Definition:
Impermanent loss (IL), also called divergence loss, is the difference between the value of the assets an LP withdraws from a pool and what those same starting assets would be worth if simply held, when their relative prices change. It is an opportunity-cost comparison: an LP can still finish with more dollars than they started with and have underperformed holding.
What the formula measures
For a standard 50/50, full-range constant-product pool such as the simplified Uniswap v2 model, let r be the ending price ratio between the two pool assets divided by their starting price ratio. Before fees and other costs, the divergence loss as a share of the hold-only value is:
IL loss fraction = 1 − (2 × √r) ÷ (1 + r)
The formula compares the LP position with the original token amounts held outside the pool. It assumes a constant-product, equal-value starting position and does not include trading fees, incentives, gas, slippage, taxes, or a concentrated price range. Reciprocal moves such as a 2× rise and a 0.5× ratio produce the same percentage in this model.
| Ending price ratio (r) | Loss versus holding, before fees |
|---|---|
| 0.25× | 20.0% |
| 0.5× | 5.7% |
| 1.25× | 0.6% |
| 1.5× | 2.0% |
| 2× | 5.7% |
| 4× | 20.0% |
Worked example
Suppose an equal-value position starts with 1 ETH and 1,000 USDC, when ETH is $1,000. Its starting value is $2,000. If ETH later trades at $4,000, the relative price ratio is 4. In an ideal constant-product pool, arbitrage trading changes the position to about 0.5 ETH and 2,000 USDC, worth $4,000 together. Simply holding the original 1 ETH and 1,000 USDC would be worth $5,000. The $1,000 difference is 20% of the hold value, before fees and costs. The LP position has grown in dollar value, but it lagged the hold-only comparison.
Fees, rewards, and actual results
Trading fees or incentives can offset some or all of this difference, but they are not guaranteed and should not be assumed from a displayed APY alone. A practical comparison is the value of the withdrawn tokens plus collected fees and rewards, minus costs, versus the value of the same starting tokens held over the same period. Trading volume, token prices, time in range, and withdrawal costs all matter.
Why concentrated liquidity is different
The simple formula above is not a calculator for concentrated-liquidity positions such as Uniswap v3 or v4. An LP chooses a price interval, and the token mix changes as the price moves through it. If the price leaves the interval, the position becomes inactive and stops earning swap fees until price returns; at a boundary it can consist of only one asset. Range choice and management therefore add risks that the full-range formula does not capture.
Why “impermanent” can mislead
The name describes a relative-price comparison that can shrink if prices return to their starting ratio in the simple full-range model. It does not promise that a loss will reverse, and it does not include fees, costs, contract risk, or the path a concentrated position took. The term is most useful when the comparison is stated clearly: pool position versus holding the same initial assets.
Related Terms
See Also
- What Is MEV — And Why Every Ethereum Transaction Is a Game — how transaction ordering can affect swaps.
- What Is Restaking — And Why EigenLayer Made It the Most Debated Idea in DeFi — a different way protocols package crypto returns and risk.
- What Is Tokenomics — And Why It Determines Whether a Crypto Project Survives — context for the value and supply of incentive tokens.
- Swap crypto with ChangeNOW
Social Media Sentiment
In a small r/defi weekly discussion posted October 18, 2026, a few commenters described monitoring concentrated-liquidity ranges and watching for impermanent loss if prices move sharply. This is anecdotal conversation from one thread, not a survey or a measure of overall LP sentiment. Read the discussion.
Last updated: 2026-10
Sources
- Uniswap Developers — Understanding Returns (v2) — derives the constant-product position quantities and the loss-versus-holding formula, and explains how fee income affects the comparison.
- Uniswap Labs — What Is Impermanent Loss? — defines the price-divergence effect and explains the x × y = k pool model.
- Uniswap Developers — Concentrated Liquidity — describes v3/v4 price intervals and why a position outside its interval is inactive and earns no fees.