# Trade Tokens

In Uniswap, there is a separate exchange contract for each ERC20 token. These exchanges hold reserves of both ETH and their associated ERC20. Instead of waiting to be matched in an order-book, users can make trades against the reserves at any time. Reserves are pooled between a decentralized network of liquidity providers who collect fees on every trade.

Pricing is automatic, based on the `x * y = k`

market making formula which automatically adjusts prices based off the relative sizes of the two reserves and the size of the incoming trade. Since all tokens share ETH as a common pair, it is used as an intermediary asset for direct trading between any ERC20 ⇄ ERC20 pair.

## ETH ⇄ ERC20 Calculations

The variables needed to determine price when trading between ETH and ERC20 tokens is:

- ETH reserve size of the ERC20 exchange
- ERC20 reserve size of the ERC20 exchange
- Amount sold (input) or amount bought (output)

### Amount Bought (sell order)

For sell orders (exact input), the amount bought (output) is calculated:

`// Sell ETH for ERC20`

const inputAmount = userInputEthValue

const inputReserve = web3.eth.getBalance(exchangeAddress)

const outputReserve = tokenContract.methods.balanceOf(exchangeAddress).call()

// Sell ERC20 for ETH

const inputAmount = userInputTokenValue

const inputReserve = tokenContract.methods.balanceOf(exchangeAddress).call()

const outputReserve = web3.eth.getBalance(exchangeAddress)

// Output amount bought

const numerator = inputAmount * outputReserve * 997

const denominator = inputReserve * 1000 + inputAmount * 997

const outputAmount = numerator / denominator

### Amount Sold (buy order)

For buy orders (exact output), the cost (input) is calculated:

`// Buy ERC20 with ETH`

const outputAmount = userInputTokenValue

const inputReserve = web3.eth.getBalance(exchangeAddress)

const outputReserve = tokenContract.methods.balanceOf(exchangeAddress).call()

// Buy ETH with ERC20

const outputAmount = userInputEthValue

const inputReserve = tokenContract.methods.balanceOf(exchangeAddress).call()

const outputReserve = web3.eth.getBalance(exchangeAddress)

// Cost

const numerator = outputAmount * inputReserve * 1000

const denominator = (outputReserve - outputAmount) * 997

const inputAmount = numerator / denominator + 1

### Liquidity Provider Fee

There is a 0.3% liquidity provider fee built into the price formula. This can be calculated:

`fee = inputAmount * 0.003`

### Exchange Rate

The exchange rate is simply the output amount divided by the input amount.

`const rate = outputAmount / inputAmount`

## ERC20 ⇄ ERC20 Calculations

The variables needed to determine price when trading between two ERC20 tokens is:

- ETH reserve size of the input ERC20 exchange
- ERC20 reserve size of the input ERC20 exchange
- ETH reserve size of the output ERC20 exchange
- ERC20 reserve size of the output ERC20 exchange
- Amount sold (input) or amount bought (output)

### Amount Bought (sell order)

For sell orders (exact input), the amount bought (output) is calculated:

`// TokenA (ERC20) to ETH conversion`

const inputAmountA = userInputTokenAValue

const inputReserveA = tokenContractA.methods.balanceOf(exchangeAddressA).call()

const outputReserveA = web3.eth.getBalance(exchangeAddressA)

const numeratorA = inputAmountA * outputReserveA * 997

const denominatorA = inputReserveA * 1000 + inputAmountA * 997

const outputAmountA = numeratorA / denominatorA

// ETH to TokenB conversion

const inputAmountB = outputAmountA

const inputReserveB = web3.eth.getBalance(exchangeAddressB)

const outputReserveB = tokenContract.methods.balanceOf(exchangeAddressB).call()

const numeratorB = inputAmountB * outputReserveB * 997

const denominatorB = inputReserveB * 1000 + inputAmountB * 997

const outputAmountB = numeratorB / denominatorB

### Amount Sold (buy order)

For buy orders (exact output), the cost (input) is calculated:

`// Buy TokenB with ETH`

const outputAmountB = userInputTokenBValue

const inputReserveB = web3.eth.getBalance(exchangeAddressB)

const outputReserveB = tokenContractB.methods.balanceOf(exchangeAddressB).call()

// Cost

const numeratorB = outputAmountB * inputReserveB * 1000

const denominatorB = (outputReserveB - outputAmountB) * 997

const inputAmountB = numeratorB / denominatorB + 1

// Buy ETH with TokenA

const outputAmountA = userInputEthValue

const inputReserveA = tokenContractA.methods.balanceOf(exchangeAddressA).call()

const outputReserveA = web3.eth.getBalance(exchangeAddressA)

// Cost

const numeratorA = outputAmountA * inputReserveA * 1000

const denominatorA = (outputReserveA - outputAmountA) * 997

const inputAmountA = numeratorA / denominatorA + 1

### Liquidity Provider Fee

There is a 0.30% liquidity provider fee to swap from TokenA to ETH on the input exchange. There is another 0.3% liquidity provider fee to swap the remaining ETH to TokenB.

`const exchangeAFee = inputAmountA * 0.003`

const exchangeBFee = inputAmountB * 0.003

Since users only inputs Token A, it can be represented to them as:

`const combinedFee = inputAmountA * 0.00591`

### Exchange Rate

The exchange rate is simply the output amount divided by the input amount.

`const rate = outputAmountB / inputAmountA`

## Deadlines

Many Uniswap functions include a transaction `deadline`

that sets a time after which a transaction can no longer be executed. This limits miners holding signed transactions for extended durations and executing them based off market movements. It also reduces uncertainty around transactions that take a long time to execute due to issues with gas price.

Deadlines are calculated by adding the desired amount of time (in seconds) to the latest Ethereum block timestamp.

`web3.eth.getBlock('latest', (error, block) => {`

deadline = block.timestamp + 300 // transaction expires in 300 seconds (5 minutes)

})

## Recipients

Uniswap allows traders to swap tokens and transfer the output to a new `recipient`

address. This allows for a type of payment where the payer sends one token and the payee receives another.

## ETH ⇄ ERC20 Trades

Coming soon...

## ERC20 ⇄ ERC20 Trades

Coming soon...

## Custom Pools

Coming soon...