Direct Answer
An arithmetic (linear) price scale spaces equal dollar amounts equally on a chart, so a $10 move looks the same whether a stock is at $20 or $200. A logarithmic price scale spaces equal percentage moves equally instead, so a move from $20 to $22 (10%) looks the same as a move from $200 to $220 (10%). Logarithmic scales are commonly preferred for viewing long-term price history or securities that have moved through a wide price range, since they better represent percentage-based returns; arithmetic scales can be more intuitive for shorter timeframes or narrower price ranges.
Key Takeaways
- Arithmetic scales measure dollar distance. A $10 move takes up the same vertical space on the chart no matter what price level it happens at.
- Logarithmic scales measure percentage distance. A 10% move takes up the same vertical space whether it happens at $20 or $200.
- The underlying data never changes. Switching scales only changes how price movement is displayed, not the actual prices, candles, or volume.
- Log scales are commonly favored for long-term or wide-range charts, since they better represent percentage-based returns across very different price levels.
- Arithmetic scales can feel more natural for shorter timeframes or narrower ranges, where the dollar amounts themselves are what matters for the analysis.
- There is no universally correct scale, the appropriate choice depends on the timeframe, the price range involved, and the question the chart is being used to answer.
What Are Arithmetic and Logarithmic Price Scales?
A price chart's vertical axis has to make a decision: how much space does a given price change get? An arithmetic, or linear, scale answers that question in dollar terms. Equal dollar amounts are spaced equally, so a $10 move covers the same physical distance on the chart no matter where the price currently sits, a move from $20 to $30 looks identical in height to a move from $200 to $210.
A logarithmic scale answers the same question in percentage terms instead. Equal percentage moves are spaced equally, so a move from $20 to $22, a 10% gain, takes up the same vertical distance as a move from $200 to $220, which is also a 10% gain, even though the second move covers ten times as many dollars. On a logarithmic scale, doubling in price always covers the same amount of chart space, whether that doubling happens from $5 to $10 or from $500 to $1,000.
Both scales plot the exact same closing prices, highs, lows, and volume, nothing about the underlying data is different. The only thing that changes is the rule used to convert a price into a vertical position on the chart. That difference in rule is what makes the two views look different, sometimes dramatically so, once a security has traveled through a wide range of prices.
Hypothetical example, for education only
Consider a stock that rises from $20 to $200 over several years. Along the way, it moves from $20 to $22 (a $2, 10% move) early on, and later moves from $200 to $220 (a $20, 10% move) near the end.
- On an arithmetic scale: the $200-to-$220 move covers ten times more vertical space than the $20-to-$22 move, because $20 is ten times larger than $2 in dollar terms. The early move looks tiny by comparison, even though both represent the same 10% gain.
- On a logarithmic scale: both moves take up the same amount of vertical space, because both represent an identical 10% percentage change. The chart treats the two gains as equivalent, which is how they were equivalent to an investor holding the position through either move.
Now extend the same idea across the stock's full run from $20 to $200, a 900% increase overall. On an arithmetic scale, the early climb from $20 to roughly $40 or $50 is compressed into a thin band near the bottom of the chart, barely visible against the later climb into the hundreds. On a logarithmic scale, that early climb (also a large percentage move) gets a visual footprint proportional to its percentage size, so the whole multi-year trend is easier to read as a continuous story of percentage gains rather than a chart dominated by its most recent, dollar-largest moves.
How to Apply This, and Common Mistakes
Match the scale to the question
If the analysis concerns returns, how much a position gained or lost in percentage terms, or how one stock's percentage performance compares to another's, a logarithmic scale generally represents that better, especially over long periods or wide price ranges. If the analysis concerns specific dollar levels, where to place a stop a fixed number of dollars from entry, or reading a narrow intraday range, an arithmetic scale can be more intuitive since it shows dollar distance directly.
Check the scale before trusting a trendline
Because the two scales space the same price history differently, a trendline drawn across a wide price range can look like a clean fit on one scale and look bent or broken on the other. This is a property of the scale, not a change in what the price actually did, so it is worth confirming which scale a chart is set to before drawing conclusions from how well a trendline appears to track price over a multi-year, wide-range move.
Don't assume one scale is always correct
Neither scale is inherently right or wrong, each represents the same data through a different lens. A common mistake is treating whichever scale a charting platform happens to default to as the only valid view, without considering whether the timeframe and price range in question call for the other one.
