Introduction to AMM impermanent loss
Impermanent loss is the difference between the ending value of an automated market maker liquidity-provider position and the value of simply holding the tokens originally deposited. It is not a fee removed from a wallet. Instead, it is the opportunity cost created when an AMM automatically trades one token for the other to keep its pool price aligned with the market. This calculator makes that comparison explicit for a price scenario, a pool weight, an investment amount, and a simple estimate of fee income.
Relative prices are the important input. If Token A and Token B both double from their entry prices, their relative price is unchanged and the modeled impermanent loss is zero. If one token rises while the other stays flat, the pool sells part of the winner during arbitrage. A holder keeps all of the winner, whereas the LP ends with a rebalanced mix. The result panel keeps the HODL benchmark, LP value before fees, estimated fees, and final net comparison separate so that each part of the trade-off remains visible.
“Impermanent” describes the fact that this particular divergence can shrink if the relative price later returns to its entry level. It does not promise that an LP can exit without a loss, and it does not describe every risk of supplying liquidity. Once a position is withdrawn while prices remain apart, the comparison with HODL is realized for that exit decision. In practical terms, the question is not whether the label sounds temporary; it is whether expected trading income, rewards, and any other benefits adequately compensate for the portfolio rebalancing that occurred.
This page treats Token A and Token B as a pair of dollar-priced assets only to make the scenario easy to read. The same logic applies when a pool is quoted in another unit. What matters is the change in one asset relative to the other. A stablecoin can simplify the example, but it is still an asset with its own price, redemption, and depeg risks. Enter the values that match the pool and the withdrawal scenario you actually want to test.
How to use the impermanent loss calculator
Choose the actual pool design first. A 50/50 pool starts with equal value in each asset; 80/20 and 95/5 pools place more initial value in Token A. Enter the two entry prices and the prices you want to test at withdrawal. The total investment determines the initial quantities. Finally, enter a conservative annual fee and reward estimate plus the number of days in the pool. Press Calculate Impermanent Loss to compare the modeled LP against retaining those initial quantities outside the pool.
Token labels are for readability only. Prices and investment are expressed in dollars, APR is an annual percentage, and days are calendar days. The fee calculation is simple interest on the original investment, not a forecast of changing volume, compounding, reward-token prices, or retained swap fees. Testing several relative-price moves is generally more useful than relying on a single optimistic outcome.
A useful workflow is to begin with the entry prices recorded when liquidity was supplied, then run a modest move, a large Token A move, and a large Token B move. For each case, inspect the relative price ratio and the LP value before fees before looking at the final net number. This order prevents a high advertised APR from obscuring how much portfolio divergence the scenario creates. If a pool has a custom weight, use its published normalized weights rather than rounding them to a familiar allocation.
The investment field is the combined entry value, not the amount of only one token. For example, a $10,000 50/50 position begins with approximately $5,000 of each asset. An 80/20 Token A/Token B pool begins with approximately $8,000 of Token A and $2,000 of Token B at the stated entry prices. The calculator uses those starting quantities to construct the fair HODL comparison, so the benchmark always matches the portfolio that entered the AMM.
Impermanent loss formulas for 50/50 and weighted pools
Plain-text formulas: 50/50 impermanent loss = 2 × sqrt(R) / (1 + R) − 1; fee income = investment × APR / 100 × days / 365.
A traditional constant-product pool holds reserves x and y whose product is k. Arbitrage moves reserves along this curve as the external market price changes.
For an equal-weight pool, let R be Token A’s price ratio divided by Token B’s price ratio. The formula below is always zero at R = 1 and otherwise negative. A twofold relative move in either direction produces the same percentage gap.
Weighted pools use a weighted geometric AMM value ratio divided by the weighted linear HODL ratio. Here r is each token’s price ratio and w is its starting pool weight.
The calculator layers a deliberately simple fee estimate over that price result. APR is entered as a percentage, so 25 means 25% per year.
These formulas compare values at the endpoints, not a chart’s day-to-day path. The AMM rebalances continuously in a live market, while this model uses the ending price relationship to express the resulting difference. That is why the calculation is well suited to transparent what-if analysis: it answers how the ending allocation compares with holding the original quantities under the stated assumptions. It does not claim to reproduce every swap, fee tier, or contract rule used by a particular protocol.
Worked example: ETH rises from $2,000 to $3,000
Suppose $10,000 enters a 50/50 ETH/USDC pool. Half buys 2.5 ETH at $2,000 and half represents 5,000 USDC. If ETH reaches $3,000 while USDC remains $1, the HODL benchmark is $12,500. The relative ratio R is 1.5. The 50/50 formula returns about −2.02%, so the LP value before fees is roughly $12,247.45 and the gap is about $252.55.
