Formula & Calculator
Impermanent Loss (Liquidity Pool)
Estimates the loss a liquidity provider experiences compared to simply holding tokens, caused by price divergence between pooled assets.
Interpretation
IL (%) = (2√(price_ratio)/(1+price_ratio) − 1) × 100. The loss experienced by a liquidity provider when the price ratio of two assets changes. Used to assess AMM LP risks.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| IL | Impermanent loss | % |
| price_ratio | Ratio of new price to original price of one token relative to the other |
What it means
Impermanent loss occurs when the relative price of assets in a liquidity pool changes compared to when they were deposited. The formula shows that the loss is a function of the price ratio change. If the ratio returns to the original, the loss disappears (hence "impermanent"). This is a key risk for liquidity providers in automated market makers (AMMs). Understanding this helps LPs assess whether fee income compensates for potential losses. It is essential for making informed decisions about providing liquidity. The formula is derived from the constant product market maker model (x*y=k).
Worked example
Impermanent Loss – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Price Ratio (new/old) | 1.25 |
| Parameter | Value |
|---|---|
| Price Ratio | 2.0 |
Common mistakes
- Price ratio: The ratio of the two token prices after the price change – must be >0.
- IL formula: Assumes a constant product AMM (Uniswap v2 style).
- Sign: IL is always negative (a loss relative to simply holding).
- Fees offset: This formula ignores trading fees earned; net IL may be reduced.
Applications
Impermanent loss (IL) in a liquidity pool measures the temporary loss experienced by liquidity providers when the price ratio between pooled assets changes. The formula calculates IL as a percentage based on the price change. Liquidity providers use this to assess the risk of providing liquidity on decentralised exchanges (DEXs) and to compare it with simply holding the assets. IL is a critical concept in automated market maker (AMM) protocols like Uniswap and PancakeSwap. By quantifying the potential loss, providers can decide whether the trading fees and potential rewards compensate for the IL risk. Understanding IL helps in optimising pool selection and in managing liquidity provision strategies.
- Risk assessment for liquidity providers in AMM pools
- Comparing IL vs. earned fees to evaluate profitability
- Optimising pool selection based on volatility and price trends
- Hedging strategies to mitigate IL exposure
- Education for DeFi liquidity providers
Frequently Asked Questions
Impermanent loss is the temporary loss of value compared to simply holding the assets. It occurs when the price ratio of the two assets in the pool changes from when you deposited. The larger the price divergence, the greater the loss.
Use the formula: IL (%) = (2 * sqrt(price_ratio) / (1 + price_ratio) - 1) * 100. For a 2x price change (price_ratio = 2), the loss is about 5.7%. This is a common reference point.
It becomes permanent only if you withdraw your liquidity when the price ratio is still diverged. If the prices return to their original ratio, the loss disappears. Hence the term "impermanent".
Sometimes yes, if the pool generates enough fees to compensate for the loss. That is why you need to calculate your net return: fees earned minus impermanent loss.
Higher volatility increases the likelihood and magnitude of price divergence, thus increasing potential impermanent loss. Stablecoin pairs have very low impermanent loss because prices barely move.
No, it is not a fee you pay. It is an opportunity cost—the difference between what you would have had by holding versus providing liquidity. It only materializes if you withdraw.
Yes, even more so. Concentrated liquidity amplifies both fee income and impermanent loss because you are exposed to a narrower price range.
As one token price goes to zero or infinity relative to the other, the loss approaches 100% (you would lose almost all value). In practice, this is rare for established tokens.