A Mathematical Breakdown of How Automated Market Makers Price Assets

This story was originally published on HackerNoon at: https://hackernoon.com/a-mathematical-breakdown-of-how-automated-market-makers-price-assets. Learn how AMMs price tokens using x·y=k, how fees accrue, and why impermanent loss hurts LPs. From Uniswap V2 to V3, the math explained clearly. Check more stories related to web3 at: https://hackernoon.com/c/web3. You can also check exclusive content about #defi, #automated-market-makers, #amm-math, #uniswap-v2, #concentrated-liquidity, #liquidity-pools, #curve-finance, #crypto-liquidity, and more. This story was written by: @durdana-yembergenova. Learn more about this writer by checking @durdana-yembergenova's about page, and for more stories, please visit hackernoon.com. AMMs use the formula x·y=k to price tokens without an order book. Swaps move reserves along a hyperbola, causing price impact on large trades. A 0.30% fee grows k over time, rewarding liquidity providers. LPs face impermanent loss — always worse than holding when price moves, calculated as IL(r) = 2√r/(1+r) − 1. Uniswap V3 improves capital efficiency via concentrated liquidity ranges, while Curve and Balancer extend the model to stablecoins and multi-asset pools.