The Dacoinminster Power Law
The Dacoinminster power law is a Bitcoin price model published in February 2013 and never changed since. This page explains the formula, what it says Bitcoin is worth today, and how it compares with the better-known Santostasi model.
Open the live Dacoinminster chartWhat is the Dacoinminster power law?
In February 2013 a Bitcointalk forum user called Dacoinminster posted a simple formula for Bitcoin's price. Bitcoin traded at about $25 at the time. The formula says the price depends on one thing only: how many days have passed since Bitcoin's first block.
Most Bitcoin power law models in use today were fitted with price data from later cycles. The Dacoinminster constants were fixed in 2013, so every price since then is a real test of the model.
The Dacoinminster power law formula
Here t is the number of days since the genesis block on January 3, 2009. The same formula in log form is:
The log form shows why it is called a power law. If you plot price against Bitcoin's age with both axes on a log scale, the model is a straight line with a slope of 5.6.
What the Dacoinminster power law says today
The fair value rises a little every day because it depends only on Bitcoin's age. These numbers are calculated when the page loads.
A ratio above 1 means Bitcoin trades above the Dacoinminster line, and a ratio below 1 means it trades below. The live Bitcoin power law chart shows the full price history against the line.
How to calculate the Dacoinminster fair value
- Count the days from January 3, 2009 to your date.
- Raise that number to the power 5.6.
- Multiply the result by 4.42 × 10−17.
For example, January 1, 2030 is 7,668 days after the genesis block. That gives a fair value of about $251,000.
Dacoinminster power law values by year
The table gives each model's fair value on January 1. These are the models' trend values, not the prices Bitcoin traded at.
| Date | Days (t) | Dacoinminster | Santostasi |
|---|---|---|---|
| Jan 1, 2014 | 1,824 | $81 | $111 |
| Jan 1, 2016 | 2,554 | $532 | $793 |
| Jan 1, 2018 | 3,285 | $2,178 | $3,453 |
| Jan 1, 2020 | 4,015 | $6,700 | $11,157 |
| Jan 1, 2022 | 4,746 | $17,095 | $29,658 |
| Jan 1, 2024 | 5,476 | $38,091 | $68,441 |
| Jan 1, 2026 | 6,207 | $76,835 | $142,362 |
| Jan 1, 2028 | 6,937 | $143,213 | $272,677 |
| Jan 1, 2030 | 7,668 | $250,982 | $489,741 |
| Jan 1, 2035 | 9,494 | $830,114 | $1,706,832 |
| Jan 1, 2040 | 11,320 | $2,223,117 | $4,772,351 |
On the day the model was published, February 13, 2013, its own fair value was about $27.
Dacoinminster vs. Santostasi
Giovanni Santostasi's model is the best-known Bitcoin power law. Both models use the same formula, Price = A × tn, with different constants.
| Dacoinminster | Santostasi | |
|---|---|---|
| Exponent (n) | 5.6 | 5.845 |
| log₁₀(A) | −16.355 | −17.016 |
| Fair value, Jan 1, 2026 | $76,835 | $142,362 |
| Fair value, Jan 1, 2030 | $250,982 | $489,741 |
| Constants fixed | 2013 | Fitted with later cycles |
The lower exponent makes the Dacoinminster line climb more slowly, so it gives the lower fair value today and the gap widens over time. The Santostasi constants were fitted with more data, so part of how well that model matches the past is hindsight.
How fast the model grows
A power law does not grow at a fixed yearly rate. The same number of days is a smaller share of Bitcoin's age each year, so growth slows. The Dacoinminster line rises about 38% from the start of 2026 to the start of 2027, and about 30% from the start of 2030 to the start of 2031. The price doubles each time Bitcoin's age grows by about 13%.
Limits of the model
The Dacoinminster power law describes the long-run trend of past prices. It does not explain why Bitcoin should keep following that trend, and nothing forces it to. Bitcoin has traded several times above the line near cycle tops and well below it near cycle bottoms, so the fair value is a poor guide to the price in any single month.
For informational purposes only; not financial advice.
Dacoinminster power law FAQ
What is the Dacoinminster power law?
The Dacoinminster power law is a Bitcoin price model that a Bitcointalk forum user called Dacoinminster published in February 2013, when Bitcoin traded at about $25. It says the price follows a fixed power of Bitcoin's age in days, and the constants have not been changed since it was posted.
What is the formula for the Dacoinminster power law?
Price = 4.42e-17 × t5.6, where t is the number of days since the Bitcoin genesis block on January 3, 2009. The same formula in log form is log10(Price) = -16.355 + 5.6 × log10(t).
Who is Dacoinminster?
Dacoinminster is the username of the Bitcointalk forum member who posted the model in February 2013. The model is named after that username.
How do I calculate the Dacoinminster fair value for a date?
Count the days from January 3, 2009 to your date, raise that number to the power 5.6, and multiply by 4.42e-17. For January 1, 2030 that is 7,668 days, which gives about $251,000.
What is the difference between the Dacoinminster and Santostasi power laws?
Both models use Price = A × tn. Dacoinminster uses an exponent of 5.6 and Santostasi uses 5.845, so the Dacoinminster line climbs more slowly and sits lower today. For January 1, 2026 the Dacoinminster value is about $76,800 and the Santostasi value is about $142,400.
What does the Dacoinminster power law predict for 2030?
The formula gives about $251,000 for January 1, 2030. That figure is the model's trend line, and Bitcoin has traded far above and below its trend for long periods.
How fast does Bitcoin grow under the Dacoinminster power law?
Growth slows every year because the price depends on a power of Bitcoin's age. The line rises about 38% from the start of 2026 to the start of 2027 and about 30% from the start of 2030 to the start of 2031. The price doubles each time Bitcoin's age grows by about 13%.
Is the Dacoinminster power law reliable?
Its constants were fixed in 2013, so everything since then is a real test of the model and not a fit made after the fact. It is still only a description of past prices. Nothing forces Bitcoin to keep following it, and this is not financial advice.
See it on the live chart
The StreetAlpha Bitcoin power law page plots Bitcoin's full price history since 2010 against the Dacoinminster line. It also shows the model's year-by-year record since 2013 and lets you switch to the Santostasi, live-fit and custom models.
Open the live Dacoinminster chart