Log vs Linear Charts: Why Long-Term Charts Use a Log Scale

Two kinds of scale

There are two ways to draw the vertical axis of a price chart. A regular (arithmetic, or linear) scale draws the same difference in amount at the same height: the distance from 10,000 to 20,000 is the same as from 100,000 to 110,000. A logarithmic scale draws the same ratio at the same height: 10,000 to 20,000 and 50,000 to 100,000 are both a doubling, so they are equally tall, and gridlines that grow by multiples, such as 1, 2, 4 and 8, sit at equal spacing. Most charting programs use a linear scale by default and let you switch to log in the settings. In formula terms, height on a log scale is proportional to the logarithm of price. So the height between two prices is set by their ratio rather than their difference, and a 10% rise is drawn at the same height at any price level. For someone who thinks of gains and losses in percent, a log scale is closer to how it actually feels; for someone who thinks in amounts, a linear scale is closer.

The same doubling, different heights

A rise from 10 to 20 and a rise from 1,000 to 2,000 are both a doubling, a gain of +100%. Your money doubled either way, yet on a linear scale the second move is drawn 100 times taller than the first. On a log scale the two moves are the same height. Declines work the same way: a halving (−50%) and a doubling (+100%) are the same height on a log scale, so the chart shows plainly that a price cut in half has to double to get back to where it was. That is why a log scale is used to fit an asset whose price has multiplied dozens of times over onto a single screen. This asymmetry matters most when you look at losses. Recovering from a 30% drop takes a rise of about 43%, and recovering from a 75% drop takes 300%. On a linear scale a rebound near the bottom is drawn small and can easily look insignificant, but on a log scale a doubling from the bottom is drawn at the same height as a doubling from the top.

Nine years of Bitcoin on a linear scale

The figure below plots the closes of 109 completed months of Binance BTCUSDT (August 2017 to August 2026) on a linear scale. The decline from 13,716 USDT in December 2017 to 3,434 USDT in January 2019 was −75%, and the decline from 61,300 USDT in October 2021 to 16,542 USDT in December 2022 was −73%. As percentages they are almost the same decline, but measured against the full span from the lowest close to the highest, the first is drawn at about 9% of that height and the second at about 40%. The moves of 2017 to 2020 are squashed against the bottom and look almost flat. Drawn this way, only the moves of recent years feel big and rough, and the early declines are easily read as if they had been minor. Yet the share of value lost by someone holding through either period was around three quarters both times.

The same data on a log scale

Plot the same monthly closes on a log scale and the two big declines look similar in height: against the full span, the first is about 39% and the second about 37%. The horizontal dotted lines at 10,000, 20,000, 40,000 and 80,000 USDT, which were crowded toward the bottom on the linear scale, spread out at equal intervals on the log scale, meaning that every doubling climbs the same height. Multi-year Bitcoin charts are viewed on a log scale because the early moves can then be compared with today's moves on the same yardstick. On a log scale, the amount represented by equally spaced gridlines grows as you go up, so estimating a price difference by counting gridlines will mislead you. In this figure, first confirm that one step means a doubling, not 10,000 USDT, before you read it. Changing just the habit of how you read the gridline numbers can greatly change your impression of a long-term chart.

Trendlines are drawn differently on each scale

The dots in both figures are the monthly closes of January 2019 and December 2022, and the line joining them is extended to the right edge. A straight line on a linear scale rises by the same amount every month, while a straight line on a log scale rises by the same percentage every month, so joining the same two points gives two different lines. On the linear scale the March 2020 close of 6,410 USDT dropped below the line, but on the log scale it stayed above it. Conversely, the June and July 2026 closes were below the log-scale line yet well above the linear-scale line. On the very same chart, the verdict of a 'trendline break' can go either way depending on the scale. If you make decisions based on trendlines, it is a good idea to record which scale each line was drawn on. And when you hear someone say 'trendline break' about their chart, you need to check first whether that chart is linear or log to know whether you are looking at the same line.

