Arithmetic vs. Logarithmic Scale
March 9, 2022

Arithmetic vs. Logarithmic Scale

Scales are rarely addressed, yet they may make a significant difference in trendline analysis and interpretation.

Scales are rarely addressed, yet they may make a significant difference in trendline analysis and interpretation. So, it is a good idea to discuss them. Charts are either plotted on an arithmetic or logarithmic scale. Before we go into the key distinctions between these two scales, it's crucial to remember the basics of charting: date plotted on the x-axis (except point-and-figure charts) and price plotted on the y-axis.

The vertical axis distinguishes these two scales. The vertical distance between points or dollar amounts in arithmetic charts is constant at all price levels, whereas the vertical separation in logarithmic charts varies depending on the percentage change between points or dollar amounts and hence, the distance decreases as the price of a security increases.

For example, if the price of a stock changes by $1.00, the distance between $1.00 and $2.00 on the arithmetic scale will be identical to the distance between $101.00 and $102.00; however, one is a 100% change in price and the other is only a 0.99% change in price (as you would expect). As a result, on the logarithmic scale, the distance between $1.00 and $2.00 is greater than the distance between $101.00 and $102.00.

Moreover, the arithmetic scale dampens price fluctuations at low levels of the chart yet exaggerates them at high points. Since the logarithmic scale exposes change in percent, rather than absolute terms, it solves this problem by proportionately displaying price trends, making it a suitable choice over the arithmetic one. This is critical to keep in mind since individuals on social media or in the news frequently utilize an arithmetic scale to overstate or convey a false message about significant price movement, but if you translate it into a logarithmic scale throughout an extended period of time, the price change may not be anything special - this is a simple exaggeration of common events into dramatic.

In conclusion, the logarithmic scale is better than arithmetic in that it depicts price movements at a percentage rate rather than a specific dollar amount for each distance. In other words, it's perfect for long-term trend analysis since it provides a more realistic perspective and thus, is naturally preferred by traders.

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