The constant product formula is the pricing model used by many automated market makers in DeFi, especially platforms like Uniswap. It keeps trading smooth by ensuring that the product of the two token reserves in a liquidity pool always stays the same. The formula is written as **x × y = k**, where x and y are the quantities of the two tokens in the pool, and k is a constant that cannot change during trades.

When someone swaps one token for another, the pool adjusts the reserves so the equation still holds. If a trader adds token X to the pool, the value of x increases, so the pool must reduce the amount of token Y to maintain the constant product. This is what causes the price to move automatically. As traders buy more of one token, it becomes more expensive because the pool has less of it left.

This mechanism allows trading without an order book, matching engine or counterparty. It also encourages arbitrage traders to step in and correct price differences between the pool and the broader market, which helps keep prices aligned.

The constant product formula is simple but powerful. It ensures liquidity at all times, no matter how large or small the trade is. It also sets the foundation for many modern AMM designs, helping create open and decentralised markets where anyone can trade or provide liquidity.