> For the complete documentation index, see [llms.txt](https://docs.houstonswap.io/houstonswap/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.houstonswap.io/houstonswap/advanced-topics/formula.md).

# Formula

### Dynamic Fee

<figure><img src="/files/YgCEIU0uRQuRRhCh8DyC" alt=""><figcaption><p>Step Function of Sigmoids</p></figcaption></figure>

<figure><img src="/files/5jJ5PP7brpW5ehckPlVG" alt=""><figcaption><p>Major Formula</p></figcaption></figure>

Where:<br>

<figure><img src="/files/a26MAMwBWTbVEREzsaux" alt=""><figcaption></figcaption></figure>

<figure><img src="/files/a6q1rJJFgkjONUY79VHm" alt=""><figcaption></figcaption></figure>

<figure><img src="/files/XLXZcAU58t5GLrPNO5H0" alt=""><figcaption></figcaption></figure>

The sum of 3 components has similar effect as Triple Tier Fee model.

![](/files/gSTFyLELHa3SAT16hnRi): adjust the max. cap for each absolute fee tier

![](/files/jNw194Ojrc9jKiSDi8z6): shift the fee tier adjustment threshold - the larger beta , the greater the volatility allowed for fee tier change

![](/files/YbEt2c6lKI0UQJXRfibK): adjust the slope of fee changes when it comes across 2 absolute fee tier

Note:

* ![](/files/glXOrX9gRPX2n3yWehbt)is capped by 1
* `Gammas must be > 0`