When should you use a logarithmic scale on a chart axis, and what does it change about interpretation?
A log scale is appropriate when data spans multiple orders of magnitude, when multiplicative growth is the natural frame of reference, or when you want to compare percentage change rather than absolute change. On a log scale, equal visual distances represent equal ratios, not equal differences.
How to think about it
What a log scale does
On a linear scale, the distance from 10 to 20 equals the distance from 1,000 to 1,010 (both are 10 units). On a log10 scale, the distance from 10 to 100 equals the distance from 100 to 1,000 (both are one order of magnitude, a factor of 10). This makes a log scale the natural frame for multiplicative relationships.
When to use it
- Data spanning multiple orders of magnitude — country GDPs, earthquake magnitudes, file sizes. On a linear scale, all small values collapse to near zero and are invisible.
- Multiplicative or exponential growth — viral spread, compound interest, population growth. On a log scale, exponential growth appears as a straight line, making it easy to spot where growth rate changed.
- Power-law distributions — income, city sizes, website traffic. A log-log scatter plot reveals whether a power law fits (it linearizes the relationship).
- Percentage-change comparisons — when you care whether revenue grew 10 % (not whether it grew by $1 M), a log scale on the y-axis makes equal-percentage moves look equal regardless of the absolute level.
When not to use it
- When the audience is non-technical: log scales require explanation and are frequently misread.
- When the data contains zeros or negatives (log is undefined at zero; workarounds like log(x+1) distort the scale).
- When absolute differences matter more than ratios — e.g., budget allocations where a $1 M difference has the same operational impact regardless of the base.
Labeling
Always label log axes with the original values (10, 100, 1,000), not the exponents (1, 2, 3). Add an explicit note in the chart title or subtitle: “y-axis is log scale.” Gridlines should appear at each order of magnitude.