Author: Analyst Lu Mingyu
Does equal chart distance represent an amount or a percentage?
After a gold trading chart switches to a logarithmic price scale, straight trendlines drawn through the same two price-time anchors may correspond to different reference prices elsewhere. On a linear axis, a straight line represents constant absolute price change per unit of time; on a logarithmic axis, it represents a constant percentage change over equal intervals. The same quotation can therefore sit above one line and below another. Changing the display scale does not change the original quotes or prove that the market suddenly reversed.
A linear, or arithmetic, scale assigns equal vertical distances to equal price differences. A rise from USD 2000 to 2200 per ounce and a rise from USD 3000 to 3200 per ounce both add USD 200 and therefore occupy equal heights on the same linear scale. Their percentage gains, however, are 10% and approximately 6.67%. These prices are hypothetical teaching values.
A logarithmic scale assigns distance according to price ratios. A rise from 2000 to 2200 and a rise from 3000 to 3300 are both 10%, so they occupy equal vertical distances on the same log scale, although the absolute increases are USD 200 and USD 300. StockCharts' guide to price charts discusses these approaches. In a typical semi-logarithmic chart, only the vertical price axis is logarithmic; the horizontal axis still uses ordinary time spacing.
Linear charts are convenient for reading absolute price distances, while logarithmic charts help compare percentage changes, especially across long periods with substantial price-level changes. Neither scale guarantees better trading decisions. For another illustration of amounts versus percentages, see ATR and Percentage Comparisons.
The same anchor points can generate different reference prices
Imagine a hypothetical completed daily gold chart with price-time anchors at USD 2000 on day 0 and USD 2420 on day 10. Extend the straight line to day 20. Times are recorded in Beijing time and the three days are equally spaced on the horizontal axis. All quoted prices are hypothetical completed daily closes. The intervening price history is not provided, and the two anchors have not been established as actual swing lows.
The linear line gains USD 420 per ounce over ten days. Extending by the same amount gives a day-20 reference of 2420 + 420 = 2840. The logarithmic line multiplies by 2420 ÷ 2000 = 1.21 over ten days. Applying that ratio again gives 2420 × 1.21 = 2928.2.
| Hypothetical day | Teaching quote (USD/oz) | Linear reference | Log reference |
|---|---|---|---|
| Day 0 | 2000 | 2000 | 2000 |
| Day 10 | 2420 | 2420 | 2420 |
| Day 20 | 2880 | 2840 | 2928.2 |
On day 20, the hypothetical close of 2880 is USD 40 above the linear line but USD 48.2 below the logarithmic line. The quote is on opposite sides because the mathematical scales differ. Two points define a line, but the table does not establish a valid market trendline, identify the first break or predict a reversal.
The formulas are: linear reference = 2000 + 420 × t ÷ 10; logarithmic reference = 2000 × 1.21^(t ÷ 10), where t is the time elapsed since day 0. StockCharts' trendline guide also discusses how price-scale choices affect trendline interpretation.
Adding 420 every ten days or multiplying by 1.21 is a mathematical extension of a line, not a forecast that gold will continue rising at that rate. Even though a third selected quote falls on one side of a reference line, the example lacks other price touches, intraperiod highs and lows, and future observations. Making a reference price reproducible improves the comparison; it does not give the line more predictive power.
What changes and what stays the same?
The calculation assumes that separate straight lines are drawn through the identical time-and-price anchors on the two price scales. Chart platforms may preserve or reinterpret drawings differently when their scales change. Their actual behavior must be checked rather than assumed to be universal.
A fixed horizontal price line is different. USD 2300 per ounce remains USD 2300 on both scales, although its screen location and distances to other prices may change. The numerical open, high, low and close of a conventional candle also remain unchanged when only the vertical display scale changes.
On-screen angles additionally depend on window dimensions, horizontal compression and vertical zoom. The same movement can look very steep or relatively flat, so a trendline appearing steeper than 45 degrees does not prove that the rise cannot continue. For comparisons, specify the amount or percentage change per unit of time and preserve matching time and price conventions.
Record the scale before declaring a trendline break
When reviewing a screenshot that supposedly shows a trendline break, verify the instrument, contract, quote provider and price units, then the timeframe, candle boundaries, vertical scale and both anchor points. Preserve the time and price axes in the screenshot; the visual shape alone is insufficient to reconstruct the line's reference price.
If the method requires closing confirmation, check that the relevant candle has finished. Consistent scales do not prevent the current candle from changing. See Unclosed Candlesticks and Closing Confirmation. Daily session boundaries can depend on server time zones, so record the original timestamps as well as their Beijing-time conversions.
If the software retains a drawing after changing scales, read back the anchor times and prices and the line's value at the observation point. A line appearing in the same area of the screen does not establish that every setting is identical; a resized screenshot cannot replace numerical records.
Both scales can be saved for different analytical purposes, but one should not select whichever scale best supports an earlier opinion after seeing the outcome. Establish the scale and rules first, then examine whether the chosen anchors and price structure have sound support.
The choice of scale cannot replace risk analysis
A visually small distance on a log chart may still represent a large absolute price difference. Stops, targets and profits or losses should be calculated from actual prices, contract point values and quantities, not screen distances. See Stop-Loss Distance and Position Risk.
Risk warning: This article provides chart-reading education and does not constitute personalised investment advice. Hypothetical quotes are neither live market prices nor actual trades. Breaking a trendline does not guarantee a reversal, and staying above it does not guarantee continuation. Margin trading can cause loss of principal, and actual stop execution may differ from the preset price.