# Calculation Methodologies

**Exchange Rate Calculation**

**Exchange Rate Calculation**

We use the formula below to calculate the exchange rate:

`rcv = a * B / (A + a) `

`rcv_net = rcv * (1 - fee)`

where `a`

is the amount of token X sent by swapper and `A`

is the total amount of tokens X in the pool before the swap

Then, the exchange rate is simply `lim a -> 0 (rcv / a)`

which equates to `B/A`

.

In terms of how much a user shall receive `b`

given `a`

supplied:

`b = a * B / (A + a) * (1 - fee)`

## Asset Price Calculation

Internally, a fixed pricing algorithm is used to calculate the spot $USD price of assets swapped via the Pact AMM pools. To achieve this the algorithm tracks every SWAP pool call, distinguishing between swaps with:

Stablecoin Swaps (USDT or USDC) and;

General Swaps (all other assets)

#### Stablecoin Swaps

For swaps with either USDT or USDC (let’s call them STABLE), it assumes the stablecoin has price of $1 and uses the following formula:

$price_{STABLE}$ is the price of STABLE (1$)

$total_{STABLE}$ is a total number of STABLE in pool after SWAP

$total_{asset}$ is a total number of asset in pool after SWAP

$decimals_{asset}$ asset’s decimals

$decimals_{STABLE}$ STABLE’s decimals

#### General Swaps

For swaps between other assets, the price will only be calculated if there has been a prior SWAP app call to the `STABLE/A`

or `STABLE/B`

pool, because in this case `A/B`

already have an implicit price calculated. From here, the formula is similar:

$price_B$ is the price of `B`

calculated from SWAP app call in `STABLE/B`

pool

$total_A$ is a total number of `A`

in pool after SWAP

$total_B$ is a total number of `B`

in pool after SWAP

$decimals_A$is `A`

’s decimals

$decimals_B$is `B`

’s decimals

Note: If there are no `STABLE/A`

or `STABLE/B`

pools, then the price won't be calculated and the value will be set to "-".

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