Data visualization aims to make it easy for users and stakeholders to infer values from complex data and ultimately make data-driven decisions. This involves being able to accurately represent the story your data tells. To do this, you must understand the two components of data visualization — the data itself and the plane of representation. This is because the size of this plane, in other words, the scale, drastically affects your audience’s perception of any data charts.
In this case, the value you’ll infer from a given chart is as good as your choice of scale. So, which scale is suitable for your data type? Linear vs. Logarithmic? In this article, you’ll learn the difference between linear vs. logarithmic scales and which you should use for your data. But before we dive into all that, let’s define the scale. What exactly is a scale, and how does it impact your chart’s perception?
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In this case, the value you’ll infer from a given chart is as good as your choice of scale. So, which scale is suitable for your data type? Linear vs. Logarithmic? In this article, you’ll learn the difference between linear vs. logarithmic scales and which you should use for your data. But before we dive into all that, let’s define the scale. What exactly is a scale, and how does it impact your chart’s perception?
For example, let’s assume the following data set represents the number of unique customers that walk into a supermarket each month.
But what if we want to showcase this success using a pie chart or a bar chart? Without scales, we’ll be using data values as display values. In other words, the bar chart for the first month would be 1000 pixels tall. Your users would require screens, at least the size of your largest data value (in pixels), to see the height of each bar.
This is where scales play a crucial role in visualizing our data values. Scales affect charts the same way, regardless of their real-world application. In a stock chart, a trader’s interpretations or inferred values largely depend on the price scale used during analysis.
There are different types of scales; however, we’ll be discussing the two most common scale types, particularly for measuring price movement —
Another name for the linear price scale is the arithmetic chart. It does not plot price movements according to their percent change. Rather, the linear scale represents each unit change with a constant unit value. Because each value change is constant, the linear price scale is easy to understand. This makes it the most common of the two price scales discussed in this article.
The listed prices on a linear scale, mainly on the y-axis—vertical—side of the chart, are equidistant. Also, a linear scale results in a linear graph. And, being a linear chart means having a constant slope. In other words, each unit price change remains constant, irrespective of the price the change occurs.
Logarithmic scales are used in charts and graphs for two main reasons.
Unlike the linear scale, a log scale is not plotted with price levels separated by equal distances. Rather, it is in such a way that similar percent changes, which could be different numerical values, are plotted as the same vertical distance. For example, the vertical distance between $1000 and $2000 is the same as that between $500 and $1000. This is because both distances represent a 100% price increase.
This scale type is the most used among traders and price movement analysts. This is because, compared to linear price scales, they better represent less severe price increases or decreases. They make it easier to visualize or project the percentage increase or decrease an asset’s value must undergo to reach a buy or sell target. However, if price changes are in small percentages over long periods, a log scale chart becomes congested and difficult to interpret.
Below you will find a clear distinction between Linear vs. Logarithmic charts aiding you in understanding which one is better:
| Linear Chart | Logarithmic Chart |
|---|---|
| On a linear chart, a price increase will be represented by the same upward movement, regardless of the price level at which this change occurs. | However, a logarithmic chart will show the same price movements, as in the example above, at different vertical distances. While both movements constitute the same dollar value, they represent different percentage increases. |
Let’s understand this with an example:
A price movement from $20 to $40 will have the same vertical distance as an increase from $40 to $60. Both involved a $20 increase, which the linear chart represents equally. Below is an image that will help you get a better understanding of linear scale example:
In the logarithmic chart, the first movement – $20 to $40 – shows a 100% increase, and the second – $40 to $60 – shows a 50% increase. In this case, the first price movement -100% – will have a longer vertical distance than the second – 50%. That said, we can have equal vertical distances between the prices on a logarithmic scale.
This is when the percentage change between assets’ price values is equal. Using the above example, the distance between the price movement from $20 to $40 would be equal to that of $80 to $160. This is because they both represent a 100% price increase. Here is a graph representing the above-stated points:
A general practice among most traders and charting software is the use of logarithmic scales. However, we recommend you explore other approaches to determine what best suits your trading style. Below are other key differences between linear and logarithmic scales.
The difference between Linear vs. Logarithmic charts in terms of measuring prices is quite straightforward. Price distribution using a linear scale is equal. In other words, we have an equal distribution of price values along the y-axis of a linear chart. For example, a scale of 100 units would mean a distance equivalent to 100 units between each price value. (i.e., 0, $100, $200, $300, $400, $500, $600, $700).
