Calculate impermanent loss for a 50/50 constant-product pool from token price changes—or solve for a target loss—with LP vs HODL values, fees, and costs.

Choose what to solve
Required: both tokens’ initial and current prices plus starting position value.
Assumes half the starting value was allocated to each token.
Advanced: fees, rewards, and costs
Returns the reciprocal up and down price-ratio changes that create the same loss.
Model: full-range 50/50 constant-product pool, before protocol-specific mechanics. Concentrated liquidity, unequal weights, changing fees, slippage, and active rebalancing require different models.
Pure impermanent loss
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Relative price ratio—
HODL value—
LP value before fees—
Loss versus HODL—
Net LP value after fees and costs—
Net versus HODL—
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Educational scenario estimate only, not financial, investment, tax, or protocol advice. Values exclude price impact, changing liquidity, token emissions, smart-contract risk, MEV, taxes, and protocol-specific behavior.

Impermanent Loss Formula

The following formula is used to calculate impermanent loss (relative to holding), based on the change in the price ratio between the two assets and the pool weights:

r & = ((PA / PB)current) / ((PA / PB)ᵢₙᵢₜᵢₐₗ) = ((PA,1 / PA,0)) / ((PB,1 / PB,0)) \ IL & = (rw) / (w × r + (1 - w)) - 1 \ For w = 0.5: IL & = (2√(r)) / (1 + r) - 1

Variables:

  • IL is the impermanent loss as a decimal (e.g., −0.134 = −13.4%). Multiply by 100 to express it as a percentage.
  • r is the relative price change, defined as (A/B)current ÷ (A/B)initial.
  • w is the pool weight of Asset A (as a fraction from 0 to 1). For a 50/50 pool, w = 0.5.

To calculate impermanent loss, compute the initial and current price ratio PA/PB, take their ratio to get r, and then apply the formula above (using your pool weight).

What is an Impermanent Loss?

Impermanent loss occurs when the price of assets in a liquidity pool changes after a liquidity provider has deposited them into the pool. The loss is ‘impermanent’ because it can be recovered if the prices return to their original state at the time of deposit. It is a risk associated with providing liquidity in automated market maker (AMM) platforms.

How to Calculate Impermanent Loss?

The following steps outline how to calculate the Impermanent Loss.

  1. First, determine the initial price of Asset A and Asset B.
  2. Next, determine the current price of Asset A and Asset B.
  3. Compute the initial price ratio (PA/PB)initial and the current price ratio (PA/PB)current.
  4. Compute r = (PA/PB)current ÷ (PA/PB)initial.
  5. Choose the pool weight w for Asset A (for a 50/50 pool, use w = 0.5) and apply the impermanent loss formula.
  6. Use the calculator above to verify your results.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Initial Price of Asset A = $100

Initial Price of Asset B = $200

Current Price of Asset A = $150

Current Price of Asset B = $100

For a 50/50 pool: r = (150/100) ÷ (100/200) = 3, so IL = 2√3/(1+3) − 1 ≈ −0.13397 (≈ −13.40%).