Technical analysis · Chart basics
Linear vs logarithmic price scale: which chart to use and why
How linear and log price scales differ, 33 years of SPY drawn both ways, the math of percentage moves, and when each scale gives the honest picture.
On this page
The vertical axis of a price chart can be drawn two ways. On a linear scale (also called arithmetic), equal distances mean equal dollar amounts: the gap from $100 to $200 is the same height as the gap from $700 to $800. On a logarithmic scale (log or semi-log), equal distances mean equal percentage changes: the gap from $100 to $200 is the same height as the gap from $400 to $800, because both are a doubling.
For a few weeks of prices the choice barely matters. For years or decades it changes the story completely. A linear chart of a stock that has compounded for 30 years makes the early decades look flat and the recent years look explosive, and it makes a 25% fall today look bigger than a 50% fall twenty years ago. This guide draws 33 years of the SPDR S&P 500 ETF (SPY) both ways, explains the math, and gives rules for choosing.
How the two scales work
On a linear scale the price axis is spaced evenly in dollars. Grid lines might sit at $0, $200, $400, $600 and $800, each the same distance apart.
On a log scale the axis is spaced by the logarithm of the price. In practice that means each doubling takes the same height: $50, $100, $200, $400 and $800 are evenly spaced. So is every other equal ratio. A 10% rise from $50 to $55 is exactly as tall as a 10% rise from $500 to $550.
That is why a log chart answers the question most investors actually care about: what percentage did I make or lose? A linear chart answers a different question: how many dollars per share did the price move?
Thirty-three years of SPY, drawn both ways
SPY closed its first full month, February 1993, at $44.41. In October 2026 it was at $769.36, about 17.3 times higher, a price gain of roughly 8.8% a year before dividends.
On the linear chart (top), the 1990s and 2000s are squeezed into the bottom fifth of the panel. The dot-com bust and the financial crisis look like ripples. The last decade dominates, and the line appears to accelerate sharply after 2020. The 2022 dip looks like one of the deepest falls on the chart.
On the log chart (bottom), the 1990s rally is as visible as any later one, the 2000–02 and 2007–09 bear markets are the two deep valleys they were, and the 2022 decline is clearly shallower than either. The line after 2009 looks like a steady climb rather than a takeoff, because a steady percentage gain is a straight line on this scale.
The doubling test
Doublings make the difference concrete. SPY first closed a month above $100 in February 1998, above $200 in August 2014, and above $400 in April 2021.
- From $100 to $200 took about 16.5 years. On the linear chart that rise is short.
- From $200 to $400 took about 6.7 years. On the linear chart it is twice as tall.
On the log chart the two doublings are the same height, which is the honest comparison: each one doubled the money of anyone who held through it. The linear chart makes the second look twice as important because it was worth twice as many dollars per share.
Measuring the big declines
| Decline | Peak month (close) | Trough month (close) | Dollars lost | Percent lost |
|---|---|---|---|---|
| Dot-com bust | Aug 2000 ($152.34) | Sep 2002 ($81.79) | $70.55 | 46.3% |
| Financial crisis | Oct 2007 ($154.65) | Feb 2009 ($73.93) | $80.72 | 52.2% |
| Covid crash | Dec 2019 ($321.86) | Mar 2020 ($257.75) | $64.11 | 19.9% |
| 2022 rate shock | Dec 2021 ($474.96) | Sep 2022 ($357.18) | $117.78 | 24.8% |
In dollars, 2022 was the worst of the four. In percent, it was roughly half as deep as 2007–09. That is the trap of a linear chart over long periods: the higher the price, the larger every ordinary move looks.
Two caveats keep this honest. First, these are monthly closes, which smooth the extremes. The Covid crash looks like a 19.9% decline here, but on daily closes the S&P 500 fell about 34% from February 19 to March 23, 2020. Second, the prices are not adjusted for dividends. SPY paid dividends throughout, so a holder's total loss in each decline was slightly smaller than the price loss shown.
Why percentages are the right yardstick
Recovery math works in percentages. A 52.2% fall needs a 109% gain to get back to even, because the rebound starts from a smaller base: 1 ÷ (1 − 0.522) ≈ 2.09. A 24.8% fall needs only a 33% gain. On a log chart those recoveries look exactly as hard as they were. SPY regained its 2007 high close in March 2013, more than five years after the peak. It regained its 2021 high close in December 2023, two years after.
