Bitcoin Power Law Model (Live Chart)
Bitcoin's price since 2010 against a power law of time since the genesis block, with support and resistance lines fitted through every cycle's bottom and top.
Hover the price for the model's reading on any day; hover the dashed line for projections. Bold purple and red stretches mark closes above resistance or below support, and lighter ones mark closes within 10% of a line; dotted lines show the largest breaks since 2011. Prices before Sep 18, 2014 are daily reference closes (CoinMetrics); later prices are Yahoo Finance, updated every 30 minutes.
Band position
Where today's price sits between support (0%) and resistance (100%), measured on the log scale.
The formula
Is the model breaking down?
Each model gets the same checks, recalculated from the price data every time the page loads. Green means the data still fits the model, amber is a warning, and red means the data is contradicting it.
Exponent drift
The exponent n refitted using only the prices available at the end of each year. A steady n supports the power law. An n that keeps falling means growth is slowing faster than a power law allows, which is what an S-curve looks like from the inside.
Same idea, different answers
Every model below uses the same formula. Small differences in the two constants move today's fair value a long way, so treat any single "fair price" with care.
| Model | log₁₀(A) | n | Fair today | Price ÷ fair | Fair in 2030 |
|---|
Cycle tops and bottoms
Each halving era's highest close and the lowest close after it. These points define the support and resistance lines. Multiples are against the selected model's fair value on that day.
| Era | Top | Top price | × fair | Bottom | Bottom price | × fair | Drawdown |
|---|
Overshoots and undershoots
Each row is one stretch where price sat at or beyond a line, counting days within 10% of it. An undershoot or overshoot closed past the line on 3+ days; a test stayed within 10% for 14+ days without breaking it. The key day is the furthest break, or the closest approach for a test. The dotted lines on the chart sit at the largest overshoot and undershoot since 2011, carried forward.
| Type | Started | Ended | Days | Days past line | Key day | Price | From line |
|---|
How the model works
A power law says price grows as a fixed power of time: Price = A × tn, where t is days since the genesis block on January 3, 2009. Plotted with both axes on log scales, that curve is a straight line, which is why Bitcoin's long history looks so orderly in the log view.
Santostasi uses the widely cited constants popularised by Giovanni Santostasi. Dacoinminster 2013 is the fit a Bitcointalk user published in February 2013, when Bitcoin was about $25, and never changed. Live fit is a least-squares regression on every daily close in this dataset, recalculated each time the page loads. Custom lets you set both constants yourself.
Support and resistance don't depend on the model you pick. They are separate power laws fitted through the cycle bottoms and tops listed above. The resistance line has been rising more slowly than fair value because each cycle's peak has been smaller relative to trend.
A power law is a description of past prices, not a mechanism that forces future ones. Projections assume the pattern continues. For informational purposes only; not financial advice.