Impermanent Loss Calculator
Use our free Impermanent loss Calculator to plan your crypto trading strategy. Get detailed breakdowns, charts, and actionable insights.
Impermanent Loss Calculator
Calculator
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Formula: IL = 2 × √(price_ratio) / (1 + price_ratio) - 1
Worked example — IL: 2.0204% | Hold Value: $12,500 | LP Value: $12,247.45 | Loss: $252.55
Formula
IL = 2 × √(price_ratio) / (1 + price_ratio) - 1
Impermanent loss is calculated using the price ratio between the current and initial price of the volatile token in a 50/50 liquidity pool. This calculator assumes one asset is a stablecoin (e.g., USDC) whose price does not change, and Token A is the volatile asset. The formula compares the value of assets in the pool (LP value) to the value if you had simply held the assets (hold value). The result is always negative or zero, representing the percentage loss from providing liquidity.
Worked Examples
Example 1: ETH Price Increase in ETH/USDC Pool
Problem:You provide $10,000 to an ETH/USDC pool when ETH is $3,000. ETH rises to $4,500. What is your impermanent loss?
Solution:Price ratio = $4,500 / $3,000 = 1.5 IL = 2 × sqrt(1.5) / (1 + 1.5) - 1 = 2 × 1.224745 / 2.5 - 1 = -2.0204% Hold Value = $10,000 × (1 + 1.5) / 2 = $12,500 LP Value = $12,500 × (1 - 0.020204) = $12,247.45 Dollar Difference = -$252.55
Result:IL: 2.0204% | Hold Value: $12,500 | LP Value: $12,247.45 | Loss: $252.55
Example 2: Token Price Drop by 50%
Problem:You provide $20,000 to a TOKEN/USDC pool. Token A drops from $100 to $50. Calculate the impermanent loss.
Solution:Price ratio = $50 / $100 = 0.5 IL = 2 × sqrt(0.5) / (1 + 0.5) - 1 = 2 × 0.7071 / 1.5 - 1 = -5.72% Hold Value = $20,000 × (1 + 0.5) / 2 = $15,000 LP Value = $15,000 × (1 - 0.0572) = $14,142 Dollar Difference = -$858
Result:IL: ~5.72% | Hold Value: $15,000 | LP Value: ~$14,142 | Loss: ~$858
Frequently Asked Questions
What is impermanent loss in DeFi?
Impermanent loss (IL) is the difference in value between holding tokens in a liquidity pool versus simply holding them in your wallet. It occurs because automated market makers (AMMs) like Uniswap constantly rebalance the ratio of tokens in the pool as prices change. When one token's price increases relative to the other, the AMM sells the appreciating token and buys the depreciating one, resulting in fewer of the winning token than if you had just held. The loss is called 'impermanent' because it only becomes permanent if you withdraw your liquidity. If the token prices return to their original ratio, the impermanent loss disappears.
How is impermanent loss calculated?
Impermanent loss is calculated using the formula: IL = 2 × sqrt(price_ratio) / (1 + price_ratio) - 1, where price_ratio is the current price divided by the initial price of the volatile token. For a 50/50 liquidity pool, if one token doubles in price (2x), the IL is approximately 5.7%. If it triples (3x), IL is about 13.4%. If it goes to 5x, IL reaches 25.5%. The formula applies regardless of which direction the price moves — a 50% price decrease also results in 5.7% IL. This means any deviation from the initial price ratio results in some degree of impermanent loss, with larger deviations causing exponentially greater losses.
Can trading fees offset impermanent loss?
Yes, trading fees earned from the liquidity pool can offset impermanent loss, and this is the primary reason liquidity providers participate despite IL risk. Every time someone trades through the pool, a fee (typically 0.3% on Uniswap V2) is distributed proportionally to all liquidity providers. High-volume pools with many trades generate substantial fee income that can exceed the impermanent loss. For example, a pool earning 50% APY in fees but experiencing 5% IL would still net 45% returns. However, in low-volume pools or during extreme price movements, fees may not be sufficient to cover IL. Always evaluate the expected fee income against potential impermanent loss before providing liquidity.
How can I minimize impermanent loss?
Several strategies can help minimize impermanent loss. First, provide liquidity to stablecoin pairs (like USDC/USDT) where price deviations are minimal. Second, use concentrated liquidity positions on Uniswap V3 with tight price ranges that earn more fees. Third, choose correlated pairs like stETH/ETH where both assets move similarly. Fourth, use protocols with IL protection like Bancor which reimburse IL over time. Fifth, select high-volume pools where fee income compensates for IL. Sixth, consider single-sided staking protocols that eliminate IL entirely. Finally, actively manage your positions — adding liquidity when prices are stable and removing when significant price movements occur.
Is impermanent loss always negative?
Yes, impermanent loss is always a cost compared to simply holding the assets. The formula always yields a negative result (or zero if prices remain unchanged), meaning you always have fewer assets in dollar terms as a liquidity provider compared to holding. However, the total return from liquidity provision includes both IL and earned fees. When trading fees exceed the impermanent loss, your total return is positive and can exceed simple holding. This is why it is essential to consider IL as one component of the total return equation, not the only factor. Many profitable liquidity providers accept IL as a cost of doing business, similar to how insurance companies accept claims as a cost of collecting premiums.
How does the constant product formula x × y = k produce impermanent loss?
A constant product market maker holds reserves x and y such that x times y equals a fixed constant k, with the pool price equal to y divided by x. Arbitrageurs trade against the pool to keep that price matched to the outside market, so at any price P the pool ends up holding the square root of k over P of the volatile token. Its total value is then twice the square root of k times P, and dividing that by the value of an untouched 50/50 holding reduces exactly to the formula above.
Does impermanent loss depend on the path the price took or only on where it ended?
Only on the endpoints. The formula consumes a single ratio of current price to entry price, so a token that ran to 3x and fell back to 1.5x shows exactly the same impermanent loss as one that drifted straight to 1.5x. If price returns to where you started, the ratio is 1 and the loss is zero, which is what impermanent refers to. Fee income is the opposite: it is entirely path dependent, because a volatile round trip generates far more trading volume to earn from.
What happens to a Uniswap V3 position when price moves outside my chosen range?
A V3 position is defined between a lower and an upper tick. While price sits inside that band your capital behaves like a 50/50 pool but concentrated, so both fee income and divergence loss are amplified relative to a full-range position. Once price trades above the upper bound the position has been fully sold into the stable asset; below the lower bound it is entirely in the volatile one. In either case it stops earning fees until price returns, which is why tight ranges demand active rebalancing.
How does the calculation change for a pool of two volatile tokens rather than a stablecoin pair?
The formula needs only one ratio, so Impermanent Loss Calculator treats Token A as the volatile leg and assumes the other side is a stablecoin pinned near a dollar. For a pool of two volatile assets the same mathematics holds, but r becomes their relative price change rather than one token's dollar move. If ETH and BTC both double, their ratio is unchanged, r equals 1 and impermanent loss is zero even though both legs gained. Correlation between the pair, not absolute volatility, drives the loss.
How do weighted pools such as an 80/20 Balancer pool change impermanent loss?
Weighted pools spread the loss unevenly because pool value is the product of each reserve raised to its own weight rather than a plain 50/50 split. With 80 percent of the pool in the volatile asset, a doubling in that token produces roughly 3.3 percent impermanent loss instead of the 5.7 percent a 50/50 pool suffers. The trade-off is directional exposure: an 80/20 position behaves much more like simply holding the volatile token, capturing more upside and more of the drawdown.
References
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer · Editorial policy
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