# Pool Yield

This document describes how pool yield is calculated in the Cauldron user interface.

## Pool Yield

Pool Yield is calculated as follows

\[
\left( \frac{\sqrt{k_{\text{latest}}} - \sqrt{k_{\text{current}}}}{\sqrt{k_{\text{current}}}} \right) \times 100
\]

Where K is the CPMM formula of a Cauldron liquidity pool.

\[
K = \text{satoshis} \times \text{token}
\]

Yield is collected by increasing K with every trade. The constant product is squared in the yield formula to get a more accurate representation of the yield. The CPMM formula (K = x * y) creates a non-linear relationship between the liquidity pool size and the impact of liquidity provision on asset prices and trading.

## APY

Pool APY is calculated as follows:

\[
\left( \left( \frac{\text{pool yield}}{100} + 1 \right)^{\text{years elapsed}} - 1 \right) \times 100
\]

where years elapsed is

\[
\text{years elapsed} = \frac{365.25}{\text{days elapsed}}
\]

and days elapsed is

\[
\text{days elapsed} = \frac{\text{period start} - \text{period end}}{86400}
\]