Impermanent Loss Explained: The Formula and How to Calculate It
Impermanent loss explained with the actual formula and a reference table: how much you lose at each price ratio, when fees cover it, and which pool types reduce or avoid it entirely.
Last updated: 30 July 2026
Impermanent loss is the most-cited and least-quantified risk in DeFi. Almost every guide to liquidity provision mentions it. Very few tell you how much it actually costs at a given price move, which is the only form in which the information is useful.
This guide gives you the formula, a reference table you can read off directly, the point at which fees cover the loss, and the pool designs that reduce or sidestep it.
What impermanent loss actually is
Impermanent loss is the difference between the value of assets deposited in a liquidity pool and the value those same assets would have had if you had simply held them.
It is not a fee, and nobody takes it from you. It emerges from arithmetic. A standard automated market maker holds two assets and keeps their product constant. When the external price of one asset moves, arbitrageurs trade against the pool until its internal price matches the market. That trading rebalances your share: you end up holding less of the asset that rose and more of the asset that fell.
The pool has done its job correctly. You are simply worse off than a passive holder, because the pool systematically sold the winner on the way up.
The word "impermanent" is misleading and worth flagging. The loss reverses only if prices return to their original ratio. Withdraw at any other ratio and it is entirely permanent.
The formula
For a standard 50/50 constant-product pool, where r is the price ratio change of one asset relative to the other:
IL = 2 × √r / (1 + r) − 1
The result is negative, expressed as a percentage of what you would have had by holding. Two properties are worth internalising:
- Direction does not matter. A 2x rise and a 50% fall produce identical impermanent loss. The formula is symmetric in the ratio.
- It accelerates, then flattens. Small divergences cost very little. Large ones hurt, but with diminishing marginal damage.
How much you actually lose
| Price change of one asset | Ratio (r) | Impermanent loss |
|---|---|---|
| +10% or −9% | 1.10 | −0.11% |
| +25% or −20% | 1.25 | −0.62% |
| +50% or −33% | 1.50 | −2.02% |
| +75% | 1.75 | −3.44% |
| +100% (2x) or −50% | 2.00 | −5.72% |
| +200% (3x) | 3.00 | −13.40% |
| +300% (4x) or −75% | 4.00 | −20.00% |
| +400% (5x) | 5.00 | −25.46% |
Read that table before your next LP decision. The numbers are smaller than most people fear at moderate moves and larger than most people expect at extremes.
A 2x move on one asset, entirely routine in crypto, costs about 5.7% against holding. If the pool paid you 8% in fees over that period, you are ahead. If it paid 3%, you are behind, and no amount of "the loss is impermanent" changes that when you withdraw.
A worked example
You deposit 1 ETH and 3,000 USDC, with ETH at 3,000. Total value 6,000.
ETH doubles to 6,000. Arbitrage rebalances the pool, and your position now holds roughly 0.707 ETH and 4,243 USDC, worth about 8,485.
Had you simply held, you would have 1 ETH at 6,000 plus 3,000 USDC, worth 9,000.
The gap is 515, or about 5.7%. Note that you are still up in absolute terms: the position grew from 6,000 to 8,485. Impermanent loss is an opportunity cost against holding, not a nominal loss, and conflating the two is the most common misunderstanding.
When fees cover it
Liquidity provision is profitable when fee income exceeds impermanent loss. The variables that decide it:
- Volume relative to liquidity. Fees accrue from trading. High volume against a small pool means high fee income per unit of capital.
- Volatility without direction. The ideal condition is heavy two-way trading that ends near where it started: maximum fees, minimum divergence. The worst is a single sustained trend, which generates one-directional flow and maximum divergence.
- Fee tier. Volatile pairs carry higher tiers precisely to compensate for expected divergence.
- Time in position. Fees accumulate; impermanent loss depends only on start and end prices, not the path. Longer exposure in a range-bound market favours the LP.
The practical implication: a pair that trends strongly in one direction is a bad LP position no matter how attractive the advertised APR, because you are being paid a fee for systematically selling the asset that is going up.
How to reduce or avoid it
Correlated and stablecoin pairs
The most direct mitigation. Two assets that track each other barely diverge, so impermanent loss stays negligible. A stablecoin-to-stablecoin pool sits near a ratio of 1 permanently, absent a depeg. An asset paired with its own liquid staking token behaves similarly, since the LST tracks the underlying. Our guide to stablecoin yield farming covers this approach.
Single-sided liquidity
The mechanism that drives impermanent loss requires two assets rebalancing against each other. Provide liquidity with one asset quoting one side of the market, and that two-asset divergence is largely removed from the picture.
It replaces the risk rather than deleting it. A single-sided position carries directional exposure instead: fund buy orders as a market falls and you accumulate an asset now worth less than the currency you spent. Many providers find that easier to reason about than two-asset divergence. Our explainer on single-sided liquidity covers how JewelSwap applies it in NFT AMM and DCA pools on MultiversX.
Lending instead of pooling
Supplying an asset to a money market earns borrower interest with no second asset and therefore no divergence at all. Returns are usually lower than a productive LP position, and the risk profile is simpler. JewelSwap's money markets run in isolated and cross configurations, priced by Pyth, Umbrella, AshSwap and xExchange.
Auto-compounding
Not a mitigation for divergence, but it raises the fee side of the equation. Automatically harvesting and reinvesting rewards compounds fee income without per-harvest effort or cost, which shifts the break-even. JewelSwap's yield farms auto-compound by default.
Frequently asked questions
What is impermanent loss?
The difference between the value of assets held in a liquidity pool and their value if simply held. It arises because the pool rebalances as prices diverge, leaving you with less of the asset that rose and more of the one that fell.
What is the impermanent loss formula?
For a standard 50/50 constant-product pool, IL = 2 × √r / (1 + r) − 1, where r is the price ratio change of one asset relative to the other. The result is a negative percentage relative to holding, and it is symmetric: a 2x rise and a 50% fall cost the same.
How much is impermanent loss at 2x?
Approximately 5.72% relative to holding. At 3x it is about 13.4%, at 4x about 20%, and at 5x about 25.5%. At smaller moves it is very small: a 25% price change costs roughly 0.62%.
Is impermanent loss really impermanent?
Only if prices return to the ratio at which you deposited. If you withdraw at any other ratio, the loss is realised and entirely permanent. The name causes real misunderstanding.
How do I avoid impermanent loss?
Use correlated or stablecoin pairs where divergence is minimal, provide single-sided liquidity so no two-asset rebalancing occurs, or lend into a money market instead of pooling. Each reduces or removes divergence risk, and each substitutes a different risk in return.
Do fees make up for impermanent loss?
Sometimes. LP profitability is fee income minus impermanent loss. High two-way volume relative to pool size favours the provider; a strong one-directional trend does not, because you are paid a fee for systematically selling the rising asset.
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