LP Math — AMM Liquidity Provision Mathematics

Automated Market Makers (AMMs) replace traditional orderbooks with liquidity pools. Instead of matching buyers and sellers, a mathematical formula determines prices based on reserve ratios. Liquidity providers (LPs) deposit both assets into a pool and earn fees from every trade.

Understanding the math behind AMMs is essential for:

• Evaluating whether providing liquidity is profitable after impermanent loss
• Estimating price impact before executing large trades
• Comparing capital efficiency across pool types (constant product vs concentrated)
• Calculating expected fee revenue for a given pool position

Related skills: See impermanent-loss for IL calculations, yield-analysis for LP yield modeling, liquidity-analysis for pool depth assessment.

1. Constant Product AMM (xy = k)

The foundational AMM model used by Raydium V4 and most Solana DEXes.

Core Invariant