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1982issue C051-3

Constructing semi-log scales for trend channels

Semi-logarithmic chart paper is used to compare percentage price changes rather than absolute price changes. Only the price axis is logarithmic, time stays linear, and special graph paper lets prices be plotted without first calculating logarithms.

  • Semi-logarithmic chart paper is used when the task is to compare percentage price changes rather than absolute price changes.
  • A fixed percentage change produces equal differences between the logarithms of the prices, so a three-dollar level can be compared with a thirty-dollar level on the same scale.
  • In stock and commodity charting, price is commonly placed on a logarithmic vertical axis and time on a linear horizontal axis.
  • A logarithmic price scale has no zero baseline and is used to compare proportional rates of change across series that differ widely in dollar size.
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Current trackChart scale analysis14 readings

What a semi-logarithmic chart is

Semi-logarithmic chart paper is used when the task is to compare percentage price changes rather than absolute price changes. Semi-logarithmic means only the price axis is logarithmic. Logarithmic means both axes are logarithmic.

In stock and commodity charting, price is commonly placed on a logarithmic vertical axis and time on a linear horizontal axis. The result is a semi-logarithmic chart: a chart that places only the price axis on a logarithmic scale while time remains linear. A logarithmic chart, by contrast, places both axes on logarithmic scales.

How the price scale is built

A fixed percentage change between two price pairs produces equal differences between the logarithms of those prices, so a three-dollar level can be compared with a thirty-dollar level on the same scale. Plotting the logarithm of price instead of raw price makes a constant rise or fall correspond to a constant percentage gain or loss.

A percentage price change is a proportional move in price, compared by equal log-price distances rather than equal dollar distances. Special logarithmic graph paper is used so prices can be plotted directly without first calculating logarithms.

Comparing arithmetic and logarithmic scales

A logarithmic price scale has no zero baseline. It does not provide a starting line at price zero. The scale is used to compare proportional rates of change and to place series that differ widely in dollar size on one chart.

An arithmetic price scale is a linear price axis on which equal vertical distances represent equal absolute price units. A paired illustration of an arithmetic price scale and the matching logarithmic scale is supplied so the two constructions can be compared directly.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
1 of 14 in the Chart scale analysis track
19881-5 pp.Next on Chart scale analysisTreat a suspected bend as a construction testWhen a plotted series flattens with a downward bend or accelerates upward, a curved trendline can describe the path more usefully than a straight trendline.
All readings on this track · 14 readings
  1. 1982Constructing semi-log scales for trend channels
  2. 1988Treat a suspected bend as a construction test
  3. 1989Constructing percentage-box point-and-figure charts
  4. 1989Constructing point-and-figure objectives across chart scales
  5. 1991Unfinished point-and-figure until filter, scale, and pivots measure percent
  6. 1992A logarithmic point-and-figure construction with weekly breadth scores
  7. 1995Constructing a least-squares trend channel with two-standard-deviation rails
  8. 1995Percentage boxes turn a three-box reversal into a scale decision
  9. 2003Log scale trendlines and compound growth
  10. 2007Trendline and channel construction on linear versus log scales
  11. 2012Constructing trend-intensity overlays across chart scales
  12. 2015Index drawdown caps, chart-scale stops, and leverage
  13. 2016Evaluating breakouts by share-price band
  14. 2016Constructing chart scale with a golden-rectangle aspect ratio
By fieldTrend and channels228 readingsBy year198223 readings
All 14 readings tagged Chart scale analysis
Also on Chart scale analysis5 readings
1988Treat a suspected bend as a construction test1989Constructing percentage-box point-and-figure charts1989Constructing point-and-figure objectives across chart scales1991Unfinished point-and-figure until filter, scale, and pivots measure percent1992A logarithmic point-and-figure construction with weekly breadth scores