What impermanent loss is, and how to calculate it

Impermanent loss is the difference between what a liquidity provider’s deposited assets are worth if withdrawn from a pool, and what those same assets would be worth if the provider had simply held them in a wallet. It is calculated with the formula IL = 2×√d/(1+d) − 1, where d is the ratio between the token’s price at withdrawal and its price at deposit, according to Coinbase Learn’s glossary entry, BydFi’s guide (published 13 April 2026) and Speedrun Ethereum’s guide, all of which state the identical formula. Chainlink’s education page (last updated 6 April 2026) does not write out this closed-form equation, but demonstrates the same result through the constant-product formula and a worked numerical example, described below. Why it happens Most standard decentralized exchanges use a constant-product formula, written as x × y = k, where x and y are the quantities of the two pooled tokens and k is fixed after every trade, per Chainlink and Speedrun Ethereum. The pool itself does not know the external market price. When that outside price moves, the pool’s internal price only catches up because arbitrage traders step in: if ETH becomes more expensive on the open market than inside the pool, traders buy ETH from the pool until its internal price matches the outside one, per Chainlink. That buying removes ETH from the pool and adds the other token, so the liquidity provider ends up holding less of the asset that rose in price and more of the one that fell, per Chainlink and Speedrun Ethereum. The arbitrageur pockets the difference; the liquidity provider absorbs it as impermanent loss. A worked example Chainlink’s education article walks through a full example, dated 6 April 2026. A provider deposits 1 ETH and 1,000 USDC into a pool where 1 ETH is worth 1,000 USDC, for a total deposit value of 2,000 USDC. The pool already holds 10 ETH and 10,000 USDC, so the provider owns a 10 percent share, and the constant product k is 100,000 (10 × 10,000), per Chainlink. Suppose ETH’s external price doubles to 2,000 USDC. Arbitrageurs buy ETH from the pool until its internal price also reads 2,000 USDC. After that rebalancing the pool holds roughly 7.071 ETH and 14,142 USDC — the product is still 100,000 — per Chainlink. The provider’s 10 percent share is now 0.7071 ETH and 1,414.2 USDC, worth 2,828.4 USDC combined. Had the provider simply held the original 1 ETH and 1,000 USDC, the ETH alone would be worth 2,000 USDC, for a total holding value of 3,000 USDC. The shortfall is 171.6 USDC, or 5.7 percent of the holding value — the impermanent loss, per Chainlink.