If the position earns a constant 25% APR for 365 days under this page’s simple assumption, estimated fees are $2,500. The fee-adjusted LP total is then about $14,747.45, ahead of the $12,500 HODL benchmark. That does not mean a live pool will pay that amount: realized returns depend on volume, liquidity share, incentives, price paths, and costs. The break-even APR of about 2.53% only says what simple rate would offset this modeled gap over this exact duration.
Now consider the same price change in an 80/20 ETH/USDC pool, with ETH as Token A. The starting HODL portfolio contains more ETH, so it has greater directional ETH exposure than the 50/50 example. It also has a different rebalancing profile because the pool weight is different. This illustrates an important comparison rule: a weighted pool should be measured against holding its own entry allocation, not against a separate 50/50 wallet. A smaller impermanent-loss percentage may accompany a portfolio that intentionally took more or less exposure to the volatile asset.
Interpreting LP value, HODL value, and break-even APR
A negative impermanent-loss percentage means the AMM position before fees is worth less than holding the starting quantities. Net versus HODL adds the entered fee estimate to that LP value. A positive net result therefore means assumed income exceeded the modeled divergence gap, not that impermanent loss vanished. Break-even APR is a stress-test threshold: it is the annual simple rate on the initial investment needed to cover the dollar gap during the selected days.
Read the result as a set of related measures rather than a single verdict. HODL value answers what the original deposited quantities would be worth. LP value before fees answers what the simplified AMM rebalanced position would be worth. Estimated fee income is an assumption entered by the user, and net versus HODL combines those components. When the net figure is negative, the scenario’s assumed income did not cover the modeled gap. When it is positive, the entered income estimate did cover it under the model, but future fee generation remains uncertain.
Break-even APR becomes especially useful when comparing durations. A small dollar gap over a short holding period can require a high annualized rate to offset it, while the same gap spread across a longer period needs a lower annual rate under simple interest. Do not interpret that number as a promised yield target. Instead, use it to ask whether the pool’s historical fees, emissions, and your expected share make the required rate plausible after costs and risks.
Limitations of this impermanent loss model
This calculator uses entry and ending prices, so it cannot model the route between them or the changing trading volume that generates fees. It does not include gas, slippage, MEV, taxes, depegs, smart-contract risk, changing liquidity share, range orders, dynamic fees, or protocol-specific mechanics. Concentrated-liquidity positions can behave very differently when price leaves their range. Use real pool weights and a defensible fee assumption, and treat this output as a transparent baseline rather than a forecast.
APR deserves particular caution. A dashboard rate may combine swap fees with temporary token incentives, may be based on a short lookback window, or may change as liquidity joins and leaves the pool. A reward token can fall in price even if its token count is earned as projected. Likewise, an LP’s share of a pool can change through deposits, withdrawals, compounding choices, or protocol rules. The simple estimate here intentionally does not hide these uncertainties behind a more elaborate-looking forecast.
Pool type also matters. The 50/50 relationship is a convenient standard model, whereas weighted AMMs use the weights shown in the form. Stable-swap curves, concentrated liquidity, lending-linked pools, rebasing tokens, transfer-fee tokens, and pools with asymmetric or dynamic logic may not match these formulas. Before making a decision, review the pool’s documentation and consider testing both adverse price moves and a lower fee estimate.
Impermanent loss questions for AMM liquidity providers
Does impermanent loss disappear when the relative price returns?
In this simplified ending-value model, yes. When the relative price returns to its entry ratio, the modeled LP-versus-HODL gap returns to zero. Fees earned along the route remain separate income. A real position can still have incurred transaction costs, changed liquidity share, or protocol-specific effects that this endpoint model does not include.
Why can a weighted pool have less impermanent loss?
A weighted pool starts with more exposure to its dominant asset and rebalances less aggressively away from it. It also represents a different portfolio, so it should be compared with the pool’s real allocation rather than selected only for a favorable result. Weighting changes the trade-off; it does not make price risk disappear.
Are fees included in the impermanent-loss percentage?
No. The impermanent-loss percentage compares LP value before fees with the matching HODL value. The calculator then estimates fee income separately and shows net versus HODL. Keeping them separate makes it easier to distinguish portfolio divergence from the return assumption used to offset it.
What price should be entered for a stablecoin?
Use the price you want to test, including any potential depeg scenario. Entering $1 at both dates assumes the stablecoin holds its peg in the model. If its market price changes, that changes the relative price and the HODL benchmark just as it would for any other token.
LP Drift mini-game: manage divergence and fees
LP Drift is an optional timing challenge based on the same relative-price idea as the calculator. Guide the liquidity beacon by moving your pointer or finger. Collect green fee pulses when they appear inside the bright safe band, but avoid amber divergence waves outside it. Every 20 seconds the market becomes more volatile, shrinking the band and increasing both possible fees and impermanent-loss risk. It does not change your calculator result.
Best score is saved on this device. Educational takeaway: larger relative-price moves increase the LP-versus-HODL gap faster than a fixed fee assumption can reliably offset it.