On the other hand, price distribution on the logarithmic scale uses price scaling rather than the units of measure. In other words, rather than prices separated by a unique unit value, the y-axis of a logarithmic chart represents each distance between price values as a percentage change in an asset’s price.
For example, a logarithmic chart can have values like the following on its y-axis: ….. $141.60 – $141.90 – $142.30 – $142.70 – $144.50 – $145.00 Here, the price change – $141.90 to $142.30 – represents a $0.40 increase, but a 0.28% change. While $144.50 – $145.00 shows a $0.50 and 0.34% increase.
A linear chart could probably suffice if the asset has a steady price action with small price changes. However, price movements for penny stocks and most securities are hardly steady. If anything, they’re becoming more and more volatile with each passing year. The log scale price chart is best for visualizing these volatile price movements. This is because it can show abrupt large price movements, as well as small price changes.
The linear and logarithmic charts for the same asset might appear similar. However, the difference lies in the interpretation of the y-axis price distribution. Since the price distribution on the linear scale is in absolute unit terms, it can give a misleading impression.
For example, a linear chart can give the impression that the price moved slowly. When, in reality, the price saw a steady 1% increase, as would be seen in a log chart. In a nutshell, a logarithmic chart will deliver the most accurate results when it comes to volatile price movements.
It can more accurately represent the rise and fall of prices with a fairly straight trajectory. If there’s a change in the pace of growth, a logarithmic chart would accurately adjust to represent the change. This isn’t the case for a linear price scale, as the values remain the same regardless of the rate of change.
When it comes to long-term usefulness between Linear vs. Logarithmic charts, the latter is a better option. Logarithmic price scales are particularly more accurate than linear scales when it comes to long-term price changes. Since the price distribution on a linear scale is equal, a move from $10 to $15, representing a 50% price increase, is the same as a price change from $20 to $25.
On this linear chart, the price distribution is $5 per unit. But using a logarithmic graph, you can infer an initial 50% price increase from $10 to $15 and a 25% increase from $20 to $25. Long-term perspectives involve large price movements. In this case, it’s better to interpret percentage moves rather than constant units.
Conversely, linear scales are best suited for day trading. Daily price movements often involve tight ranges or short time frames. In this case, a linear chart provides a clearer view of the whole and makes it easy to identify breakouts. The equal price distribution of the linear scale in absolute unit terms can make it easy to identify upside and downside targets.
This is because both targets can fall within the vertical distance. Thereby making it easy to interpret short-term price charts. However, while the linear scale can make short-term trading easier, the logarithmic scale can yield similar results. By understanding the difference between log vs linear scale, you can pick the one that will aid you while day trading.
Stock prices are typically examined in terms of relative value. Popular financial ratios include the price-earnings ratio and price book values. Therefore, showing or assessing the security’s stock movement in percentages rather than in absolute numbers makes more sense when representing price movements. That said, traders will likely automatically be presented with the correct price scale, even though they may not be aware of the distinction between the two categories of price scales.
However, whether you should use a linear price scale or a logarithmic scale chart depends on the asset and the purpose of the analysis. Price movements are not the same for all securities. Many experience extremely volatile and explosive price changes over certain periods. Yet, there are stocks that record almost unnoticeable changes over long periods.
A linear scale plots data points using a unique unit value to give an equal vertical distance between values. On the other hand, a logarithmic chart scaling plots using percentage change as the distance between data points. Due to the use of percentage change, logarithmic charts are best suited for analyzing assets with volatile price action.
However, assets confined to a certain range over long periods can easily be analyzed using linear scales. We’ve seen the differences between Linear vs. Logarithmic scales. While each scale type has its areas of success, the idea is to understand your charts and why you’re using the scaling method. Whatever scale type you want to implement, you can do so using FusionTime Charts.
Download the trial to see for yourself.
A linear scale displays data with equal intervals between values, making it ideal for datasets with consistent changes. A logarithmic scale uses a ratio-based approach, where equal intervals represent exponential growth (e.g., 10, 100, 1000).
👉 When should I use a logarithmic scale?A logarithmic scale is best used when your data spans a wide range, such as exponential growth or percentage changes. It’s ideal for visualizing trends in financial charts, scientific data, or population growth, where small values and large values coexist.
👉 When to use a logarithmic scale in trading?In trading, a logarithmic scale is used when analyzing price movements over large ranges or extended time periods. It is especially useful for comparing percentage changes, representing proportional increases or decreases more effectively than a linear scale.
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