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Impermanent Loss Calculator

Calculate the impermanent loss on a 50/50 liquidity position and the fee yield needed to offset it.

Providing liquidity to an automated market maker (AMM) means depositing two tokens into a liquidity pool that trades between them, and this impermanent loss calculator measures what that costs against simply holding the pair. The pool holds a constant product of the two balances, so as the price moves it automatically sells whichever token is rising and buys whichever is falling.

Formula: IL = 2*sqrt(r) / (1 + r) - 1

Your figures

Total value added to the pool, split evenly between the two tokens.

Leave at 1 for a stablecoin.

Leave at 1 for a stablecoin.

Optional — trading fees earned, as a percentage of the deposit.

Results

Impermanent loss

-5.72%

versus simply holding both tokens

Value if simply held
US$15,000.00
Value in the pool
US$14,142.14
Difference before fees
-US$857.86
Relative price changeToken A's move divided by token B's move.
2.0000×
Fee yield needed to break even
8.579%

What this means

Because the two tokens moved 2.000× relative to each other, the pool rebalanced along the way and the position is worth 5.72% less than simply holding both tokens would have been. Earning 8.579% in trading fees would exactly offset that. The loss is symmetric — a halving costs the same as a doubling — and reverses entirely if the price ratio returns to where it started.

  • Applies to 50/50 constant-product pools. Weighted and concentrated-liquidity pools behave differently, and concentrated positions can lose considerably more.
  • Excludes gas costs and any token incentives paid on top of trading fees.
  • The loss only becomes permanent when liquidity is withdrawn at a different price ratio.

Impermanent loss: -5.72%

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Continue with these figures

About the Impermanent Loss calculation

That rebalancing has a cost. When the two tokens' prices diverge, the position ends up worth less than simply holding both would have been. The gap is the liquidity provider's loss — impermanent loss — and it runs in either direction, since a fall produces the same shortfall as an equivalent rise.

Used as a liquidity pool calculator, it estimates that loss for a 50/50 pool and shows the trading-fee yield that would exactly offset it. Fees are the compensation for taking this risk, so whether providing liquidity in DeFi was worthwhile depends entirely on that comparison.

Impermanent Loss formula

r  = (token A change) ÷ (token B change)
IL = 2√r ÷ (1 + r) − 1

for a 50/50 deposit:
  hold value = deposit × (A change ÷ 2 + B change ÷ 2)
  pool value = hold value × 2√r ÷ (1 + r)

break-even fee yield = |pool value − hold value| ÷ deposit × 100
IL
Impermanent loss. DeFi dashboards and IL calculators use the abbreviation and the full term interchangeably.
r
Relative price change between the two tokens. r = 1 means no divergence.
√
Square root. It is the source of the loss's characteristic shape.
impermanent
The loss reverses if the price ratio returns to where it started.
two denominators
The loss percentage is measured against the value you would have held; the break-even fee yield is measured against the amount deposited, because that is what fees accrue on. The two differ, and the deposit figure is the one fees must clear.

The square root is where the loss comes from. A constant-product pool always holds the geometric mean of the two positions rather than the arithmetic mean, and the geometric mean is never larger. The formula 2√r ÷ (1 + r) is exactly that ratio, and it equals 1 only when r = 1.

The loss is symmetric in a way people find counterintuitive. A doubling and a halving both give a 5.72% loss, because both represent the same proportional divergence. A 4× move costs 20%, and a 10× move costs about 42% — it grows, but far more slowly than the price move itself.

It is called impermanent because the position recovers fully if prices return to their starting ratio. It becomes permanent the moment liquidity is withdrawn at a different ratio, which is why the term is somewhat misleading: for anyone who exits after a large move, the loss is entirely real.

Impermanent Loss: a worked example

$10,000 deposited into an ETH/USDC pool with ETH at $2,000. ETH later trades at $4,000; USDC is a stablecoin, so its price is unchanged.

  1. Token A change4,000 ÷ 2,000 = 2.0
  2. Token B change1 ÷ 1 = 1.0
  3. Price ratio, r2.0 ÷ 1.0 = 2.0
  4. Pool ratio factor2 × √2 ÷ 3 = 0.9428
  5. Impermanent loss0.9428 − 1 = −5.72%
  6. Value if held10,000 × (2.0 ÷ 2 + 1.0 ÷ 2) = $15,000
  7. Value in the pool15,000 × 0.9428 = $14,142

The pool position is worth $14,142 against $15,000 for simply holding — $858 less. That is 5.72% of the $15,000 you would have held, but 8.58% of the $10,000 originally deposited, and the deposit is what fees accrue on. Earning more than 8.58% in trading fees over the period would have made providing liquidity the better outcome.

How to use the Impermanent Loss calculator

  1. Enter the total value you deposited into the liquidity pool.
  2. Enter each token's price at the time you deposited and its price now.
  3. For a stablecoin pair, leave token B at 1 for both prices.
  4. Optionally enter the fees you have earned as a percentage of the deposit, to see the net position against holding.
  5. Compare against the break-even fee yield — that is the figure that determines whether the position was worthwhile.

Limitations of the Impermanent Loss calculator

Every calculation makes assumptions. These are the ones that matter here.

  • Applies to 50/50 constant-product pools. Weighted pools such as 80/20 have a different curve, and concentrated-liquidity positions can lose considerably more within their range.
  • Excludes gas costs for depositing, withdrawing and claiming, which are significant on small positions.
  • Excludes token incentives paid on top of trading fees, which many pools use to offset this loss.
  • Assumes you held the position throughout. Adding or removing liquidity partway changes the arithmetic.
  • Compares only against holding both tokens. It says nothing about whether holding either token was itself a good outcome.

Frequently asked questions about Impermanent Loss

Why is it called impermanent if it costs me money?

Because the loss reverses entirely if the price ratio returns to where it started — while liquidity remains deposited, nothing is realised. It becomes permanent the moment you withdraw at a different ratio. For most providers exiting after a large move, the loss is real.

Does impermanent loss happen if the price falls?

Yes, and by the same amount as an equivalent rise. Halving and doubling both produce a 5.72% loss, because the formula depends on the proportional divergence rather than its direction.

How large does AMM impermanent loss get?

It grows with divergence but slowly: a 2× move costs 5.7%, 4× costs 20%, 5× costs about 25%, and 10× about 42%. It never reaches 100%, but it can comfortably exceed the fees earned on a pair where one token moves sharply.

How do I avoid impermanent loss?

Pools of two tokens that track each other closely — two stablecoins, or two derivatives of the same asset — have very little divergence and therefore very little impermanent loss. That is a description of the mechanism, not a suggestion about where to provide liquidity.

Do trading fees make up for impermanent loss?

Sometimes. The break-even fee yield shown here is exactly the figure to compare against what the pool has actually paid you. On a volatile pair with low volume, fees frequently do not cover it.

Last reviewed . See our methodology and editorial policy.

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