What is impermanent loss?

The shortfall of a liquidity-pool position versus simply holding the two assets, caused by the AMM rebalancing against you as relative prices move. It is 'impermanent' only until you withdraw.

How is it calculated?

For a 50/50 constant-product pool with price ratio r: IL = 2√r ÷ (1 + r) − 1. It depends only on the relative price change, in either direction.

−0.6% at a 1.25× move, −2.0% at 1.5×, −5.7% at 2×, −13.4% at 3×, −20.0% at 4× and −25.5% at 5×. Small divergences are cheap; large ones are not.

Why is it the same up or down?

The formula is symmetric in the ratio: a 2× move and a 0.5× move both give −5.72%, because the pool rebalances toward the weakening asset either way.

Can fees offset impermanent loss?

Yes — that is the LP business model. If fee-plus-incentive yield over your holding period exceeds the IL from price divergence, the position beats holding.

Does this cover concentrated liquidity (Uniswap v3)?

No — concentrated ranges amplify both fees and IL, and the maths depends on your chosen range. This tool models the classic full-range 50/50 pool.

Crypto

Impermanent Loss Calculator

Calculate impermanent loss for a 50/50 liquidity pool from the deposit price and current price — LP value versus holding, in percent and dollars.

Impermanent loss is the shortfall of a liquidity-pool position versus simply holding its two assets, caused by the pool rebalancing as relative prices diverge.

Impermanent loss

-5.72%

LP position value: $1,414.21
Value if held: $1,500.00
Difference: -$85.79
Price ratio: 2×

Classic 50/50 constant-product pool, excluding trading fees and incentives — the income side of LP economics.

Worked example

A provider deposits $1,000 into a 50/50 ETH/USDC pool when ETH is $1,500. ETH doubles to $3,000.

Price ratio: r = 3,000 ÷ 1,500 = 2
Impermanent loss: 2√2 ÷ (1 + 2) − 1 = −5.72%
Value if held: $1,000 × (1 + 2) ÷ 2 = $1,500
LP value: $1,000 × √2 = $1,414.21

The LP position is worth $1,414 versus $1,500 for holding — an $86 (5.72%) impermanent loss. Trading fees earned by the pool must exceed that for the LP to come out ahead.

How this is calculated

A constant-product pool (x·y = k) rebalances continuously, selling the appreciating asset for the depreciating one. With price ratio r = current ÷ initial:

LP value = deposit × √r
hold value = deposit × (1 + r) ÷ 2
IL = 2√r ÷ (1 + r) − 1

The formula depends only on the relative price change and is symmetric: a 2× move and a ½× move both cost 5.72% versus holding. IL is zero only when the price returns to its deposit-time ratio — hence "impermanent" — and becomes permanent on withdrawal.

Trading fees and liquidity incentives are the offsetting income; an LP position beats holding when cumulative fees exceed the IL.

When to use this calculator

Use this before providing liquidity to any volatile pair: test the price scenarios you actually expect (±25%, 2x, 4x) and see the IL each implies. If plausible fee income doesn't cover the worst realistic divergence, the pool is a bad trade versus holding.

Use it again before withdrawing. IL is only locked in when you exit, so knowing the current shortfall versus holding helps decide whether to wait out a divergence or realise it.

It is also the fastest way to build intuition for LP risk in general: seeing that a 2x move costs 5.7% but a 10x costs 25.5% explains why stable-stable pools dominate passive LP capital.

Common mistakes

Comparing the LP value to the initial deposit instead of to holding — the pool position still grew; it just grew less than holding would have.
Forgetting fees and incentives: IL is only half the ledger; APR from fees can more than offset it in active pools.
Assuming stablecoin pairs are immune — a depeg is exactly the large price divergence that maximises IL.

Frequently asked questions

What is impermanent loss?: The shortfall of a liquidity-pool position versus simply holding the two assets, caused by the AMM rebalancing against you as relative prices move. It is 'impermanent' only until you withdraw.
How is it calculated?: For a 50/50 constant-product pool with price ratio r: IL = 2√r ÷ (1 + r) − 1. It depends only on the relative price change, in either direction.
How big does it get?: −0.6% at a 1.25× move, −2.0% at 1.5×, −5.7% at 2×, −13.4% at 3×, −20.0% at 4× and −25.5% at 5×. Small divergences are cheap; large ones are not.
Why is it the same up or down?: The formula is symmetric in the ratio: a 2× move and a 0.5× move both give −5.72%, because the pool rebalances toward the weakening asset either way.
Can fees offset impermanent loss?: Yes — that is the LP business model. If fee-plus-incentive yield over your holding period exceeds the IL from price divergence, the position beats holding.
Does this cover concentrated liquidity (Uniswap v3)?: No — concentrated ranges amplify both fees and IL, and the maths depends on your chosen range. This tool models the classic full-range 50/50 pool.