Blog / Historical Archive

History of AMMs: Uniswap v1 to v4

x*y=k to hooks.

Uniswap v1

Hayden Adams launched Uniswap v1 on November 2, 2018, inspired by a Vitalik Buterin post. Each pool paired a token with ETH and used the constant product rule x × y = k, so swapping changes reserves along a hyperbola.

Curve's StableSwap

Curve launched in January 2020 with an invariant mixing constant sum and constant product, controlled by an amplification coefficient A. That allows very low slippage between pegged assets such as USDC and DAI.

Uniswap v2

Released May 2020, v2 enabled any ERC-20 pair, flash swaps and time-weighted average price oracles. Its 0.30 percent fee and simple LP tokens were copied by SushiSwap, PancakeSwap and hundreds of forks.

Uniswap v3 concentrated liquidity

v3 launched May 5, 2021. LPs provide liquidity within price ranges defined by ticks of 1.0001^i, making capital up to 4,000 times more efficient within a narrow range, but positions stop earning fees outside it and have amplified impermanent loss.

Uniswap v4 hooks

v4 went live in January 2025 with a singleton contract, flash accounting and hooks that let pools run custom logic, such as dynamic fees or on-chain limit orders.

By the numbers

For History of AMMs, the reference figures are v1 of Nov 2018, v2 of May 2020, v3 of May 2021, v4 of Jan 2025. The comparison table below lines up version, launch, key feature — v1: Nov 2018 / ETH pairs, x·y=k; v2: May 2020 / ERC-20 pairs, TWAP; v3: May 2021 / Concentrated liquidity; v4: Jan 2025 / Hooks, singleton.

Modeling History of AMMs with the AMM Impermanent Loss Calculator

The AMM Impermanent Loss Calculator takes three inputs — Price ratio change (x), Deposit ($), Fee APR (%). IL = 2√r ÷ (1 + r) − 1. With its default inputs (Price ratio change (x) = 2; Deposit ($) = 10000; Fee APR (%) = 20) it returns -5.72 %; swap in the figures from History of AMMs above to reproduce the scenario yourself.

Modeling History of AMMs with the Concentrated Liquidity CLMM Range Calculator

The Concentrated Liquidity CLMM Range Calculator takes three inputs — Lower price ($), Upper price ($), Current ($). Capital efficiency ≈ 1 ÷ (1 − (Pa/Pb)^¼). With its default inputs (Lower price ($) = 2500; Upper price ($) = 3500; Current ($) = 3000) it returns 12.4 x; swap in the figures from History of AMMs above to reproduce the scenario yourself.

Data Table

For educational and informational purposes only. Not financial, investment, tax or legal advice. Figures are approximate and historical; crypto assets are volatile and you may lose capital. Do your own research.