Over short periods the difference is small

Over stretches where price moves within a few tens of percent, such as a chart spanning a few days to a few weeks, the two scales differ very little. For example, when drawing the range from 100 to 110, the price that sits exactly in the middle is about 104.9 on a log scale and 105 on a linear scale. The difference grows when you fit a long period in which price moved several-fold onto one screen. The scale is also only a way of drawing, so the values of indicators such as moving averages or RSI do not change. What changes is the lines you draw by hand and how large the moves feel to the eye. Generally, if price moved within about 20 to 30% on the screen, the difference between the two scales is hard to tell by eye; if it moved more than twofold, the slope and position of lines differ clearly. That is why you rarely need to think about the scale when viewing about a day on 1-minute or 1-hour candles, but when viewing several years on weekly or monthly candles, checking the scale comes first.

Long-term tools on this site and their scales

The Bitcoin Long-Term Indicators tool plots price together with the 200-week and 200-day moving averages on a log chart. In the Crypto DCA Simulator you can also switch the price chart to a log scale and compare price changes over long periods as ratios. The Bitcoin Monthly Returns tool compares each month's move in percent rather than in amount, which rests on the same idea as a log scale: the same ratio is shown at the same size. When you look at a long-period chart, it helps to make a habit of checking first which scale the chart is on. Even within one tool, shortening the period shrinks the difference between the scales and lengthening it widens the difference. When you look at DCA results, switching the price chart to log makes it easier to compare the early buying stretch, which looked squashed against the bottom on a linear scale, with later stretches on the same yardstick. It also helps to check that the scale setting stays the same each time you change the period.

What a log scale does not tell you

A straight line on a log scale is only a summary saying that price has moved at a steady rate so far; it is not evidence that the rate will continue. People sometimes extend a long trendline or a curved band on a log chart into the future and use it like a price target, but that is simply the assumption that past growth rates will hold, turned into a picture. Even in this article's figure, the June and July 2026 closes fell below the log-scale straight line that joins the two lows of 2019 to 2022 and extends forward. And since a log scale cannot draw zero or negative numbers, it is not used for values that swing back and forth across zero, such as returns or funding rates. A log scale also makes large declines look less dramatic. A stretch that looks like a small dip on a long-term log chart may in fact be a period in which more than half of the asset's value disappeared, so it pays to check the percentage decline as a number, separately from the height on the chart.

How scales look different in crypto and stocks

How much you need a log scale depends on how many times over an asset has moved. For an asset like Bitcoin, which has repeatedly risen dozens of times over within a few years and fallen more than 70%, the early years are barely visible on a linear scale, so viewing long-term charts in log is effectively the default. US indexes run into the same problem when decades are fitted onto one screen, and comparing a crash from long ago with a recent decline requires a log scale. On the other hand, for a stock whose price moved within two or three times over a period of a few years, the difference between the two scales is relatively small. Even large Korean stocks such as Samsung Electronics and SK hynix accumulate several-fold moves when ten or twenty years are put on one screen, and then a log scale becomes meaningful. In stocks you also need to check whether the chart uses prices adjusted for stock splits and dividends. On a chart that does not reflect a split, the price looks as if it fell to a fraction overnight, and on a log scale that drop remains as one big step. Crypto has no splits, but switching between charts quoted in different currencies, such as a won pair and a USDT pair, mixes in exchange-rate moves and can change the shape of a long-term chart.

Reading scales on a live chart

If you keep a log scale on in a live chart, remember that the axis range is recalculated every time you zoom or change the period. Most charting programs stretch and shrink the vertical axis automatically to fit the highest and lowest prices of the candles on screen, so when the candle in progress makes a new high or low, the whole axis changes, and the slope of a line you drew by hand can look different on screen. Also, if you switch a line drawn on a linear scale to a log scale, the prices it passes through between the same two points change. If you watch live prices against a long-term trendline, decide in advance which scale the line is drawn on, and whether you will judge a break by the close of a finished candle rather than by the candle in progress. For a line based on monthly candles, the price of the current month moves up and down all month and is fixed as a single point only on the last day. That is also why the figures in this article use only completed monthly closes and leave out the month in progress.

Common mistakes

Here are the mistakes most often seen around chart scales. Most of them start from not checking which scale the chart in front of you uses.

• Concluding from a long-term linear chart that the latest decline is the biggest ever (in percent it may be similar or smaller)
• Extending a straight trendline on a log chart into the future and using it like a price target
• Trying to confirm someone else's trendline break on a chart with a different scale
• Misreading price differences by counting gridlines on a log axis
• Comparing prices on a long-term stock chart that are not adjusted for splits and dividends
• Trying to use a log scale for values that can be zero or negative, such as returns or funding rates