# Flashloan fee of Uniswap v2

###### tags: `uniswap` `flashloan` `fee` `uniswap-v2`

Refer to [Uniswap v2 Whitepaper](https://uniswap.org/whitepaper.pdf), each swap should satisfy following formula:

$$
(x_1 - 0.003 \cdot x_{in}) \cdot (y_1 - 0.003 \cdot y_{in}) \ge x_0 \cdot y_0 \tag{1}
$$

To simplify the calculation on-chain:

$$
(1000 \cdot x_1 - 3 \cdot x_{in}) \cdot (1000 \cdot y_1 - 3 \cdot y_{in}) \ge 1000000 \cdot x_0 \cdot y_0 \tag{2}
$$

When we flash loan from Uniswap v2 pair, what is the amount including fee we should repay?

Suppose we flash loan amount of token $y$: $y_{out}$.

$x_{in}$ and $y_{in}$ are the amount of token $x$ and token $y$ to repay.

$x_0$ and $x_1$ are the balance of token $x$ before and after flash loan, respectively, $y_0$ and $y_1$ are the balance of token $y$ before and after flash loan.

The problem is to calculate $y_{in}$ using $y_{out}$.

Since we don't flash loan token $x$, so $x_{in} = 0$, $x_{out} = 0$, $x_0 = x_1$, we can simplify formula (2):

$$
1000 \cdot y_1 - 3 \cdot y_{in} \ge 1000 \cdot y_0 \tag{3}
$$

$$
y_1 - y_0 \ge \frac{3}{1000} \cdot y_{in} \tag{4}
$$

The relation between $y_{in}$ and $y_{out}$ is:

$$
y_{in} = y_1 - ( y_0 - y_{out}) \tag{5}
$$

Using formula (4) and (5):

$$
y_{in} - y_{out} \ge \frac{3}{1000} \cdot y_{in} \tag{6}
$$

We can calculate $y_{in}$:

$$
y_{in} \ge \frac{1000}{997} \cdot y_{out} \tag{7}
$$

In Solidity contract, to avoid rouding down error, we should add 1 to round up:

uint256 repayAmount = amountOut.mul(1000).div(997).add(1)

where repayAmount is $y_{in}$, amountOut is $y_{out}$.

So the flashloan fee of Uniswap v2 is:

$$
\frac{1000}{997} - 1 \approx 0.0030090271 \approx 0.30090271\% \tag{8}
$$