How to use the impermanent loss calculator
- Enter the price of each token on the day you deposited and the price now, in the same currency.
- Enter the value you deposited. The page assumes it was split 50/50 at the deposit prices.
- Read the price ratio change, the impermanent loss, the value of holding and the pool value.
- Use the table to see the loss for other price ratio changes.
Formula
ka = price A now / price A at deposit, kb = the same for token B, k = ka / kb
pool value = deposit x sqrt(ka x kb)
hold value = deposit x (ka + kb) / 2
impermanent loss = pool value / hold value - 1 = 2 sqrt(k) / (1 + k) - 1
In a constant product pool the two reserves keep a fixed product, so the pool sells the token that rises and buys the one that falls. The result depends only on the ratio of the two price changes.
Token A doubles against token B
Deposit $10,000 when token A costs $100 and token B costs $1. Later token A costs $200 and token B still costs $1, so ka = 2, kb = 1 and k = 2. Holding would be worth $10,000 x (2 + 1) / 2 = $15,000.00. The pool is worth $10,000 x sqrt(2) = $14,142.14, which is 5.719 percent less than holding.
Fees would have to add about 6.07 percent of the pool value to break even. A fall of token A by half gives the same 5.719 percent, because the formula depends on the ratio only and 0.5 is the inverse of 2.
Why it is called impermanent
The loss exists only compared with holding. If the price ratio returns to its starting value, the loss disappears. It becomes permanent when you withdraw at a different ratio.
Pools also earn fees and sometimes rewards, which this page leaves out. Whether the fees outweigh the loss depends on the pool, and the page cannot know that.
What the table shows
The table lists the loss for ratio changes from 0.25 to 5. A change of 1.25 times or 0.75 times costs about 0.6 and 1.0 percent. A change of 4 times costs about 20 percent. The shape is the same whether the ratio goes up or down by the same factor.
This is an educational model of a plain 50/50 constant product pool. It is not advice, and it ignores taxes, gas fees and smart contract risk.
Assumptions and limits
- The pool is a constant product pool with a 50/50 split at the deposit prices.
- No fees, rewards, taxes or transaction costs are included.
- Prices are for the same moments and in the same currency.
- The loss is measured against holding both tokens, not against cash.
- Weighted pools and concentrated liquidity follow different formulas and are not modeled.
Frequently asked questions
Is impermanent loss a real loss of money?
It is a shortfall compared with holding. You could still gain overall if the tokens rose or if fees were large. It becomes realized when you withdraw.
Why does the loss look the same for a rise and a fall?
Only the ratio of the two prices matters. A rise by a factor of 2 and a fall to one half are the same ratio change in opposite directions, and the formula gives equal loss.
How large must fees be to cancel the loss?
The page shows the break even fee as a percentage of the pool value. Real fee income depends on trading volume and your share of the pool, which are outside this calculation.
Does this work for stablecoin pairs?
The formula works for any pair in a 50/50 constant product pool. If both prices move together the ratio stays near 1 and the loss is tiny.