What Is AMM Curve?
An AMM curve is the mathematical formula that an automated market maker uses to determine token prices based on the quantities of assets in a liquidity pool. The most common is the constant product formula (x * y = k) used by Uniswap V2: as one token is bought (reducing its quantity in the pool), its price increases along a hyperbolic curve, ensuring that the pool is never fully depleted.
How AMM Curve Works
Different curves serve different purposes. Constant product (x * y = k) works for volatile pairs but causes significant price impact for large trades. Stableswap curves (Curve Finance) are flatter around the 1:1 ratio, enabling large stablecoin swaps with minimal slippage. Concentrated liquidity (Uniswap V3) allows custom curves by letting LPs choose price ranges. Each design trades off between capital efficiency and the range of prices it can support.
Why It Matters for Traders
Understanding AMM curves helps traders minimize execution costs. For large swaps of volatile pairs, the constant product curve creates significant price impact that grows quadratically with order size. Splitting orders across multiple pools or DEXs reduces total impact. For stablecoin swaps, using a stableswap-optimized AMM dramatically reduces costs versus a constant product AMM. DEX aggregators (1inch, ParaSwap) automatically route through the optimal curves for each trade.