Impermanent Loss Calculator

Impermanent loss (IL) is the difference in value between holding tokens in an automated market maker (AMM) liquidity pool versus simply holding those tokens in your wallet. It is called “impermanent” because the loss is not realized until you actually withdraw from the pool — if prices return to where they were when you deposited, the loss disappears.

Why does it happen?

AMMs like Uniswap v2 use the constant product formula:

x × y = k

Where x and y are the quantities of the two tokens, and k is a constant. When the price of one token changes, the pool rebalances automatically by adjusting the quantities. If ETH doubles in price, the pool sells some of your ETH (to arbitrageurs) and gives you more USDC. You end up holding less ETH than if you’d just held, exactly the amount you missed the upside on.

The impermanent loss formula

For a 50/50 pool where one asset (Token A) changes price by a ratio k (new price ÷ initial price):

IL % = (2 × √k / (1 + k)) − 1

LP Value = Initial Investment × 2√k / (1 + k)

Held Value = Initial Investment × (1 + (k − 1) / 2)

The difference between “Held Value” and “LP Value” is your impermanent loss in dollars.

Worked example

You deposit $10,000 into an ETH/USDC pool. ETH starts at $2,000 and rises to $4,000.

• Price ratio r = 4,000 / 2,000 = 2.0
• IL % = 2√2 / (1+2) − 1 = 2(1.4142)/3 − 1 = 0.9428 − 1 = −5.72%
• Held Value (if you had just kept the coins): $10,000 × (1 + 2) / 2 = $15,000
• LP Value (your pool share): $10,000 × √2 = $14,142
• Loss vs holding: $15,000 − $14,142 = $858, which is 5.72% of the held value

Both positions grew. The pool position is worth more than your $10,000 deposit, just $858 less than plain holding would have been. That gap is the impermanent loss, and trading fees have to earn more than $858 before the pool comes out ahead.

Impermanent loss reference table

Note: IL is symmetric — a 2× price increase causes the same IL % as a 50% price decrease.

Concentrated liquidity (Uniswap v3)

Uniswap v3 introduced concentrated liquidity, allowing LPs to provide liquidity only within a specified price range. This earns much higher fees on the same capital. But if the price moves outside your range, you stop earning fees and experience maximum IL.

When is it worth providing liquidity?

Providing liquidity is profitable when: Trading Fees Earned > Impermanent Loss. High-volume, lower-volatility pairs (e.g., USDC/USDT, ETH/USDC on a busy DEX) typically generate enough fees to offset IL. Highly volatile pairs with low trading volume are the most dangerous for LPs.