How AMMs Work

AMM (Automated Market Maker) is the engine that powers DEXes like Uniswap. Understanding AMMs is crucial for advanced DeFi usage.

The Constant Product Formula

Most AMMs use a simple formula:

x × y = k

Where:

• x = quantity of Token A in pool
• y = quantity of Token B in pool
• k = constant that never changes

How Trading Works

When you swap, you add tokens to one side and remove from the other - but k must stay constant.

Example:

Pool has 1000 ETH × 1,000,000 USDC = 1,000,000,000 (k)

You want to buy ETH with 10,000 USDC:

• USDC in pool: 1,000,000 + 10,000 = 1,010,000
• Solve for new ETH: 1,000,000,000 ÷ 1,010,000 = 990.1
• ETH you receive: 1000 - 990.1 = 9.9 ETH

Price Impact & Slippage

Larger trades move the price more. This is slippage:

• Small trades: minimal slippage
• Large trades: significant slippage

This is why liquidity matters - more liquidity = less slippage for traders.

Impermanent Loss Preview

The math that makes AMMs work also causes impermanent loss for liquidity providers. We'll cover this in depth next.

⚙️ Understanding x×y=k is the key to understanding all of DeFi.