What Is Impermanent Loss?

Impermanent loss measures the gap between holding tokens and depositing them into an AMM liquidity pool. Learn the formula, worked math, and risks.

Updated October 2026 · Reviewed by the PipeFlare team

Impermanent loss is the difference in value between holding two tokens in your wallet and depositing them into an automated-market-maker pool, which grows when the tokens' relative price moves away from where it was at deposit.

A liquidity position can end up worth less than simply keeping both assets in your own wallet if the trading fees you collect fail to outpace relative price divergence.

About impermanent loss

Impermanent loss is the difference in value between holding two tokens in your wallet and depositing them in an automated-market-maker pool. This divergence grows when the relative price of the two deposited tokens moves away from what it was at the moment of deposit. The shift occurs regardless of whether that price ratio goes up or down. If the price ratio returns to its starting point before you withdraw, the loss shrinks back to zero. If you withdraw while the relative price remains displaced, that unrealized gap becomes permanent. Trading fees earned while serving as a liquidity provider can offset the gap, but they do not eliminate the underlying math.

How it actually works

An automated market maker balances liquidity using mathematical formulas rather than traditional order books. When you supply liquidity to a standard constant-product pool, traders swap against your shared capital by adding one token and removing the other. If the market price of one asset rises outside the pool, arbitrage traders buy that cheaper asset from the pool until the pool's ratio matches external prices. This automatic rebalancing means the pool continuously sells the asset that is gaining value and accumulates more of the asset that is falling in value. You end up with less of the outperforming token and more of the underperforming token compared to holding both in your crypto wallet.

For a standard fifty-fifty constant-product pool, such as a Uniswap v2 style pool, the exact divergence follows a mathematical relationship. Let r equal the new price ratio of the two tokens divided by the initial price ratio at deposit. The impermanent loss formula is 2 * sqrt(r) / (1 + r) - 1. A negative outcome indicates that your pool share is worth less than simply holding those initial tokens. Because this formula is symmetrical, a ratio change of r produces the exact same percentage loss as a ratio change of 1/r. Relative price stability results in zero loss, meaning r = 1 yields 0.00%. At r = 1.25, the loss is -0.62%. At r = 1.5, the loss reaches -2.02%. If the relative price doubles so that r = 2, the loss is -5.72%. Further divergence widens this gap rapidly: r = 3 results in -13.40%, r = 4 results in -20.00%, r = 5 produces -25.46%, and a ten-fold divergence at r = 10 generates a -42.50% loss.

Consider a hypothetical worked example to see the cash value of this divergence. Suppose you deposit 1 ETH and 2,000 USDC when 1 ETH trades for 2,000 USDC, representing a total deposit value of 4,000 USD. If the market price of ETH doubles to 4,000 USDC, an investor who merely held those original assets in a personal wallet would possess 1 ETH worth 4,000 USD and 2,000 USDC, for an overall portfolio value of 6,000 USD. Inside the rebalanced liquidity pool, the position is worth approximately 5,657 USD before accounting for accumulated trading fees. Calculating 6,000 USD multiplied by 0.9428 yields that 5,657 USD value, which corresponds to the exact -5.72% divergence predicted by the constant-product formula.

Concentrated-liquidity architectures introduce additional operational dynamics. Platforms like Uniswap v3 allow liquidity providers to allocate capital within customized price boundaries rather than across a zero-to-infinity range. According to Uniswap documentation, concentrating liquidity allows capital to earn more fees with the same principal because trades execute against a deeper local pool. However, this exact concentration magnifies exposure to price moves when the token ratio shifts within or beyond the selected band. The standard fifty-fifty formula applies strictly to full-range constant-product pools, meaning concentrated positions require a dedicated calculator to track asymmetric shifts. In all automated pools, liquidity providers collect a share of trading fees, yet whether cumulative fees outpace impermanent loss depends on trading volume, fee tier, and total price movement.

