> For the complete documentation index, see [llms.txt](https://hummus-exchange.gitbook.io/hummus-exchange/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://hummus-exchange.gitbook.io/hummus-exchange/concepts/swap-slippage.md).

# Swap Slippage

The swap slippage is given by:

$$
S\_{i \rightarrow j} = S\_i + (-S\_j) = S\_i - S\_j
$$

and

$$
S\_i = \dfrac{g(r'\_i) - g(r\_i)}{r'\_i - r\_i}
$$

$$
r'\_i   +    r\_i
$$

where <img src="broken://files/Igz2KkE32RN1iOnxw8i4" alt="" data-size="line"> is the original coverage and<img src="broken://files/eWaJWBxt5MQaFRlRuZW3" alt="" data-size="line">  is the final coverage.

If the swap amount is small, the slippage can be give by

$$
S\_{i \rightarrow j} = g'(r\_i) - g'(r'\_i)
$$

###

### Practical example of slippage calculation

We take the coverage ratio of USDT at 0.909 and ETH at 1.033. Working this out, we’d get:

#### USDT:

$$
g'(0.909) = -\dfrac{0.00002\*7}{0.909^8} = 0.03%
$$

#### ETH:

$$
g'(1.033) = -\dfrac{0.00002\*7}{1.033^8} = 0.01%
$$

Hence we have

$$
S\_{USDT \rightarrow ETH} = 0.03% - 0.01% = 0.02%
$$

This represents the marginal slippage when someone is performing a small amount of swap at this coverage ratio. And yes, the slippage is positive and user can benefit from the swap!