# Understanding Log-Normal Distribution: Definition, Uses, and Calculations

## What Is a Log-Normal Distribution?

A log-normal distribution represents a set of data that follows a normal distribution when logarithms are applied to its values. Though often overlooked compared to the familiar bell curve of a normal distribution, the log-normal distribution is essential in financial analyses, especially for modeling stock prices and returns. Understanding how to transition between normal and log-normal distributions and effectively utilize them, including leveraging Excel for calculation, can provide deeper insights into financial data patterns.

### Key Takeaways

*   A log-normal distribution is derived from logarithmic values of a normal distribution and can be converted back using logarithmic calculations.  
    
*   Unlike a normal distribution, which can allow for negative values, a log-normal distribution consists of positive values only.  
    
*   Log-normal distributions are common in finance, especially in analyzing stock prices and expected compound returns.  
    
*   In Excel, the LOGNORM.DIST function can be used to model log-normal distributions by specifying the value, mean, and standard deviation of the logarithmic values.

![Image](https://www.investopedia.com/thmb/dmWOsjhPLEXqOnOFh7_0v3E4wUs=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/dotdash_Final_Log_Normal_Distribution_Nov_2020-01-fa015519559f4b128fef786c51841fb9.jpg)

**

## Differences and Connections Between Normal and Log-Normal Distributions

A normal distribution is a probability distribution of [outcomes that are symmetrical](https://www.investopedia.com/articles/active-trading/092914/normal-distribution-table-explained.asp) or form a bell curve. In a normal distribution, 68% of the results fall within one standard deviation, and 95% fall within two standard deviations.

Most people know about normal distributions, but fewer are familiar with log-normal distributions. Using logarithms, a normal distribution converts into a log-normal distribution. This is because log-normal distributions arise from normally distributed variables.

Log-normal distributions are often used alongside normal distributions. They're usually created by taking the natural log with a base of e=2.718, but using a different base changes the shape of the distribution.

A log-normal distribution plots the log of random variables from a normal curve. The log is the exponent needed to raise a base number to produce a normally distributed random variable (x).

## Practical Applications of Log-Normal Distribution in Financial Analysis

Normal distributions can allow negative values, which log-normal distributions solve by only including positive values.

In finance, log-normal distributions help analyze stock prices. Potential stock returns fit a normal distribution, while stock prices use a log-normal distribution, helping to identify expected compound returns over time.

Note that log-normal distributions are positively [skewed](https://www.investopedia.com/terms/s/skewness.asp) with long right tails due to low mean values and high variances in the random variables.

**Lognormal Distribution in Excel**

Lognormal distribution can be done in Excel. It is found in the statistical functions as LOGNORM.DIST.

Excel defines it as the following:

_LOGNORM.DIST (x,mean,standard\_dev,cumulative)_

_Returns the lognormal distribution of x, where ln(x) is normally distributed with parameters mean and standard\_dev._

To calculate LOGNORM.DIST in Excel, you will need the following:

x = value at which to evaluate the function

Mean = the mean of ln(x)

Standard Deviation = the standard deviation of ln(x), which must be positive

## The Bottom Line

The log-normal distribution plays a crucial role in finance, particularly in analyzing stock prices and potential returns. Unlike a normal distribution, a log-normal distribution accounts for solely positive variables, offering a more accurate representation of outcomes like stock prices. Understanding how to utilize log-normal distributions, both conceptually and practically in tools like Excel, equips investors with better insights into potential financial outcomes, such as compound returns over time.  

> **Article Sources**
>
> 1.  Microsoft. "[LOGNORM.DIST function](https://support.microsoft.com/en-us/office/lognorm-dist-function-eb60d00b-48a9-4217-be2b-6074aee6b070)."