What Is the Significance of the Constant Product Formula ($x Y=k$)?

The constant product formula, $x y=k$, is the core algorithm used by many AMMs like Uniswap. It dictates that the product of the quantities of the two assets in the pool ($x$ and $y$) must remain constant ($k$).

This formula ensures that there is always liquidity available for a trade, no matter how large. It automatically determines the new price ratio after a swap, creating a smooth, continuous price curve.