# UNIT's Algorithm

[*The UNIT* paper](https://github.com/toknowwhy/the-unit-paper/blob/main/the_unit_paper.pdf) describes the basis of the UNIT's algorithm. UNIT's algorithm aims to track what it would be to hold the top cryptocurrencies over the long haul.

## How to Obtain UNIT's Value

In short, the value of 1 UNIT comes from the relative price motions of the top cryptocurrencies. To follow the value of UNIT we display three charts of the value of 1 UNIT over time on our website: the [Bitcoin chart](https://app.unitindex.org/unit/btc) (denominated in SATS), the [Ethereum chart](https://app.unitindex.org/unit/ETH) (in Finney), and the [USD chart](https://app.unitindex.org/unit/USD).

## Calculating the Value of UNIT

First, we chose the first cryptocurrency ever created, Bitcoin, to price other coins in terms of that one.

We define the weight $$w\_{C, m}$$ of a coin $$C$$ on a given month $$m$$ as the market cap of that coin at the beginning of the month over the total market cap of all coins in the UNIT at the given month.

$$
w\_{C,m}= \frac{M\_{C,m}}{\sum\_iM\_{i,m}}
$$

As usual, the total market capitalization is calculated by adding the circulating supplies $$S\_i$$ times the price of each cryptocurrency in the UNIT, $$P\_{i}$$, in terms of the first cryptocurrency, Bitcoin.

$$
\displaystyle\sum\_{i} S\_iP\_{i}
$$

Let the UNIT on month $$m$$, $$Ø\_m$$, be defined by

$$
Ø\_m = \left(\sum\_{i}\frac{P\_{i,m}}{P\_{i,m-1}} w\_{i,m-1}\right) U\_{m-1}
$$

where $$P\_{i,m}$$ is the price of a coin $$i$$ in the Unit at month $$m$$ and $$w\_{i,m}$$ is the weight of a coin $$i$$ in the Unit at month $$m$$.


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