AMM math — the x × y = k formula

A Uniswap V2 pool holds reserves of two tokens: x (e.g., ETH) and y (e.g., USDC). Its invariant:

x × y = k

Where k is constant across trades (it only grows from fees). When someone swaps dx of X for dy of Y:

(x + dx) × (y − dy) = k = x × y
solve for dy:
dy = y × dx / (x + dx)

Pool: 100 ETH, 300,000 USDC (price = 3000 USDC/ETH). You swap 1 ETH for USDC.

dy = 300,000 × 1 / (100 + 1) ≈ 2970.30 USDC
effective price = 2970.30 USDC/ETH (worse than 3000 — slippage)
new pool = 101 ETH, 297,029.70 USDC
new mid price = 297,029.70 / 101 ≈ 2941.88 USDC/ETH

One trade:

• You got less than mid price (slippage)
• It moved the pool price from 3000 to ~2942 (price impact)

Compute the dy for a given pool + swap using the formula.