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.

Quote all four token prices in the same currency. Initial position value is split equally between the tokens.

Full-range 50/50 constant-product pool at the new price ratio. Excludes concentrated liquidity, unequal weights and protocol-specific behavior.

Optional settings

Blank means zero. Enter their value at the comparison time.

Blank means zero. Holding costs are assumed zero.

Impermanent Loss Formula

The following signed formula compares pool value with holding the initial token quantities. The calculator uses the full-range 50/50 constant-product case and displays the positive loss magnitude, the negative of signed IL. Unequal-weight models are shown only for context and are not supported by this calculator:

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.

Use prices in the same currency to compute r. For this calculator use w = 0.5 and positive loss magnitude L = 1 − 2√r/(1+r). The Uniswap return model neglects fees. This tool adds separately entered fee/reward value and LP-specific costs to its approximate monetary comparison, with zero holding costs; it does not simulate reserve changes caused by fees.

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. In the ideal model, the relative shortfall returns to zero if the relative A/B price ratio returns to its initial value; both absolute prices need not return. This does not guarantee recovery of the original dollar investment or cover protocol risks and costs. 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. Use w = 0.5 for this calculator. Enter a starting position value allocated equally to the two assets; optional fees/rewards and costs default to zero when blank.
  6. Select Calculate to compare LP and holding values. Reverse mode accepts 0% ≤ loss < 100% and returns reciprocal relative-price scenarios; at zero loss both coincide at1×. It cannot determine unique token prices. Reset clears this calculator’s saved state.

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. Signed IL = 2√3/(1+3) − 1 ≈ −0.1339746. The calculator displays the positive loss magnitude, approximately13.3975%, relative to holding. This is distinct from the portfolio’s return versus the initial deposit.