A linear price scale gives equal distances to equal price differences. A conventional logarithmic scale gives equal distances to equal ratios between positive prices. Switching the axis changes presentation rather than historical trades, but can alter the appearance of trends, declines and drawn lines. State what the comparison is intended to measure.
One comparison holds absolute differences equal; the other holds price ratios equal.
BTKWIN.COM · EDUCATIONAL EXAMPLECheck one: what vertical distance represents
On a linear scale, ten to twenty and one hundred to one hundred ten have equal vertical distances because both differences are ten. Their returns differ: the first is +100% and the second +10%. Equal visual movement does not establish equal proportional change from the starting price.
On a conventional positive-price logarithmic scale, ten to twenty and one hundred to two hundred have equal distances because both double. The StockCharts chart explanation distinguishes arithmetic and logarithmic presentation. Neither axis changes the amount paid or the asset quantity held.
Logarithmic price presentation usually refers to the vertical axis. It does not itself alter elapsed time along the horizontal axis. However, zooming can change how much time is visible, so fix the window and display dimensions when making a controlled visual comparison.
Use quantity or invested amount when calculating money results
Assume two hypothetical assets move from ten to twenty and from one hundred to two hundred. Both rise 100%. Someone holding one unit gains ten on the first and one hundred on the second before costs. Equal logarithmic distances express equal price ratios, not equal cash gains for equal asset quantities.
If instead one thousand monetary units is allocated to each at entry, the first buys one hundred asset units and the second ten. After both prices double, each holding is worth two thousand and each gross gain is one thousand. Equal starting capital and equal percentage change now create equal gross results.
| Hypothetical move | Price difference | Price return | Gain on one unit |
|---|---|---|---|
| 10 to 20 | 10 | 100% | 10 |
| 100 to 200 | 100 | 100% | 100 |
| 100 to 110 | 10 | 10% | 10 |
These examples assume fully paid spot holdings, complete purchases and no fees or precision limits. A derivative or a different settlement currency needs its own contract and conversion calculation. The price axis alone cannot determine the account’s profit or obligations.
Check two: declines and recoveries use different bases
Moving from one hundred to fifty is a 50% decline. Returning from fifty to one hundred is a 100% rise. The endpoints have the same distance when direction reverses on either fixed axis, while conventional percentage change differs because the starting denominator changes.
Likewise, visually compressing high price levels does not reduce a cash loss. A unit falling from one thousand to five hundred loses five hundred before fees regardless of its screen distance. Use actual prices and quantities rather than candle height or line angle to estimate the monetary effect.
A constant percentage increase over successive periods can look more regular on a logarithmic axis while absolute increases expand on a linear axis. This is a mathematical description of the chosen data, not evidence that the growth rate must persist. The recovery calculator explores percentage bases without forecasting future price paths.
Check three: a straight line can represent a different path
Hold hypothetical endpoints at 100 and 400 two equally spaced periods apart. The arithmetic midpoint is 250. A straight line in a conventional log-price coordinate corresponds to a geometric midpoint of 200, because 100 to 200 and 200 to 400 are equal ratios.
An actual midpoint price of 220 therefore sits below the linear interpolation but above the logarithmic interpolation. A claim about crossing the line can change even though the endpoints and observed price are unchanged. The interpolation definition is different.
That does not prove either line predicts better. If testing a rule, specify scale and anchor points in advance and preserve failed cases. Redrawing after observing the outcome and presenting selected earlier touches as validation obscures which rule was available at decision time.
Drawing-based alerts can also have implementation-specific behavior. The TradingView log-scale alert note describes a limitation and its suggested linear-scale workaround. Read the current instructions for the actual tool rather than extending that behavior to all charting systems.
Check four: logarithmic, percentage and indexed displays differ
An interface can offer linear, logarithmic, percentage and indexed-to-one-hundred views. These are not interchangeable labels. Rebasing two series to one hundred can support relative comparison, but does not alone specify how distances between subsequent values are distributed on the axis.
The TradingView settings guide describes separate presentation controls. For a percentage display, record the price or date representing zero. Changing that base can change displayed numbers at an unchanged actual market price.
In a hypothetical comparison, one asset rises from twenty to thirty and another from two hundred to two hundred sixty. Indexed to one hundred at the common beginning, they finish at 150 and 130. That represents price changes of 50% and 30%, without automatically adding distributions, rewards or trading fees.
Prepare a comparison someone else can reproduce
Open the same market, price series, timeframe and window. Capture linear and logarithmic versions with axes visible. Choose known endpoints and calculate absolute and percentage changes independently. If the historical prices themselves change, investigate another setting such as a transformed chart or adjusted data source.
Check axis direction too; some interfaces can invert it. Automatic fitting and differing image proportions change apparent steepness. Two cropped screenshots with different dimensions cannot establish a numerical acceleration simply from their angles.
Include at least one direct check beside a shared chart. For example, eighty to one hundred is a twenty-unit increase and a 25% return. Those results remain the same on another viewer’s screen regardless of the visual distance between endpoints.
Respect the domain and keep conclusions within the display
A conventional real logarithm does not define zero or negative inputs. Software can apply a special transformation to series containing them; inspect the method instead of inferring it from appearance. An indicator in another pane can also have an axis independent of the asset’s price axis.
Save the market, scale, base and capture time in watchlist notes when comparing observations. Use the view that makes the intended difference or ratio clear, while calculating costs and returns from actual data. Scale selection makes the question more legible; it does not establish future price behavior or replace account-risk analysis.
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English content and examples reviewed: 27 October 2026. Read the Arabic edition.
