Impermanent Loss Calculator

AMMs like Uniswap hold two tokens in a pool. Prices are determined by the ratio between them, using the formula x * y = k. When someone trades, they add one token and remove the other, shifting the ratio and changing the price. You deposit equal value of both tokens to provide liquidity. Here's the problem: when prices move, the AMM automatically rebalances. As ETH rises against USDC, the pool sells ETH and buys USDC to stay balanced. As an LP, you end up with less ETH and more USDC than you started with. If you had just held, you'd have more ETH at the higher price. That difference is impermanent loss. The AMM sold your winners and bought your losers, automatically.

Impermanent loss can be calculated precisely using the formula: IL = 2√r/(1+r) - 1, where r is the price ratio (new price/old price). Let's walk through an example. You deposit $1,000 into an ETH/USDC pool when ETH is $2,000: $500 of ETH (0.25 ETH) and $500 of USDC. If ETH doubles to $4,000, the AMM rebalances. Using the constant product formula, you now have approximately 0.177 ETH and $707 USDC. Your LP position is worth ~$1,414 ($707 + $707). If you had just held, you'd have 0.25 ETH ($1,000) + $500 USDC = $1,500. The $86 difference (~5.7% of $1,500) is your impermanent loss. Critically, IL is symmetric: whether ETH goes 2x up or 2x down (0.5x), the IL is the same ~5.7%. At 3x, IL reaches ~13.4%. At 5x, it's ~25.5%. The more prices diverge, the worse IL becomes - though the loss accelerates more slowly at extreme divergences.

IL matters most for volatile asset pairs with significant price divergence potential. An ETH/SHIB pool could see one asset move 10x while the other moves 2x - that relative 5x divergence creates substantial IL. Conversely, IL barely matters for stable pairs. USDC/USDT pools experience minimal IL because both tokens maintain near-1:1 pricing. Correlated asset pools like ETH/stETH or BTC/WBTC also minimize IL since the tokens move together. IL must always be weighed against fee earnings. A high-volume pool generating 20-30% APY in fees can easily overcome 5-10% IL. A low-volume pool generating 2% fees while suffering 10% IL represents a bad investment. The time horizon matters too: IL is 'impermanent' because if prices return to their original ratio, the loss disappears. Long-term LPs in assets expected to maintain their relationship may experience IL temporarily but recover as prices revert. However, if one asset permanently outperforms, IL becomes permanent when you withdraw.

Not all AMMs create equal IL. Standard 50/50 pools (Uniswap V2-style) follow the formula we've discussed, with IL determined purely by price ratio changes. Weighted pools (like Balancer's 80/20 pools) reduce IL because rebalancing pressure is asymmetric - an 80/20 ETH/USDC pool experiences less IL than 50/50 because less rebalancing occurs as prices move. Stablecoin-optimized pools (Curve's StableSwap) use different invariants that assume tokens should trade near parity, minimizing IL for pegged assets but potentially creating larger losses if a token depegs. Concentrated liquidity (Uniswap V3) allows LPs to provide liquidity within specific price ranges. Within the range, capital efficiency improves (more fees per dollar deposited), but IL intensifies. If price moves outside your range, your position becomes 100% the worse-performing asset. V3 requires active management - it's more like market-making than passive LP. Understanding these differences helps match pool type to your assets and strategy.

Successful liquidity provision requires fee earnings to exceed impermanent loss plus opportunity cost. Calculate your expected fee APY from the pool's volume and your share of liquidity. Compare this against expected IL based on price volatility estimates. If a pool generates 15% annual fees and you expect 5% IL, you're theoretically profitable. However, several factors complicate this. Fee income is relatively predictable based on historical volume, but IL depends on future price movements you cannot know. Volume can decrease, reducing fee income while prices diverge. Gas costs for entering, exiting, and claiming rewards reduce net returns. Risk-adjusted, many LPs underperform simply holding - studies suggest the majority of Uniswap V3 positions would be better off holding the underlying assets. This doesn't mean LP is never profitable, but it means casual liquidity provision without careful analysis often disappoints.

Several strategies can reduce IL's impact on your returns. Choose stable or correlated pairs: stablecoin pools, ETH/stETH, BTC/WBTC minimize IL by design. These pools offer lower yields but more predictable returns. Target high-volume pools: more trades mean more fees to offset IL. Volume/TVL ratio indicates fee generation efficiency - higher is better. Avoid low-liquidity pools with minimal trading activity. Time your entries: entering LP positions when you believe prices are temporarily diverged (expecting reversion) can result in negative IL - your position benefits as prices reconverge. Use weighted pools: 80/20 or 95/5 pools dramatically reduce IL exposure while still earning fees, useful when you want to maintain exposure to one asset. Farm incentives: many protocols offer liquidity mining rewards that can substantially exceed IL - but evaluate whether incentive tokens will maintain value. Single-sided liquidity: some protocols allow depositing one asset, with the protocol managing rebalancing. This eliminates IL but typically offers lower yields or has other constraints.

