Linear vs. Logarithmic Scales: What’s The Difference?

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 and 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?

How To Define Scale?

A scale is a set of values or numbers that indicate certain intervals on a chart or graph for measurement. Data visualization involves representing data sets in pixels. However, the values in any data set cannot all correspond to pixel measurements. Scales provide a way to represent data values as new pixel values. For example, let’s assume the following data set represents the number of unique customers that walk into a supermarket each month. Var NumberOfCustomers = [ 1000, 2000, 3000, 4000, 5000 ] We can see that the supermarket records 1000 additional customers each month. Business is flourishing! 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 of 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 — linear and logarithmic scales. 

What Is Linear Scaling?

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. 

What Is Logarithmic Scaling?

Logarithmic scales are used in charts and graphs for two main reasons. 

1. To represent changes or skewness due to large data values in a dataset. For instance, where some values are larger than the majority within a dataset. 
2. To represent the percent rate of change over time or a multiplicative factor.

Unlike the linear scale, a logarithmic price 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 logarithmic chart becomes congested and difficult to interpret. 

What Are The Key Differences?

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. For 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. 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. 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 are 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.  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. 

Measuring Prices

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.

More Volatility = Logarithmic Scale

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. To visualize these volatile price movements, the logarithmic price chart is best. 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. 

Logarithmic Scales Are Useful For Long-Term Perspective

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. 

Linear Scale For Day Traders

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.

Which Price Scale To Use?

Stock prices are typically examined in terms of relative value. Popular financial ratios include the price-earnings ratio and price book values. Therefore, it makes more sense to show or assess the security’s stock movement in percentage rather than in absolute numbers when representing price movements. That said, likely, traders will 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.  

Which Trends Are Better With A Log-Scale Chart?

There are different types of trend lines. However, they don’t all perform the same on every chart. You can do a personal experiment to better understand how trends work on each chart. First, draw the same trend lines for the same asset on linear and logarithmic charts. Then see for yourself how the trend lines evolve on both charts. You’ll notice that the logarithmic price scale shows a more accurate representation of the trend lines.

Ready To Get Started Building Powerful Charts?

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 and 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.