Impermanent loss calculator
How do you calculate impermanent loss?
Work out k, how far one token’s price moved against the other’s, then IL = 2√k ÷ (1 + k) − 1 for a 50/50 pool: a token that doubles against its partner leaves the pool −5.72% behind simply holding both tokens. The loss only becomes real when you withdraw, and the fees the pool pays can make up for it, which is what this calculator compares.
Providing liquidity pays fees, but when the two tokens’ prices move apart the pool ends up holding more of the one that fell. This calculator shows that cost against simply holding, adds the fees the pool paid, and tells you the fee APY you would need to break even. Nothing is saved or sent anywhere: the maths runs in your browser.
What is the impermanent loss formula?
For a 50/50 pool, where k is the change in one token’s price relative to the other:
IL = 2 × √k ÷ (1 + k) − 1
For a weighted pool with weight w on token A, and price multipliers a and b (1.5 means up 50%), compare the pool with holding: the pool is worth aw × b1−w of what you put in, holding is worth w × a + (1 − w) × b, and IL = pool ÷ hold − 1. At w = 0.5 this is the same as the 50/50 formula.
- Find the price ratio change. Divide token A’s new price by its starting price, and do the same for token B. Then divide A’s result by B’s. If A doubles and B stays the same, k = 2 ÷ 1 = 2.
- Apply the formula. For a 50/50 pool, IL = 2 × √k ÷ (1 + k) − 1. With k = 2: 2 × 1.4142 ÷ 3 − 1 = −5.72%.
- Compare values in dollars. Multiply what holding would be worth by (1 + IL). $10,000 split 50/50 becomes $15,000.00 if held, and $14,142.14 in the pool before fees.
- Add the fees the pool paid. Fees are added on top of the pool value. At a 10% fee APY for a year the position is worth $15,556.35, which beats holding; the fee APY that only breaks even is 6.07%.
How much impermanent loss does each price move cause?
One token’s price changes and the other stays where it was. The loss is against holding the same two tokens, before any fees:
| Token A price change | 50/50 pool | 80/20 pool |
|---|---|---|
| −90% | −42.50% | −43.40% |
| −75% | −20.00% | −17.53% |
| −50% | −5.72% | −4.28% |
| −25% | −1.03% | −0.70% |
| +25% | −0.62% | −0.38% |
| +50% | −2.02% | −1.20% |
| +100% | −5.72% | −3.27% |
| +200% | −13.40% | −7.38% |
| +400% | −25.46% | −13.72% |
| +900% | −42.50% | −23.05% |
Two things stand out. The loss grows quickly with the size of the move, and a 50/50 pool loses the same for a token that falls to half as for one that doubles, because only the ratio between the two prices matters.
What can’t an impermanent loss calculator tell you?
- Future fees. A pool’s fee APY follows its trading volume and changes every day. Use the APY a pool actually paid over the period, not today’s figure.
- Concentrated liquidity. Positions with a price range lose more for the same move, and earn nothing once the price leaves the range.
- Reward tokens. If part of the APY is paid in a token whose price falls, the fees are worth less than the APY suggests. The APY calculator shows how much.
- Depegs and contract risk. In a stablecoin pair the loss stays small only while both coins hold their peg. No calculator models an exploit or a withdrawal queue.
Impermanent loss FAQ
What is impermanent loss?
It is the gap between what your tokens are worth in a liquidity pool and what the same tokens would be worth if you had simply held them. When prices move, arbitrage traders rebalance the pool, so you end up with more of the token that fell and less of the one that rose. It is called impermanent because it shrinks again if prices return to where they started.
Is impermanent loss a real loss?
It becomes real when you withdraw while prices are still apart. Until then it is a loss on paper compared with holding. You can still be up in dollars overall, for example if both tokens rose, and still have impermanent loss.
How much impermanent loss if one token doubles?
In a 50/50 pool, −5.72% compared with holding. If one token triples it is −13.40%, at five times it is −25.46%, and if it halves it is −5.72%. The direction does not matter, only the size of the move between the two tokens.
Do 80/20 pools have less impermanent loss?
Usually, for moderate moves of the heavier token. If the 80% token doubles, an 80/20 pool loses −3.27% against holding, compared with −5.72% at 50/50. The calculator offers 50/50, 80/20 and 20/80 so you can see both sides.
Do stablecoin pools have impermanent loss?
Very little while both coins hold their peg, because their prices barely move against each other. If one coin loses its peg, the pool sells you more of the coin that fell, so the loss can be large. That is why it is worth checking which stablecoins a pool holds before you deposit.
Do lending pools and single-asset vaults have impermanent loss?
No. Impermanent loss comes from a pool holding two or more tokens whose prices can move apart. A lending market or a single-asset vault holds one token, so its risks are different: rates, smart contracts and withdrawals.
How do I use start and end prices instead of percentages?
Work out each token’s change as (end price ÷ start price − 1) × 100. A token that went from $2,000 to $3,000 changed by +50%; one that went from $1.00 to $0.97 changed by −3%. Enter those two numbers.
Does this work for Uniswap v3 or other concentrated liquidity?
Not exactly. Concentrated liquidity magnifies impermanent loss inside your price range and stops earning fees outside it, so the loss for the same move is larger than this calculator shows. Treat the result as the smallest loss you could expect.
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