 2010
=LOGNORM.INV(probability, mean, standard_dev) - Native function in Excel 2010, 2013, 2016, 2019, 365✓Google Sheets
=LOGNORM.INV(probability, mean, standard_dev) - Fully supported with identical syntaxGoogle Sheets implements the same lognormal inverse function with complete compatibility. Results are mathematically identical to Excel versions.
✓LibreOffice
=LOGNORM.INV(probability, mean, standard_dev) - Supported in LibreOffice Calc with identical parameters and behavior