How do you calculate LP value and impermanent loss in a 50/50 pool?
An LP value calculation estimates what a 50/50 constant-product liquidity position is worth after a relative price change. Impermanent loss then compares that LP value with simply holding the same starting assets.
The 50/50 LP value and impermanent-loss formulas
r = Price now ÷ Price at depositHold value = Deposit × (1 + r) ÷ 2Pool value = Deposit × √rImpermanent loss = (Pool value ÷ Hold value − 1) × 100Assumes a 50/50 pool and one token priced against a stable one.LP value after one relative price change
The default case treats one asset as changing relative to a stable counterpart. It calculates LP value, hold value and the pool-versus-hold difference from the price ratio rather than predicting either asset’s future price.
Illustrative inputs; currency amounts below use USD. Rates and prices are assumptions, not live quotes.
- Value deposited
- $10,000.00
- Token price at deposit
- $2,000.00
- Token price now
- $3,400.00
Step-by-step calculation
- Relative price ratio = 3,400 ÷ 2,000 = 1.7.
- Holding the original assets gives 10,000 × (1 + ratio) ÷ 2 = 13,500; the 50/50 pool gives 10,000 × √ratio = 13,038.40481.
- Pool-versus-hold return = (13,038.40481 ÷ 13,500 − 1) × 100 = -3.419224%. Trading fees and rewards are excluded.
Intermediate figures are rounded for reading. Results use the full calculation precision.
A shortfall versus hold, not always a cash loss
The displayed percentage is a relative shortfall against holding, not necessarily a negative currency return. Fee income can offset it, but fees are not included in this formula.
Pool designs this formula cannot model
This formula does not apply unchanged to concentrated liquidity or pools with weights other than 50/50.
- The pool uses a 50/50 constant-product weighting.
- One asset is measured against a stable comparison asset.
- Trading fees, incentives, slippage and concentrated ranges are excluded.
Calculations related to impermanent loss
The following tools examine neighbouring parts of the same calculation without changing the inputs or assumptions used above.
References
Sources and conventions
- Uniswap: liquidity-provider returns
Applies to the full-range constant-product model, not concentrated-liquidity positions.
Quick answers
Frequently asked questions
How is LP value calculated in this model?
Price now is divided by price at deposit to find the price ratio. The deposited value is then multiplied by the square root of that ratio.
What pool type does this impermanent loss calculator assume?
It assumes a constant-product 50/50 pool with one token priced against a stable token.
Are liquidity-provider fees included?
No. The result isolates impermanent loss and does not add trading fees, rewards or incentives.
Is LP value the same as impermanent loss?
No. LP value estimates what the position in the pool is worth; impermanent loss is the percentage difference between that value and the modelled value of holding the original tokens.
Calculation method and limitations · Report an error
Educational content only. This guide is not financial advice.