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A log scale should be used in charts when the data being represented has a very large range of values and a standard linear scale will not properly display the variation between the values. This is because a log scale is based on orders of magnitude, meaning values are displayed in relation to one another, rather than as absolute values. This can help to better illustrate trends and patterns in the data.
There are two common scenarios where it’s a good idea to use a log scale when creating charts:
Scenario 1: A few values are significantly larger than all other values.
- By using a log scale, it’s easier to visualize the smaller values on the chart.
Scenario 2: You want to analyze percent change instead of raw change.
- By using a log scale, it’s easier to visualize percentage change in values over time.
The following examples illustrate when each scenario may occur in the real world.
Scenario 1: Using a Log Scale When a Few Values Are Much Larger than All Others
Suppose we would like to visualize the annual revenue of 10 different companies in which 2 of the companies have revenues that are significantly larger than all of the other companies.
Here’s what a bar chart would look like if we visualized the revenues on a linear scale:
Notice that it’s extremely difficult to read the smaller values on the chart and it’s tough to see the differences between the smaller values.
Here’s what the same bar chart would look like on a log scale:
Notice how it’s much easier to differentiate the smaller values using a log scale compared to a linear scale.
Scenario 2: Using a Log Scale to Visualize Percent Change
Suppose we make a $100,000 investment in a stock that grows at 6% per year.
Here’s what a line chart of the investment would look like over a 30-year period on a linear scale:
This chart is useful for visualizing how much the investment value changes in raw dollars each year, but suppose we’re more interested in understanding the percentage growth of the investment.
In this case, it would be useful to convert the y-axis to a log scale:
Using this chart, we can see that the percentage change in the investment value has been constant every year during the 30-year period.
Note: Using a log scale can be a useful way to visualize the percentage change of any variable during a time period when the variable experiences exponential growth since the change in values near the end of the time period tend to dwarf the change in values near the beginning.
The following tutorials explain how to create charts with log scales in various statistical software: