Impermanent Loss Calculator
Calculate the impermanent loss from providing liquidity in an AMM pool compared to simply holding the tokens.
Formula
The ratio of the current price to the initial price for each token in the pair.
Where r is the price ratio. IL is always negative or zero — it represents the percentage loss compared to holding.
The pool value is always less than or equal to the hold value due to IL. Fees earned may offset this loss.
Examples
- Initial: Token A = $3,200, Token B = $1.00 (stablecoin)
- Current: Token A = $6,400, Token B = $1.00
- Price ratio r = $6,400 / $3,200 = 2.0
- IL = 2√2 / (1 + 2) − 1 = 2(1.414) / 3 − 1 = −5.72%
- On a $10,000 deposit: Hold = $15,000, Pool ≈ $14,142
- Initial: Token A = $100, Token B = $1.00
- Current: Token A = $50, Token B = $1.00
- Price ratio r = $50 / $100 = 0.5
- IL = 2√0.5 / (1 + 0.5) − 1 = 2(0.707) / 1.5 − 1 = −5.72%
- On a $10,000 deposit: Hold = $7,500, Pool ≈ $7,071
- Initial: Token A = $10, Token B = $1.00
- Current: Token A = $50, Token B = $1.00
- Price ratio r = $50 / $10 = 5.0
- IL = 2√5 / (1 + 5) − 1 = 2(2.236) / 6 − 1 = −25.46%
- On a $10,000 deposit: Hold = $30,000, Pool ≈ $22,361
Key Concepts
What Is Impermanent Loss?
Impermanent loss occurs when the price ratio of tokens in a liquidity pool changes from when you deposited. The AMM rebalances your holdings, leaving you with fewer of the appreciating token and more of the depreciating one — resulting in less value than simply holding.
Why "Impermanent"?
The loss is called impermanent because it only becomes permanent when you withdraw. If token prices return to their original ratio, the loss disappears. However, if you withdraw while prices are diverged, the loss is realized and permanent.
IL Is Symmetrical
A 2x price increase and a 50% price decrease produce the same IL (−5.72%). What matters is the magnitude of price divergence, not the direction. The further prices diverge from the initial ratio, the greater the IL.
Fees Can Offset IL
Liquidity providers earn trading fees (typically 0.3% per swap on Uniswap V2). In high-volume pools, fee income can exceed impermanent loss, making LP profitable despite IL. This is why IL is sometimes tolerable.
Concentrated Liquidity & IL
Uniswap V3 concentrated liquidity amplifies both fees earned and IL. A tighter price range earns more fees per dollar but suffers higher IL if price moves outside the range. The position also stops earning fees entirely once out of range.
Stablecoin Pairs & IL
Stablecoin-stablecoin pools (USDC/USDT) have minimal IL because both tokens maintain a ~$1 peg. The price ratio stays near 1.0, keeping IL negligible. This makes stable pools popular for risk-averse LPs seeking yield.
How to Calculate Impermanent Loss
Impermanent loss is the cost of providing liquidity to an AMM compared to holding the same tokens in your wallet. It arises because the AMM's constant product formula (x × y = k) automatically rebalances your position as prices change, always selling the appreciating token and accumulating the depreciating one.
The formula IL = 2√r / (1 + r) − 1 gives you the percentage loss, where r is the price ratio between current and initial prices. At r = 1 (no price change), IL = 0. As r diverges from 1 in either direction, IL increases. At r = 4 (2x price), IL is about −5.7%. At r = 25 (5x price), IL jumps to −25.5%.
To decide whether providing liquidity is worthwhile, compare the expected IL against the fees and incentive rewards you'll earn. Many DeFi protocols offer liquidity mining rewards specifically to compensate LPs for impermanent loss risk.
Frequently Asked Questions
Can impermanent loss exceed 100%?
No. As one token's price approaches zero relative to the other, IL approaches 100% but never exceeds it. At that point, your pool position consists almost entirely of the worthless token — essentially a total loss.
Does this calculator account for trading fees?
No. This calculator shows the raw impermanent loss from price divergence. Actual LP returns = fees earned − impermanent loss ± token incentives. You need to estimate fee APR separately to determine if LP is profitable.
Is IL different for Uniswap V3 vs V2?
Yes. Uniswap V3 concentrated liquidity ranges amplify IL proportionally to the concentration factor. A position concentrated in a ±10% range experiences roughly 10x the IL of a full-range V2 position for the same price move.
How do I minimize impermanent loss?
Choose pools with correlated assets (ETH/stETH, USDC/USDT), use wider price ranges in V3, or provide liquidity in pools with high volume-to-TVL ratios where fees outpace IL. Hedging with perpetual futures is another advanced strategy.