Start here

1Evaluate the historical price correlation of the two assets you intend to pair in an automated market maker. Pairs that track identical values, such as two fiat-backed stablecoins, experience minimal relative divergence compared to pairing an unpegged token against a stable asset.
2Calculate the potential divergence percentage across several market movements using the standard 2 * sqrt(r) / (1 + r) - 1 formula before funding a pool on a decentralized exchange.
3Confirm whether the chosen pool operates as a full-range constant-product pool or a concentrated-liquidity setup, consulting a dedicated calculator if the design confines liquidity inside specific price boundaries.
4Track ongoing trading volume, fee tiers, and price changes to verify whether earned swap fees are sufficient to offset your position's divergence from an outright holding strategy.
5Record all pool entry and exit prices alongside realized fee collections, keeping accurate transaction histories for reporting obligations outlined in guides on [DeFi taxes](/tax/defi-taxes).

Strengths

Liquidity providers earn a direct share of trading fees generated by swap volume across the decentralized exchange pool.
The loss remains unrealized and shrinks back toward zero if market prices return to the original deposit ratio prior to withdrawal.
Providing liquidity to stablecoin pairs that consistently move together substantially limits relative price divergence while still collecting fees.

Common misunderstandings

Withdrawing assets while the price ratio is shifted locks in a permanent portfolio deficit compared to simply holding the tokens in self-custody.
Trading fees are not guaranteed to outpace the loss, particularly during periods of violent market divergence or thin swap volume.
Concentrated-liquidity designs magnify price exposure and require active monitoring rather than passive capital deployment.

Common questions

What is impermanent loss in crypto?

Impermanent loss is the difference in value between holding two tokens in your wallet and depositing them into an automated-market-maker pool. It develops whenever the relative price of the two assets shifts away from the ratio present at the moment of deposit. This gap grows whether the ratio moves upward or downward, as arbitrage trading constantly rebalances the pool against prevailing market prices.

How do you calculate impermanent loss?

For a standard fifty-fifty constant-product pool, you calculate the divergence using the formula 2 * sqrt(r) / (1 + r) - 1, where r represents the new price ratio divided by the deposit price ratio. If a token doubles in price relative to its pair, r equals 2, producing an unrealized shortfall of approximately -5.72% compared to holding. The math is symmetrical, meaning a price drop to half the original ratio produces the identical -5.72% loss.

How do you avoid impermanent loss?

You can reduce exposure by providing liquidity for pairs that naturally move together, such as two stablecoins pegged to the same currency. Another alternative is pursuing single-asset lending on protocols covered in What is DeFi, which eliminates paired price divergence entirely. Hedging strategies also exist to offset price swings, though hedging introduces added capital costs and protocol complexity without providing absolute protection.

Is impermanent loss permanent?

The loss is considered impermanent because it shrinks back toward zero if the relative price ratio returns to where it stood at deposit. However, it becomes fully realized the moment you withdraw your liquidity while the price ratio remains displaced. If market prices never return to their starting baseline, your pool position permanently underperforms holding the raw assets in a private wallet.

Do fees make up for impermanent loss?

Trading fees can make up for the divergence, but fee compensation is never guaranteed. Liquidity providers earn a proportional share of trading fees from token swaps, yet whether those earnings exceed the loss depends on sustained trading volume, the pool's chosen fee tier, and the severity of price swings. In high-volatility environments with low volume, the mathematical divergence can easily outstrip all accumulated fee revenue.

Does impermanent loss apply to Uniswap v3?

Yes, impermanent loss applies to Uniswap v3, but the underlying dynamics change due to concentrated liquidity. Uniswap v3 allows users to bound liquidity within specific price intervals, which concentrates capital and enables providers to earn higher fee revenue from active trading. Because capital is focused tightly, relative price movements inside or outside that custom range magnify the rate of divergence, requiring specialized range calculators rather than the basic fifty-fifty formula.

Sources

Uniswap Documentation

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