Impermanent loss is the worst-explained concept in the industry, and the one that costs the most money to people who walk into DeFi without understanding it. It is not a fee and it is not a bug: it is the unavoidable mathematical result of an automated market maker rebalancing your position every time somebody trades against it.
This calculator applies the constant-product formula, the one used by Uniswap v2's 50/50 pools and everything derived from them. Amounts are shown in dollars as illustrative figures, not conversions.
Where the loss comes from
A constant-product pool keeps the product of its two reserves fixed: x · y = k. When the outside price of one asset rises, arbitrageurs buy that asset out of the pool until the internal price matches the external one. In doing so they carry off part of the asset that appreciated and leave behind more of the one that did not.
The result is that the pool always ends up holding less of the asset that went up and more of the one that went down. Your position has rebalanced itself, in precisely the direction you would not have chosen.
The formula for the position's value against holding is exact and does not depend on the amount:
value in the pool / value if held = 2·√r / (1 + r)
where r is the ratio of the final price to the initial one. At r = 1 there is no loss. At any other value the loss is negative. It is symmetric: the price doubling and the price halving produce exactly the same relative loss.
| Price change | Impermanent loss |
|---|---|
| ±10% | −0.11% |
| ±25% | −0.60% |
| ±50% | −2.02% |
| ×2 (+100%) | −5.72% |
| ×3 (+200%) | −13.40% |
| ×5 (+400%) | −25.46% |
| −75% | −20.00% |
A worked example
You deposit $5,000: $2,500 in ether and $2,500 in a stablecoin. With ether at $2,500, that is 1 ETH and 2,500 units of the stablecoin, so k = 2,500.
Ether doubles to $5,000. Arbitrage leaves the pool holding 0.7071 ETH and 3,535.53 of the stablecoin, because the product still has to equal 2,500. Your position is now worth 0.7071 × 5,000 + 3,535.53 = $7,071.07.
Had you simply held the 1 ETH and the 2,500 stablecoins, you would have 5,000 + 2,500 = $7,500.
The gap is $428.93, or 5.72%. At an 8% fee APR the pool would have paid you roughly $1.55 a day, so you would need 277 days inside to make that loss back — and that assumes the price never moves again.
"Impermanent" is a misleading name. The loss only disappears if the price ratio returns exactly to where it started before you withdraw. The moment you pull the funds out, it is realised and every bit as permanent as any other loss.
What this calculator does not measure
- Gas on the way in and out. Adding liquidity takes two or three transactions; removing it takes as many again. On Ethereum L1 as of August 2026 that is not much money, but in a congested market it stops being trivial. The gas fees guide explains it.
- Contract risk. A flaw in the protocol can take 100% of the position, and no formula predicts that.
- Token incentives. Many pools pay part of the yield in their own token, whose price tends to fall as more of it is issued. An advertised 40% APR paid in a token that depreciates 60% is not a 40% APR.
- Concentrated liquidity. Uniswap v3 and similar designs let you concentrate liquidity inside a price range: that multiplies the fees earned within the range and multiplies the impermanent loss too, and outside the range you earn nothing at all. This calculator's formula does not apply to them.
- Stablecoin pools. Two assets that are meant to be worth the same barely generate any impermanent loss. In exchange you take on the risk of one losing its peg, as USDC did in March 2023.
The full context — where DeFi yield actually comes from and which risks stack on top of each other — is in the DeFi guide.