In addition to various price displays such as bars or bars, different chart scales are also used in technical analysis charts. There are two basic scales, linear and logarithmic. In this article, the differences between linear and logarithmic graphics and how these scales can be used are explained with examples.

If you are new to technical analysis and need more basic information about technical analysis charts, you can first read the article titled “Graph representations used in technical analysis”. While doing technical analysis, after choosing the most suitable display for you from the price bars described in the related article, you can arrange the chart scale linearly or logarithmically according to your needs. The linear scale, that is, the linear scale, is the chart scale used in most technical analysis programs or financial sites. Logarithmic (non-linear) representation has a more specific use.

This educational content

• Difference Between Linear Scale and Logarithmic Scale
• Chart Drawn with Linear and Logarithmic Scales
• Chart Drawn with Linear Scales
• Chart Drawn with Logarithmic Scales
• Trading on log scale and trading at linear scale: Why does it make a difference?

## Difference Between Linear Scale and Logarithmic Scale

The difference between the linear scale and the logarithmic scale arises because the distance between two points and the percentage change between these two points have different meanings. While price differences are always shown at equal intervals on a linear scale, price differences are not shown equally on a logarithmic scale. In logarithmic scale, the percentage change of prices is taken into account. In summary, if the price difference is equal in linear representation, the distance of the price bars is equal, and in logarithmic scale, if the percentage change in price is equal, the distance is equal.

note: unit; used in place of currencies such as the dollar, the euro and the like

For example, let’s assume that a stock traded at 5 unit in the stock market has increased to 10 unit . After this increase, the price has increased by 5 unit, in other words, it has increased by 100%. Now, let’s assume that a stock traded at 100 unit has increased to 105 unit. In this case, the price increase is again 5 unit, but the percentage change in between is 5%.

When we put these two stock charts (linear) side by side, the increase from 5 unit to 10 unit  and the increase from 100 unit to 105 unit will visually look the same, because the length of the price bar will be the same, but actually these two price movements are distanced. Although it is equal, it is not equal as a percentage change.

The example above is given on two different stocks, the example described above can be better understood if the price of the same stock shows great changes over the years. For example, if we consider that a stock was traded at 5 unit in 2000, but the share price increased to 100 unit in 2016, when we examine the 16-year graph of this stock, showing the same distance between price steps may cause visual misinterpretations. When the graph is examined as a whole, high percentage changes in the past will seem insignificant, while lower percentage changes that occur when the price rises will seem more important. It is possible to eliminate this misleading perception by using a logarithmic scale.

## Chart Drawn with Linear and Logarithmic Scales

### Chart Drawn with Linear Scales

Below is the chart between the years 2000-2016. This chart is drawn with a linear scale, the price ranges are equal in every period. The 100-point change distance that occurred when the index was at 10,000 points in 2000 and the 100-point change distance that occurred when the index was at 70,000 points in 2016 are the same as the graphic representation. This can be better understood if attention is paid to the grid drawn on the graph.

### Chart Drawn with logarithmic Scales

In the second figure below, there is a graph of the Chart index drawn with a logarithmic scale between the years 2000-2016. If we pay attention to the grid drawn on the chart, parallel to the increase in the Chart, the distance between the price changes in the past years narrows in the following years. In summary, the 100-point change that occurs when the index is at 10,000 points is shown by a longer distance than the 100-point change that occurs when the index is at 70,000. Because the 100-point change in previous years is higher in percentage.

As a result, the linear scale is the default chart scale, reflecting the price difference evenly, unchanged. The logarithmic scale, on the other hand, is based on the percentage change, the size of the price bars increase or decrease according to the percentage change. On a linear scale, an increase from 5 unit to 10 unit and an increase from 20 unit to 25 unit are shown with the same distance on the same Y-axis, while an increase from 20 unit to 40 unit with an increase from 5 unit to 10 unit on a logarithmic scale shown at the same distance.

The choice of chart scale is entirely up to the preference of the investor. My observations are that linear notation is commonly used, but if there are big differences between price levels in the past years and today’s price levels, it is useful to use the logarithmic scale to see the true magnitude of the trend. In summary, linear scale for short-term representations, logarithmic scale may be preferred when working on long-term charts such as 5 or 10 years.

Let’s give a good example from the tradingview site for better understanding.Tradingview user ‘tommyf1001’ gave a detailed example on the bitcoin chart.