Technical Analysis · Intermediate · 5 min
Linear vs. logarithmic scale
You can explain the difference between a linear and a logarithmic price scale and choose the right one for long-term charts.
Bubble or scale?
Look at a chart of a market over several decades. Often it hugs the bottom for years and then shoots almost straight up at the end. It looks like something unusual happened recently, maybe even a bubble.
Sometimes it did. But often the shape comes from the way the chart's price axis is drawn. The same prices can tell two very different stories, depending on one setting.
Points vs. percent
The price axis of a chart can be drawn in two ways.
On a linear scale, equal distances on the axis are equal steps in price. The space from 10 to 20 is the same as from 100 to 110. Both are 10 points.
On a logarithmic scale, or log scale, equal distances are equal percentage changes. The space from 10 to 20 is the same as from 100 to 200. Both are doublings, +100%.
The visual shows a fictional price growing by about 25% per step, from 10 to 150. On the linear scale, the line looks flat at first and then rises steeply, as if growth were speeding up. On the log scale, it is almost a straight line, because the growth rate stays roughly the same.
Neither scale is wrong. They answer different questions:
- Linear shows how many points a price moved. It is the usual default and works well for short periods and small ranges.
- Logarithmic shows how large a move was in percent, which is what matters for your money. As the lesson on compounding showed, steady growth in percent produces a curve that bends upward in money terms.
Over small ranges, the two scales look almost identical. A share that moves between 98 and 102 looks the same either way. The difference grows with the size of the moves. On long-term charts, on charts of assets that have multiplied, and for trendlines drawn over many years, the log scale usually gives a fairer picture.
+100% vs. +10%
A fictional share rises from 10 to 20 in its first year. Years later, it rises from 100 to 110.
- On a linear chart, both moves are 10 points tall. They look equally important.
- In percent, the first move was +100%. Money invested at 10 doubled. The second move was +10%.
- On a log chart, the first move is about seven times taller than the second, because a doubling covers more percentage ground than a 10% rise.
Now imagine the share later falls from 150 to 120, a drop of 30 points. On a linear chart, it looks like a crash compared with the early years. In percent, it is −20%, painful but no larger than many earlier swings that look tiny on the linear chart.
Common mistakes
- Judging long-term growth on a linear chart. Recent moves look bigger than they were in percent.
- Comparing trendlines across scales. A straight line on one scale is curved on the other.
- Not checking the setting. Many platforms show the scale type in a corner of the price axis.
- Expecting a difference on short charts. For small ranges, both scales look almost the same.
The takeaway
A linear scale shows equal price steps as equal distances. A log scale shows equal percentage moves as equal distances.
Check yourself
Quick quiz
4 questions. Instant feedback, nothing is saved.
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1Tap the scale on which steady percentage growth looks like a straight line.
Tap the chart.
On a logarithmic scale, each doubling takes the same vertical distance, so constant growth in percent is a straight line.
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2A share rises from 10 to 20, later from 100 to 110. On which scale do both moves look equally tall?
Linear scales measure points. The first move is +100%, the second only +10%, which a logarithmic scale would show.
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3On a logarithmic scale, what does the same vertical distance always represent?
The distance from 10 to 20 equals the distance from 100 to 200: both are a doubling.
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4When does the choice of scale matter most?
Over small ranges, the two scales look almost identical. The difference grows with the size of the moves.
of 4 correct.