# A Mathematical Breakdown of How Automated Market Makers Price Assets

Page: https://stenobird.com/podcast/web3-tech-brief-by-hackernoon-6365654/a-mathematical-breakdown-of-how-automated-market-makers-price-assets
Text version: https://stenobird.com/podcast/web3-tech-brief-by-hackernoon-6365654/a-mathematical-breakdown-of-how-automated-market-makers-price-assets.md
Podcast: [Web3 Tech Brief By HackerNoon](https://stenobird.com/podcast/web3-tech-brief-by-hackernoon-6365654)
Published: 2026-05-22T16:00:54+00:00
Episode link: https://share.transistor.fm/s/fc3b96c7
Audio file: https://media.transistor.fm/fc3b96c7/c0f8e129.mp3
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JSON: https://stenobird.com/v1/public/podcasts/web3-tech-brief-by-hackernoon-6365654/episodes/a-mathematical-breakdown-of-how-automated-market-makers-price-assets
Duration seconds: 635

## Resource

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.

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## Transcript

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