Impermanent Loss vs HODL Calculator
When you add two tokens to a constant-product AMM pool (x * y = k), the pool automatically rebalances as prices change. If token A doubles in price relative to token B, arbitrageurs buy token A from the pool, leaving you with less of the now-more-valuable token and more of the cheaper one. The result is that your LP position is worth less than if you had simply held both tokens. This value difference is impermanent loss. The formula derived from the constant-product invariant is: IL = 2 * sqrt(p) / (1 + p) - 1, where p is the ratio of the new price to the original price. Enter the price ratio change below to see your impermanent loss as a percentage.
Impermanent loss formula
IL = 2 * sqrt(p) / (1 + p) - 1
IL (%) = |IL| * 100
Where p is the price ratio change of one token relative to the other since deposit. The formula is symmetric: a 2x increase and a 0.5x decrease (50% drop) produce the same IL magnitude of about 5.72%.
Impermanent loss reference table
- 1.25x price change: approximately 0.60% IL
- 1.50x price change: approximately 2.02% IL
- 2.00x price change: approximately 5.72% IL
- 3.00x price change: approximately 13.40% IL
- 4.00x price change: approximately 20.00% IL
- 5.00x price change: approximately 25.46% IL
- 10.00x price change: approximately 42.46% IL
Impermanent loss: frequently asked questions
What is impermanent loss?
Impermanent loss (IL) is the difference in value between holding two tokens in an AMM liquidity pool versus simply holding (HODLing) those same tokens in your wallet. It occurs because the AMM rebalances the pool as prices change, causing you to accumulate more of the falling token.
Why is it called impermanent?
The loss is impermanent because if token prices return to the ratio at which you deposited, the loss disappears. However, if you withdraw while prices are at a different ratio, the loss becomes permanent. In practice, many LPs experience a lasting impermanent loss.
What does a price ratio change of 2 mean?
A price ratio of 2 means one token doubled in price relative to the other since you deposited. For example, if you deposited ETH/USDC and ETH doubled, p = 2. The IL formula is: IL = 2 * sqrt(p) / (1 + p) - 1, where p is the price ratio change.
How much IL should I expect at various ratios?
At a 1.25x ratio change: about 0.6% IL. At 1.5x: about 2.0%. At 2x: about 5.7%. At 4x: about 20.0%. At 10x: about 42.5%. Large price divergences cause disproportionately large IL.
Can I profit from providing liquidity despite impermanent loss?
Yes, if the trading fees earned exceed the impermanent loss. High-volume pools with moderate volatility are most likely to be profitable for LPs. Stable-to-stable pools (e.g., USDC/DAI) have near-zero IL and can be profitable even at modest fee rates.
Official sources
- Uniswap Foundation: Uniswap v2 Core Whitepaper (Adams et al.).
- Ethereum Foundation: Decentralized Finance (DeFi).
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.