When to use each scale
| Situation | Better scale | Why |
|---|---|---|
| Several years or more of history | Log | Compounding growth reads as a line, not a hockey stick |
| Any move of more than about 30–50% | Log | Early and late parts of the move are comparable |
| Comparing the size of past rallies and crashes | Log | Equal percentage moves look equal |
| A few weeks or months, modest moves | Either | The scales look almost identical |
| Dollar levels: stops, targets, option strikes | Linear | Distances on screen match dollars at risk |
| Assets that can go to or below zero (spreads, some rates) | Linear | A log scale cannot show zero or negative values |
What changes for technical analysis
Trend lines. A straight trend line on a log chart is a constant percentage rate of growth. On a linear chart it is a constant dollar rate. Over a long rising trend these diverge: a line drawn on a linear chart will eventually be broken from below as growth compounds, and a line on a log chart may hold. Neither is the "real" trend line. Draw yours on one scale and keep it. The Trends and trendlines: how to identify a trend and draw it correctly guide covers drawing them.
Chart patterns. Measured-move targets such as "the height of the pattern added to the breakout" give different answers on the two scales when the pattern is large. On a log scale the target is a percentage, on a linear scale a dollar amount.
Indicators. Moving averages, Relative Strength Index (RSI): how to read and use it and most other indicators are computed from the prices themselves, so the scale does not change their values, only how they are drawn on the price pane.
How Finabase handles price scales
- The Log scale toggle. Every symbol chart has a Log scale button in the toolbar. It switches the price pane to a semi-log axis on any range, for example SPY's full history. The volume and indicator panes keep their own linear axes.
- Saved per range. Signed in, the choice is saved for each range, so you can keep the maximum range on log scale and the 1-month range on linear. The setting is shared with the Stock Master apps.
- Percent comparisons. When you add comparison symbols, the chart switches to a percent axis normalized to the visible window, so symbols at very different prices can be compared directly. The Comparison page does the same for saved sets of symbols, charting their returns from a common start.
- Long histories. The 5Y and MAX ranges use weekly or longer bars, which pair naturally with a log scale.
Frequently asked questions
Is a log chart the same as a percentage chart?
Close, but not identical. A percentage chart rebases the price to 0% at a starting point and shows the change from there, usually on a linear percent axis. A log chart keeps the actual prices on the axis but spaces them by ratio. On a log chart, equal percentage changes from any starting point look equal. On a linear percentage chart they do not: a rise from +100% to +200% is a 50% gain but looks as tall as a rise from 0% to +100%.
Why do stock charts look like they are going up exponentially?
Because they are drawn on a linear scale and the price compounds. A steady 9% a year roughly doubles the price every eight years, adding more dollars in each period than the last. On a linear chart that is an upward curve; on a log chart it is a straight line. A steep linear curve on its own is not evidence of a bubble.
Should I use log scale for day trading?
It rarely matters. Over a day or a week, prices rarely move more than a few percent, and the two scales look nearly the same. Many short-term traders keep linear scale so that the distance to a stop on screen matches the dollars at risk.
Can a log scale show a stock that went to zero?
No. The logarithm of zero is undefined, so the axis can approach zero but never reach it. A stock falling toward zero on a log chart keeps dropping lower in equal steps for each halving: from $1 to $0.50 looks as large as $100 to $50, which is accurate in percentage terms.
Summary
A linear scale spaces prices by dollars; a log scale spaces them by percentage. For short periods the two look alike. Over long periods they tell different stories: SPY's 2022 decline was its largest in dollars since 1993 but, at 24.8%, roughly half the percentage loss of 2007–09, and only the log chart shows that. Use log scale for long histories, big moves and any comparison of past rallies and crashes, and linear scale for short-term trading and dollar levels. Decide which scale your trend lines live on and keep it. For how much history each bar covers, see Chart timeframes: intraday, daily, weekly and monthly charts.
Sources and further reading
- John J. Murphy, Technical Analysis of the Financial Markets (New York Institute of Finance, 1999) — arithmetic versus logarithmic scaling
- U.S. Securities and Exchange Commission, Investor.gov — Compound interest calculator
- Finabase chart data — SPDR S&P 500 ETF (SPY) monthly bars, February 1993 to October 2026 (price only, not adjusted for dividends)