Log vs Linear Charts: Why Long-Term Charts Use a Log Scale
A log scale draws equal percentage moves at equal height. How nine years of Bitcoin look different depending on the scale you choose.
📚 Chart Analysis, Properly From the Start · 3/33·⏱ About 6min read·Information updated 2026-09-23
📋 Key facts
Linear scale
The same change in amount is drawn at the same height
Log scale
The same change in percentage is drawn at the same height
Measured
The −75% and −73% drops in BTC monthly closes look about equally tall on a log scale
Caution
A trendline through the same two points becomes a different line on each 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.
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.
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.
Binance BTCUSDT monthly closes, 2017-08 to 2026-08 (109 completed months). Linear (arithmetic) scale. The horizontal dotted lines are 10k, 20k, 40k and 80k USDT; the two dots are the 2019-01 and 2022-12 closes, and the line through them is extended to the right edge. 'Below line' is the month that closed under this line (2020-03). −75% and −73% are declines measured from the preceding peak closes (2017-12, 2021-10).
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.
Binance BTCUSDT monthly closes, 2017-08 to 2026-08 (109 completed months). Log scale. The horizontal dotted lines are 10k, 20k, 40k and 80k USDT; the two dots are the 2019-01 and 2022-12 closes, and the line through them is extended to the right edge. 'Below line' marks the months that closed under this line (2026-06 and 07). −75% and −73% are declines measured from the preceding peak closes (2017-12, 2021-10).
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.
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.
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.
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.
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