Remember the data underneath is identical
Toggling between scales never changes closing prices, highs and lows, or volume. It changes only the visual spacing used to display those numbers, which is why comparing analysis done on one scale against analysis done on the other should focus on the interpretation, not on assuming the data itself disagrees.
A Trendline on One Scale Is a Different Line on the Other
Switching scales changes nothing about the data and quite a lot about anything you have drawn on top of it. A straight trendline connecting two lows on an arithmetic chart is a curve on a logarithmic one, and vice versa, so the level it projects into the future differs between the two views. The same is true of channels and of any measured move stepped off in dollar terms.
That makes the scale a decision to fix rather than a display preference to toggle. Drawing on one scale and reading levels on the other produces prices that came from neither, and it is easy to do without noticing because the candles themselves look right in both views.
Which scale suits depends on the range. Over a long history or on a security that has moved through a wide price range, a logarithmic scale is usually preferred because equal percentage moves occupy equal space, which is how returns actually work. Over a short window where price has not travelled far, the two look nearly identical and the arithmetic view is often easier to read.
The underlying prices, candles and volume never change. Any difference in what you conclude came from the geometry, which is worth remembering when a pattern appears on one scale and not the other.
FAQ
What is the difference between an arithmetic and a logarithmic price scale?
An arithmetic (linear) price scale spaces equal dollar amounts equally on a chart, so a $10 move looks the same whether a stock is at $20 or $200. A logarithmic price scale instead spaces equal percentage moves equally, so a move from $20 to $22 (10%) looks the same as a move from $200 to $220 (10%). Both scales plot the same underlying price data, they only change how vertical distance on the chart is measured.
When is a logarithmic scale generally preferred?
Logarithmic scales are commonly preferred for viewing long-term price history or securities that have moved through a wide price range, since they better represent percentage-based returns. On a stock that has grown from single digits to hundreds of dollars over many years, a log scale keeps early, lower-priced moves visually proportionate to later, higher-priced moves, rather than compressing the early history near the bottom of the chart.
When might an arithmetic scale be more useful?
Arithmetic scales can be more intuitive for shorter timeframes or narrower price ranges, where the dollar distances between prices are what a trader cares about, for example, setting a stop a specific number of dollars below entry, or reading an intraday range. Over a short window with a limited price range, the arithmetic and logarithmic views tend to look similar, so the simpler dollar-based reading is often easier to work with.
Does switching between arithmetic and logarithmic scales change the actual price data?
No. The underlying prices, candles, and volume figures are identical on both scales, only the vertical spacing used to display price changes is different. Switching scales changes how a move looks on the chart, not what actually happened to the price.
Is there a single correct scale to always use?
No, there is no universally correct scale. The choice depends on the timeframe being studied, the price range the security has traveled through, and what the chart is being used for. Many traders default to logarithmic scales for long-term or wide-range charts and switch to arithmetic scales for shorter-term, narrower-range analysis.
Can a trendline look valid on one scale and broken on the other?
Yes, this can happen. Because the two scales space price moves differently, a straight trendline drawn across a wide price range may track price closely on a logarithmic scale but appear to bend away from price on an arithmetic scale, or vice versa. This is a direct consequence of how each scale measures distance, not a change in the price data itself, and it's a reason to check which scale a chart is using before drawing conclusions from a trendline.
Can zero or negative values be plotted on a logarithmic scale?
No. The logarithm of zero is undefined and negative numbers have no real logarithm, so any series that reaches or crosses zero cannot be displayed on a log axis. This rules it out for spread series between two instruments, for indicators that oscillate around zero, and for the futures contracts that have settled below zero. Charting software typically responds by refusing the scale or by silently clipping the data.
Does a moving average look different on a logarithmic scale?
It does, and for a reason worth understanding. The average is calculated on the prices and then drawn on a transformed axis, so what you see is the arithmetic average displayed logarithmically rather than an average of the log prices. Those are different lines. Over a long history with a large price range the difference is visible, and platforms rarely state which they compute.
Should an indicator panel use the same scale as the price panel?
Usually not. A bounded oscillator already lives on a fixed linear range where equal distances are equal amounts of the statistic, so a log axis would distort it for no benefit. The price panel and the indicator panel are separate charts sharing a horizontal axis, and choosing the scale independently for each is the normal arrangement rather than an inconsistency.
References
Disclaimer
This article is for educational and informational purposes only and does not constitute personalized investment, financial, or legal advice. Chart scale is a display convention, not a trading signal, and should not be relied on alone to make trading or investment decisions. Trading involves risk, including the possible loss of principal.