Linear and Logarithmic Price Scales
On a linear scale equal distances mean equal dollars; on a logarithmic scale they mean equal percentages. Over long spans the two produce genuinely different pictures.
MadStockAlerts Research · Updated August 28, 2026
What to take away
- Linear spaces the axis by dollars; logarithmic scale spaces it by percentage change.
- Over long histories or large ranges, log scale is the honest view.
- Trendlines drawn on one scale do not transfer to the other.
- Short-span intraday charts are effectively identical either way.
- The choice has to be stated before arguing about whether a level broke.
MAD Academy Training Video · 0:46
The Setting That Redraws Your Trendline
Linear scale spaces equal dollars, log scale spaces equal percentages, and over a long move they disagree completely.
This lesson is part of a Stock Alerts + Tools plan.
The difference
On a linear axis, the gap from $10 to $20 occupies the same height as the gap from $100 to $110. The first is a doubling and the second is a ten percent move, drawn identically.
On a logarithmic axis, $10 to $20 and $100 to $200 occupy the same height, because both are a doubling. Since returns are what an investor experiences, this is usually the more faithful representation of what happened to the money.
Scroll the chart sideways to see all of it.
When it matters
| Situation | Scale that reads honestly |
|---|---|
| Multi-year history spanning a large range | Logarithmic, decisively |
| A stock that has moved several hundred percent | Logarithmic |
| A few months in a narrow range | Either; the difference is negligible |
| Intraday | Either; the range is far too small to matter |
| Comparing several securities from a common start | Logarithmic, or rebase all of them to 100 |
The classic distortion is a decades-long index chart on a linear axis. The 1987 crash becomes an invisible wobble and recent moves look unprecedented, purely because the index level is larger now. On a log axis the two are drawn at their true relative size.
That distortion is not neutral in its effects. A linear long-run chart makes every current move look historically extreme, which is a systematic bias toward alarm rather than a neutral rendering.
Trendlines do not survive the switch
A straight line on a linear chart is a curve on a logarithmic one, and the reverse. A trendline that connects three lows beautifully on one scale can miss all three on the other.
There is no correct answer to which is right, but there is a correct practice: pick one scale, use it consistently, and note which one a level was drawn on before arguing about whether it broke.
For a security that has moved a long way, the logarithmic line is usually the more defensible, because it describes a constant percentage rate of advance rather than a constant dollar one, and a constant dollar rate is a decelerating percentage rate.
Why the choice compounds over a long history
On an arithmetic axis, equal vertical distances are equal dollar amounts. On a logarithmic one, equal vertical distances are equal percentages. For a chart covering a few months of a security that has moved twenty percent, the two are almost indistinguishable. For a chart covering fifteen years of a security that has gone up thirty-fold, they are different pictures of different things.
The reason the difference grows is that a fixed percentage move is a growing dollar move. A stock going from $5 to $10 doubles, and on an arithmetic axis that move occupies five dollars of height. The same stock later going from $200 to $400 also doubles, and occupies two hundred dollars of height, forty times as much. An arithmetic chart therefore compresses a decade of early compounding into the baseline and devotes almost all of its height to the most recent doubling.
Returns are experienced in percentages. An investor who held through both doublings earned the same return on each, and a chart that draws one as a flat line and the other as a cliff is describing the arithmetic of large numbers rather than the experience of holding the security.
The practical convention that follows: any chart spanning a range where the price has more than roughly doubled is normally read on a logarithmic axis, and any chart of a short window is normally read on an arithmetic one. It is also why long-horizon charts of indices are almost always published logarithmically, and why a long arithmetic chart of the same index always looks like an unprecedented spike at the right-hand edge.
What a log axis does not fix
A logarithm is undefined at zero and for negative numbers, so anything that crosses zero cannot be drawn on one. That rules out most indicator panels: MACD oscillates around zero, rate of change goes negative, and a spread between two yields can invert. Those panels stay arithmetic even when the price panel above them is logarithmic, which is why the two halves of a chart can be on different scales without anything being wrong.
- Volume is conventionally arithmetic, because the question asked of it is relative to its own recent average rather than to a percentage of itself.
- Percentage-based indicators such as RSI already live on a fixed 0 to 100 range, so a log axis would distort a scale that was designed to be read linearly.
- A yield chart is usually arithmetic, because a move from 4 percent to 5 percent is conventionally described as a hundred basis points rather than as a twenty-five percent increase.
- Anything already expressed as a ratio, such as a relative-strength line, is a percentage view by construction.
The other thing a log axis does not fix is a badly adjusted price series. A split that has not been adjusted for still draws a cliff on a logarithmic chart, because the cliff is in the data rather than in the axis. Changing the scale changes how a series is drawn; it never changes what the series says.