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For AMM liquidity providers

Impermanent loss calculator

Providing liquidity pays fees but rebalances your holdings against you when prices diverge. See the gap between the pool position and simply holding the two assets.

Your numbers
USD
USD
USD
USD
USD

The loss is called impermanent because it reverses if prices return to their original ratio. Withdraw while they have diverged and it becomes permanent.

Result

Impermanent loss

 

Value if you had held
Value in the pool
Price ratio change
Fees needed to break even
Divergence

What impermanent loss is

An automated market maker keeps the two sides of a pool in balance by trading against you. When one asset rises, arbitrageurs buy it out of the pool and leave the other behind. You end up holding more of the loser and less of the winner than you started with.

k = price ratio change of A relative to B
IL = 2 × √k ÷ (1 + k) − 1

The formula depends only on the ratio between the two assets, not on their direction. Both doubling produces no impermanent loss at all. One doubling while the other stays flat produces about 5.7%.

How divergence maps to loss

Price ratio changeImpermanent loss
1.25x0.6%
1.5x2.0%
2x5.7%
3x13.4%
5x25.5%
10x42.5%

Small moves cost almost nothing, which is why stablecoin pairs are comfortable. Large moves cost a great deal, which is why volatile-asset pools need substantial fee income to be worth it.

A worked example

$10,000 deposited into an ETH/USDC pool at $2,500 per ETH. ETH rises to $4,000:

Price ratio change1.6x
Value if you had held$13,000.00
Value in the pool$12,649.11
Impermanent loss2.70% ($350.89)

You are still up in dollars. You are simply up less than if you had done nothing — and the fees earned over that period need to exceed $350.89 for the position to have been worth taking.

When providing liquidity pays

The mirror of that: a pool holding one asset you expect to run hard is the wrong place for it. You will systematically be sold out of the winner. If you are comparing it against a passive yield instead, the staking calculator models that side.

Common questions

What is impermanent loss?

The difference between the value of assets held in a liquidity pool and the value of simply holding them, caused by the pool rebalancing as prices diverge.

How is impermanent loss calculated?

It depends on the change in the price ratio between the two pooled assets. The standard formula is twice the square root of the ratio change, divided by one plus the ratio change, minus one.

Is impermanent loss ever permanent?

It becomes permanent the moment you withdraw while prices have diverged. If the ratio returns to where it started, the loss disappears on its own.

Do trading fees cover impermanent loss?

Sometimes. Fees accrue continuously while the loss depends on divergence, so busy pools with correlated assets often come out ahead and volatile pairs frequently do not.

Which pools have the least impermanent loss?

Pairs that move together — two stablecoins, or a token paired with its liquid staking derivative. The less the ratio between them changes, the smaller the loss.