Bitcoin · power law · explained simply
There's a line that Bitcoin's price keeps crashing down to and bouncing off of, almost never breaking below it. It isn't magic or a hunch. It falls straight out of one simple formula and a clever way of drawing a graph. Here's how it works, explained like you're twelve.
01 / THE IDEA
Bitcoin has a kind of birthday: it was "born" on 3 January 2009. Every day, it gets a little older. The power law says the price isn't random: it tends to follow a formula based on how old Bitcoin is.
Raising age to a power means the price grows fast early on, then the growth gradually slows down. That's different from "the same percent forever" (that's called exponential). A power law is the same kind of maths nature uses for earthquakes, the sizes of cities, and how animals burn energy.
02 / THE TRICK
Draw Bitcoin's price on a normal graph and it looks insane: flat and boring for years, then suddenly shooting straight up. So people switch to log scales, where 1, 10, 100, 1000 are spaced equally apart instead of the big numbers squashing everything.
Here's the magic. Take a logarithm of both sides of the formula and it turns into the straight-line equation you learn in school:
So a power law, drawn on a graph where both axes are log scales (a "log–log" plot), becomes a perfectly straight line. The crazy explosion turns into a neat diagonal:
03 / THE FLOOR
The price never sits still: it bubbles up high above the trend, then crashes back down. But it keeps falling to that lower line and bouncing off it, almost never staying below for long. That bottom line is the support line, or the floor.
Because the whole thing is a power law, the support line is also a power law, the same formula with a smaller value of A, which just slides the line downward.
One honest detail worth knowing up front: the floor isn't a wall the price physically pushes against. It's drawn at a fixed distance below the trend line, about 0.4× fair value, what statisticians call the −2σ band. That distance is chosen so the price's normal ups and downs stay inside the corridor roughly 95% of the time. So when you see the price "bounce off the floor," that's a regularity in how far Bitcoin has historically strayed from its trend, not a force shoving it back up. It's a useful line, but a measured band, not a law of physics.
Below is the real thing: Bitcoin's actual price history sitting inside a "corridor" of three power-law lines.
04 / WHY IT'S TAKEN SERIOUSLY
Three things make people take the floor seriously. They're worth understanding, but it's just as important to know what each one does not prove.
1. A straight line fits, but straight is easy here. A power law shows up as a straight line on log–log axes, and Bitcoin's data does line up straight. That's consistent with a power law; it isn't proof of one. Once you stretch both axes with logarithms across this many orders of magnitude, almost any price that mostly rises over years will look roughly straight. So the straight line is a point in favour, not a fingerprint that rules everything else out.
2. The line is calculated, not guessed. A method called regression finds the single line that sits closest to all the dots at once. That beats eyeballing, but it's a fact about how the line was drawn, not about whether a power law is the right idea. Regression will happily fit a straight line to data that isn't really a power law at all.
3. The fit is measured, but read the number carefully. R² scores how closely the line tracks the data, from 0 to 1, and here it's about 0.956. That sounds like "right 96% of the time," and it isn't. On a log–log chart the numbers are dominated by Bitcoin's enormous rise from cents to tens of thousands of dollars, so almost any model that captures "it went up a lot over fifteen years" scores above 0.95. A high R² here means the price rose steadily, not that the exponent is exactly 5.7, and not that a power law beats every other shape. And the line it's scoring is the middle of a corridor that's still about six times wide from floor to ceiling. The price also tends to stay on the same side of the line for years at a time, which means the real fit is looser than one tidy number suggests.
Taken together, these are good reasons to treat the power law as a serious description of Bitcoin's past, not as proof that the floor must hold in the future.
05 / TRY IT
Pick any date and the calculator runs the real Santostasi formula to show the model's floor, fair value, and ceiling, then compares them to a price you enter.
price = 10-16.493 × days5.688 · floor = trend × 0.398 · ceiling = trend × 2.512
06 / THE HONEST PART
The maths here is descriptive: it accurately describes what has already happened. It's not a law of nature like gravity that has to keep working.
Some people argue there are real reasons it might keep holding: Bitcoin's network of users, mining difficulty, and adoption all seem to grow in power-law ways that feed each other. But plenty of experts think it's just a pattern that has held so far and could break. Both views are reasonable.
So: the floor is "supported by maths" because the data genuinely forms a straight line and the line is calculated and fits tightly. But "the price will always stay above this line" is a bet on the pattern continuing, not something the maths can guarantee.
07 / FAQ
The Bitcoin power law is a model, introduced by Giovanni Santostasi, in which Bitcoin's price tracks a straight line on a log-log chart against time since the January 2009 genesis block. Concretely, fair value ≈ 10^-16.493 × (days since genesis)^5.688. Because both axes are logarithmic, the power-law curve appears as a straight line, and it has fit Bitcoin's 15-year history with an R² of about 0.956.
In the power-law model the price oscillates within a corridor of three parallel lines: a fair-value trend, a ceiling roughly 2.5× above it, and a support "floor" roughly 0.4× below it (the ±2σ bands, with σ ≈ 0.20). Historically every cycle bottom has fallen to that floor and bounced, so it acts as empirical support. The floor is not a law of nature. It is a regularity that has held so far.
Three times, and only briefly: a shallow ~10-week dip in Aug-Oct 2015, a one-week touch in Jul 2016, and the March 2020 COVID crash. All three recovered quickly, and every cycle bottom across more than a decade has otherwise held above the floor. See the breach timeline on the "Today" page for the exact dates and depths.
The exponent (the slope of the line on a log-log chart) is about 5.7, and this build uses 5.688. An exponent near 5.7 means the price grows fast early and then decelerates, which is the signature of a power law rather than constant-percentage exponential growth.
Projecting the support line forward, the line-to-line growth rate is around 29% over a ten-year horizon, easing toward the low-20s% over twenty years. So roughly 30% per year is a near-term figure that declines over time, not a constant rate. It is a model projection, not a guarantee.
No. The model is descriptive: it fits the past well but cannot promise the future. The fit is sensitive to the time window used, the floor has broken before, and long-horizon adoption could decelerate faster than the curve assumes. Nothing here is investment advice.