Log Scale

A logarithmic (log) scale is an axis on which equal distances represent equal ratios rather than equal differences, so each fixed step multiplies the value instead of adding to it.

On a linear axis you move by adding; on a log axis you move by multiplying. This compresses huge ranges into a readable space and turns percentage or fold changes into equal-sized steps. It is the right tool whenever the data spans several orders of magnitude or whenever proportional change is what you care about.

How a log scale works in a chart

The tick marks on a base-10 log axis fall at powers of ten: 1, 10, 100, 1000. The key property is that each of those gaps is physically the same width, because each represents the same tenfold ratio. The distance from 1 to 10 equals the distance from 10 to 100 equals the distance from 100 to 1000. A consequence is that the value 0 can never appear, since no power of ten equals zero.

A concrete example

Suppose four values are 1, 10, 100 and 1000. On a linear scale the first three would be crushed into a sliver near the bottom while 1000 dominated the axis. On a log scale they land at four evenly spaced ticks, each one step apart, because each is ten times the one before. A line connecting them becomes a straight diagonal — and on a log axis a straight line means a constant growth rate, which is exactly why analysts reach for it.

Related terms

A log scale is one type of scale for an axis; its counterpart is the linear scale, where equal distance means equal difference. Log axes are common for long time series — see the line chart guide.