Impermanent loss explained, with the formula
The hidden cost of providing liquidity, worked through step by step.
Impermanent loss is how much worse off a liquidity provider is than someone who just held the same two tokens, caused by the pool rebalancing as prices move. For a 50/50 constant-product pool it equals 2√r ÷ (1 + r) − 1, where r is the change in one token's price relative to the other: a 2x move costs about 5.7%, a 5x move about 25.5%. Trading fees have to cover it before providing liquidity pays.
What it is
When you provide liquidity to a 50/50 pool on an automated market maker, the pool sells the token that's rising and buys the one that's falling, because that's what traders and arbitrageurs do against it. You end up holding more of the loser and less of the winner than you started with. Impermanent loss is the gap between your pool position and what you'd have if you had simply kept your two tokens in a wallet.
The formula
If one token's price changes by a factor r relative to the other (r = new price ratio ÷ old price ratio), then for a constant-product (x · y = k) pool, before fees:
Impermanent loss = 2 × √r ÷ (1 + r) − 1
Where it comes from. With k = x · y and a price P = y ÷ x, the balances are x = √(k ÷ P) and y = √(k × P), so the pool is worth 2√(k × P) in the second token: it grows with the square root of the price. Holding the original tokens, half the value moves with the price. Divide one by the other and everything except r cancels, leaving 2√r ÷ (1 + r). It's 1 when r = 1 (no change) and smaller for any other r, so the result is always zero or a loss.
Worked example
You deposit 0.5 ETH and 1,000 USDC when ETH is $2,000, so $2,000 in total and k = 0.5 × 1,000 = 500. ETH doubles to $4,000 (r = 2).
- The pool's balances become √(500 ÷ 4,000) = 0.3536 ETH and √(500 × 4,000) = 1,414.21 USDC, worth 0.3536 × $4,000 + $1,414.21 = $2,828.43.
- Holding would be worth 0.5 × $4,000 + $1,000 = $3,000.
- The shortfall is $171.57, or -5.72% of the holding value, exactly what the formula gives: 2√2 ÷ 3 − 1 = -5.72%.
This matches the example in our yield farming guide. You still made money compared with the $2,000 you started with; you just made less than holding. If ETH had halved instead (r = 0.5), the loss would also be -5.72%: the formula treats a doubling and a halving the same.
How big it gets
| Price change of one token vs. the other | r | Impermanent loss vs. holding |
|---|---|---|
| +25% | 1.25 | -0.62% |
| +50% | 1.5 | -2.02% |
| +100% | 2 | -5.72% |
| +200% | 3 | -13.40% |
| +300% | 4 | -20.00% |
| +400% | 5 | -25.46% |
| −25% | 0.75 | -1.03% |
| −50% | 0.5 | -5.72% |
| −75% | 0.25 | -20.00% |
| −90% | 0.1 | -42.50% |
Small moves cost little; big moves cost a lot. A 5x move costs about a quarter of the value compared with holding. Try your own numbers in the impermanent loss calculator.
Why "impermanent", and why that's misleading
The loss disappears if prices return exactly to where they were when you deposited, because the pool's balances return too. That's the only sense in which it's impermanent. If you withdraw while prices are different, the loss is locked in. Many people now call it "divergence loss", which describes it better.
Fees versus impermanent loss
Providers earn a share of trading fees, and fees are the only reason to accept impermanent loss. Whether you come out ahead depends on trading volume, the fee rate, your share of the pool and how far prices diverge. Busy pools of tokens that move together (such as two dollar stablecoins, or ETH and staked ETH) have low impermanent loss; pools pairing a volatile token with a stablecoin can lose more to divergence than they earn in fees. Research on Uniswap v3 has found that many liquidity providers earned less in fees than they lost to impermanent loss.
- Concentrated liquidity (Uniswap v3 style) multiplies both fees and impermanent loss; the formula above understates the loss for a narrow range, and outside your range you hold only the losing token.
- Weighted pools (for example 80/20) have different, smaller impermanent loss; the formula above is for 50/50 constant-product pools.
- Advertised APRs usually show fees and rewards but not impermanent loss.
Frequently asked questions
What is impermanent loss in simple terms?
The amount a liquidity provider falls behind someone who just held the same two tokens, caused by the pool selling the rising token and buying the falling one.
What is the impermanent loss formula?
For a 50/50 constant-product pool: IL = 2√r ÷ (1 + r) − 1, where r is how much one token's price changed relative to the other. A 2x change gives about −5.72%.
Is impermanent loss permanent?
It becomes permanent when you withdraw while prices differ from your entry. It only disappears if prices return to exactly where they were.
Can trading fees make up for impermanent loss?
Sometimes. It depends on volume, the fee rate, your share of the pool and how far prices move. For volatile pairs the loss often exceeds the fees.
Do stablecoin pools have impermanent loss?
Very little, as long as both coins stay near $1. If one loses its peg, the pool fills up with the failing coin and the loss can be severe.
Where to next
Sources
- How Uniswap works (Uniswap v2 documentation)
- Concentrated liquidity (Uniswap v3 documentation)
- Impermanent loss in Uniswap v3, Loesch, Hindman, Richardson and Welch (2021)
Written for beginners and checked against the sources listed. Last reviewed November 5, 2026. This page is educational and is not financial, tax or legal advice. How we write and check pages.