Uniswap V3 and similar protocols introduced concentrated liquidity, allowing LPs to provide liquidity within specific price ranges. Within your range, your capital is more efficient - you earn the same fees as a much larger full-range position. However, this amplifies IL within the range and introduces out-of-range risk. When price moves outside your range, trading stops using your liquidity. Your position becomes 100% the worse-performing asset, and you earn no fees until price returns. This is effectively maximum IL locked in until reversion. Concentrated liquidity positions require active management - adjusting ranges as prices move, compounding earnings, and sometimes completely repositioning. Passive LPs often underperform due to ranges becoming stale. For casual LPs without time for active management, full-range positions (similar to V2) or alternative protocols may be more appropriate despite lower capital efficiency.

Several DeFi protocols attempt to address IL through protection mechanisms. Bancor offered IL protection where LPs were compensated for IL using protocol reserves and the BNT token - though this system struggled during 2022's market stress. Thorchain provides similar protection for qualifying LPs who stake for extended periods. Some protocols use protocol-owned liquidity or bonding curves designed to minimize IL exposure. Insurance options exist through protocols like Nexus Mutual or InsurAce, though IL-specific coverage may be limited or expensive. Evaluate protection mechanisms carefully: many rely on token emissions that may not maintain value, reserves that deplete during widespread IL events, or require extended lock-ups. True IL 'insurance' that reliably compensates LPs for divergence losses without significant tradeoffs remains elusive - the mathematics of AMMs make IL inherent to the design.

Consider real scenarios to appreciate IL in practice. Scenario 1: You LP $10,000 in ETH/USDC when ETH is $2,000. ETH rises to $3,000 (1.5x). IL is approximately 2%. Your LP position is worth about $12,200 instead of $12,500 if you held - $300 IL. If the pool generated $600 in fees during this period, you net +$300 vs holding. Profitable LP. Scenario 2: Same initial position, but ETH drops to $1,000 (0.5x). Same 2% IL, but now on a smaller total. Your LP position is worth about $6,900 vs $7,500 holding - $600 IL in dollar terms because you held more of the declining asset. Scenario 3: You LP $10,000 in a volatile altcoin/ETH pool. The altcoin pumps 4x against ETH. IL reaches ~20% - you've lost $2,000 vs just holding the original mix. Unless fees were exceptional, this was a bad LP decision. These examples illustrate why asset selection and realistic fee expectations matter enormously.

Impermanent loss is the opportunity cost of providing liquidity to an AMM compared to simply holding your assets. When you LP, the AMM automatically rebalances your position as prices change, selling the appreciating asset and buying the depreciating one. You end up with a different mix than you started with, and if prices diverged, your LP position is worth less than if you'd just held. It's called 'impermanent' because the loss reverses if prices return to the original ratio.

For standard 50/50 pools, IL = 2√r/(1+r) - 1, where r is the price ratio (new/old). At 1.25x price change (25% up or down), IL is ~0.6%. At 2x, IL is ~5.7%. At 3x, IL is ~13.4%. At 5x, IL is ~25.5%. The loss is symmetric - whether an asset doubles or halves relative to the other, IL is the same percentage.

Not necessarily. IL measures the difference between your LP position value and what you'd have if you held. You still have value - just less than optimal holding. More importantly, you earn trading fees as an LP. If fees exceed IL, you profit overall. Many profitable LPs generate returns above simple holding despite IL, particularly in high-volume pools or with liquidity mining incentives.

Stablecoin pairs (USDC/USDT, DAI/USDC) have minimal IL because both tokens maintain near-constant prices. Correlated asset pools (ETH/stETH, BTC/WBTC, ETH/rETH) also minimize IL since the tokens move together. Weighted pools like Balancer's 80/20 reduce IL compared to 50/50 pools. Curve's StableSwap pools are optimized for pegged assets with minimal IL.

Only if you withdraw when prices have diverged from entry or if the divergence becomes permanent. If you LP when ETH is $2,000 and it rises to $4,000 creating 5.7% IL, that loss disappears if ETH returns to $2,000 before you withdraw. However, if you withdraw at $4,000, or ETH never returns to $2,000, the loss is locked in permanently.

LPs earn a portion of trading fees (typically 0.3% per trade split among LPs). High-volume pools generate substantial fees - some pools generate 20-50%+ APY in fees during active periods. If a pool generates 25% annual fees and IL is 5%, you net +20% vs holding. The key is selecting pools where fee generation realistically exceeds expected IL based on volatility.

Concentrated liquidity in V3 amplifies both fee earnings and IL within your selected range. For the same price movement within range, V3 positions experience more IL than equivalent V2 positions. Additionally, V3 positions become 100% the worse asset if price moves outside the range. V3 offers higher capital efficiency but requires active management and carries higher IL risk.

Not necessarily - LP can be profitable with the right strategy. Choose stable or correlated pairs to minimize IL, target high-volume pools for fee generation, or leverage liquidity mining rewards. However, casual LP without careful analysis often underperforms holding. Studies suggest many Uniswap V3 LPs would be better off holding. Understand IL thoroughly before committing significant capital.

Technically yes, if you enter when prices are diverged and they converge back to your entry ratio, you benefit from rebalancing. In practice, timing such entries is difficult. Some structured products attempt this by entering LP positions after significant price moves expecting mean reversion, but predicting price movements remains challenging.

Several tools help track IL: DeFiLlama, APY.vision, Revert Finance, and Zerion show LP position performance including IL calculations. Compare your LP value to a hypothetical 'held instead' portfolio at current prices. Track fee earnings separately to determine net performance vs holding. Regular monitoring helps identify when IL exceeds fee benefits.