Why plot bitcoin on a logarithmic scale?
By: The BitLog Team | Last update: Aug. 2025 | 2 min read
We often plot data on a linear scale, where tick marks go like 1, 2, 3, 4..., indicating a constant increment.
But there are other ways to visualize data! We can also plot on what's called a logarithmic scale (i.e. constant ratio), for example, 1, 10, 100, 1000...
An advantage of a logarithmic scale is that we can see very small and very large numbers together in one plot. This is helpful for the historical price of bitcoin, which has increased from cents to 100's of thousands of dollars.
But there's another interesting advantage. Sometimes, playing around with the scales can help us discern underlying trends. To demonstrate, we plot below examples of three very common functions; linear, exponential, and powerlaw.
We can choose to make either the x or y axis logarithmic, or both. Play around with the scales and see if you can spot the behavior (we'll highlight the relevant function to help make it clear).
What did we learn? Certain functions can look like straight lines depending on the scale, so sometimes it's easy to tell what type of function you're looking at just by making a scale adjustment. Here's a summary:
| Scale | Which type of function appears straight? |
|---|---|
| Linear | Linear |
| Linear in X, Log in Y | Exponential |
| Logarithmic in X and Y | Powerlaw |
We encourage you to play around with the scales as you go through this site.
Since its inception, the price of bitcoin seems to have increased approximately like a powerlaw in time, which is why it's helpful to plot it on a logarithmic scale in both axes. For more information on whether there is good evidence for powerlaw behavior, see our next article.
Powerlaws often show up in biology, physics, and in complex networks, but they are generally rare in financial assets. This behavior in price therefore may imply something fundamental about the factors that drive bitcoin's growth. In the following articles we elaborate on what all this may mean. We leave it to the reader to draw their own conclusions.
How to use this website
Learn more about the bitcoin powerlaw in our articles.
Examine long-term trends in bitcoin price in the historical charts and stay up-to-date with live stats.
All our real-time analysis is focused on how the price behaves relative to the lower- and upper-bound powerlaw trendlines (see the chart).