Linear Versus Logarithmic Charts: Choosing the Right Scale

Alpha Sentinel is a software platform, not a registered investment adviser. This article is educational, not investment advice. Full disclaimer at the end of this post.

You are looking at two charts of the same stock on a tablet in a hospital break room. On one, a ten-year climb looks like a gentle slope that steepens only recently. On the other, the same climb looks like a steady, even ramp, and the recent stretch no longer looks dramatic. Neither chart is wrong. A linear chart spaces prices by equal dollar amounts, while a logarithmic chart spaces them by equal percentage changes, and which scale suits you depends on the question you are asking and the time span you are viewing.

Key Takeaways

• A linear scale gives equal dollar changes equal vertical distance, and a logarithmic scale gives equal percentage changes equal distance.
• The scales look alike over short spans and diverge over long ones or after large moves.
• Log charts make percentage moves comparable across time, which suits long histories.
• Linear charts keep dollar changes easy to read, which suits short spans and modest price ranges.
• Check which scale a chart uses before comparing two charts or judging a move.

Two Ways to Space the Same Prices

On a linear chart, the vertical axis is divided into equal steps of price. The distance between ten and twenty dollars is the same as the distance between ninety and a hundred. Each tick on the axis is the same dollar amount as the last, so a ten-dollar move always looks the same size, whether it happens near the bottom of the chart or the top.

On a logarithmic chart, the axis is divided into equal steps of percentage change. The distance from ten to twenty dollars, a doubling, is the same as the distance from twenty to forty, and from forty to eighty. A move from ninety to a hundred, about eleven percent, takes up far less space than the move from ten to twenty, which is a hundred percent. The axis labels bunch together as prices rise, which is the visual sign that you are looking at a log chart.

Neither scale changes the data. Every price point is identical; only the spacing between the horizontal gridlines differs. That fact is worth holding onto, because the shape of a chart can change how a move feels even though nothing about the underlying prices has changed.

Why the Same Rally Can Look Dramatic or Modest

Consider a stock that climbs from ten dollars to a hundred over many years, with the same percentage gain in each stretch. On a linear chart, the early gains look tiny, because a few dollars is a small distance on an axis stretched to a hundred. The later gains look enormous, because the same percentage gain now covers many dollars. The curve bends upward and appears to accelerate sharply near the end, even though the rate of growth was steady.

On a log chart, the same steady growth appears as a nearly straight line, because equal percentage gains occupy equal vertical distance. A straight line on a log chart roughly means a constant rate of growth, and a line that steepens means the percentage rate itself increased. That is a distinction the linear chart cannot show you at a glance.

This is why long-term histories are usually drawn on log scales. A linear chart over decades compresses the early years into a flat line near the bottom, making them nearly invisible. If you have ever wondered why an old chart seems to show nothing happening for years and then everything at once, scale is a likely reason.

When the Two Scales Barely Differ, and When They Diverge

Over short spans and small price ranges, the two scales are almost indistinguishable. If a stock moves from fifty to fifty-five dollars over a few weeks, a ten percent change, the curvature of a log axis over that narrow range is slight, and the two charts will look much alike. For the kind of weekly review many busy investors do, either scale is fine.

The scales diverge as the price range widens. A stock that has doubled or halved looks noticeably different on each. The effect is most visible after big declines. A fall from a hundred dollars to fifty is a fifty percent loss, and a rise from fifty back to a hundred is a hundred percent gain, because the base is smaller. On a linear chart, the two legs look symmetrical in dollar terms and obscure that asymmetry. A log chart draws the decline and the required recovery in proportion to their percentage size, which can be a more honest picture of what a drawdown demands.

That asymmetry is a general piece of arithmetic worth keeping in mind whenever you review a position that has fallen a long way, and it applies regardless of any chart.

Choosing the Scale for Your Own Review

A practical way to decide is to match the scale to the question. If you are asking "how much did my position change in dollars over the last few weeks," a linear chart answers it directly. If you are asking "how does this move compare with earlier moves in percentage terms" or "how has this stock behaved over the last decade," a logarithmic chart is the more faithful choice.

Whichever you pick, adopt a habit of checking the scale before drawing any conclusion. Most charting tools put a small toggle labeled "log" or "linear" near the axis, and some default to one or the other. When two people discuss a chart and disagree about whether a move looks big, a different scale setting is often the cause.

An illustrative week, not a result: an attorney reviewing a long-held position on a Saturday opens a ten-year chart and, as is her habit, toggles to logarithmic. She notes that the line is fairly straight for most of the decade and that the last year shows a sharper slope, which tells her the recent percentage growth rate was higher than earlier. She then switches to linear on a three-month view to see the dollar change over the quarter. She writes one line about each, leaves the position alone, and moves on. Using each scale for the question it answers took about five minutes.

Qualified advisors and self-directing are both legitimate approaches, and a clear sense of which scale you are reading helps either conversation.

Frequently Asked Questions

What is the difference between a linear and a logarithmic chart?

A linear chart spaces prices by equal dollar steps, while a logarithmic chart spaces them by equal percentage steps. The underlying prices are the same, but a doubling takes the same vertical distance anywhere on a log chart and a different distance at each level on a linear one.

Which is better for stocks, linear or log?

Neither is better in every case. Log scales suit long histories and comparisons of percentage moves, and linear scales suit short spans where dollar changes matter. Choose the one that matches the question you are asking.

Why does my long-term chart look flat for years and then spike?

On a linear scale, early moves occupy only a sliver of the axis because the later prices are much higher. Switching to a logarithmic scale usually shows that the early years contained meaningful percentage moves that the linear view compressed.

How can I tell which scale a chart is using?

Check the axis labels and any toggle near the axis. On a log scale, the gaps between labels shrink as prices rise and the spacing is uneven in dollar terms, while on a linear scale the gaps between labels are all equal.

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