Impermanent loss calculator — AMM LP positions

Impermanent loss is a relative performance measure. It compares the value of a 50/50 automated market maker liquidity position with the value of simply holding the same two assets outside the pool. That distinction matters because an LP position contains two different return drivers at once: basic market exposure and the pool’s internal rebalancing process. Looking only at the ending dollar value can hide the fact that part of the result comes from selling some of the outperforming asset and accumulating more of the lagging one as prices move.

This is why impermanent loss is often treated as the hidden cost of providing liquidity. The calculation isolates the structural drag created by constant rebalancing and shows whether the LP position underperformed a passive hold, even if both tokens appreciated in absolute terms. Historically, traders often interpret this as a baseline hurdle rate for the position: fee income and token incentives must first offset that gap before the LP structure adds value relative to holding. Used this way, the metric helps separate pool mechanics from market direction and makes AMM return analysis more comparable across different token pairs.

The calculator uses the two inputs as price multipliers for Token A and Token B. In other words, it reads them as how much each asset changed relative to its starting price, not as position sizes or portfolio weights. From there, it compares two paths that begin from the same initial USD amount: a simple hold of both assets, and a 50/50 liquidity position inside a constant-product AMM. In that AMM structure, the pool automatically rebalances the LP’s token quantities as relative prices change. That rebalancing is the source of impermanent loss. The key variable is not whether prices rose or fell in isolation, but how far apart the two moves are from each other. Because the formula depends on the relative price ratio between the assets, symmetric divergence produces the same impermanent loss in either direction. The calculator then reports the impermanent loss percentage, the implied LP value, the hold value, and the dollar gap between them. That dollar gap is the amount by which the LP position trails a simple hold before adding any fees, rewards, or other protocol-specific offsets.

This calculator is most useful when the goal is to evaluate the baseline economics of a 50/50 constant-product AMM position. Traders often use it before entering a pool to estimate how much price divergence between the paired assets could reduce LP performance relative to simply holding both tokens. It is also useful when comparing pools built around highly volatile assets with pools composed of more correlated pairs, since impermanent loss tends to differ sharply when the two tokens move apart at different rates. In practice, that makes it a quick screening tool for asking whether expected fee yield is likely to compensate for the structural drag created by rebalancing.

Its limits are just as important as its uses. The output does not include trading fees, incentive rewards, gas costs, or protocol-specific bonuses, so it should be read as the rebalancing effect in isolation. It is also less applicable to pools that do not follow the classic model assumed here, including non-50/50 weighted pools, concentrated liquidity ranges, or custom AMM designs with different pricing mechanics. In those cases, the relationship between price movement and LP value can differ materially from the constant-product framework.

Consider a position that starts with $10,000 in a 50/50 AMM pool. Token A doubles, so its price multiplier is 2.0, while Token B is unchanged, so its multiplier is 1.0. A simple hold of the original assets would now be worth $15,000, because half of the starting capital was exposed to the asset that rose 100% and the other half stayed flat. The LP path is different because the pool continuously rebalances as Token A appreciates relative to Token B.

Using the constant-product comparison, the LP relative value factor is calculated as 2 × sqrt(2.0 × 1.0) / (2.0 + 1.0), which is approximately 0.9428. Applied against the hold outcome, that implies an LP position value of about $14,142.86. The difference between the two paths is about -$857.14. Expressed as a percentage, the impermanent loss is about -5.72%. The example shows the core idea clearly: the position still gained in dollar terms, but it underperformed a passive hold because the AMM sold part of the stronger asset into the weaker one as relative prices changed.

A frequent input error is entering raw token prices instead of price change ratios. The calculator expects multipliers that describe how each asset moved from its starting point, so using absolute prices breaks the comparison. Another common misunderstanding is treating impermanent loss as the same thing as a realized loss. It is not. The metric describes relative underperformance versus holding the same assets outside the pool, not necessarily a negative total return in dollar terms.

Users also often overlook what the output excludes. This calculator isolates the structural effect of AMM rebalancing and does not include trading fees, farm rewards, gas, or protocol-specific incentives. That means the result is not a full net-return figure. A further pitfall is applying the formula to pools that do not match the assumed design. Non-constant-product pools, non-50/50 weights, and concentrated liquidity setups can behave differently. Finally, symmetry is often misread. Some assume that one token doubling is fundamentally different from the paired token halving, but for impermanent loss the relevant factor is the relative price ratio. Equivalent divergence produces the same result, regardless of which side moved up or down.

Impermanent loss is closely connected to fee APR because fees are the main mechanism that can offset the structural drag created by AMM rebalancing. In analytical terms, impermanent loss sets a baseline cost, while fee generation determines whether the LP structure can close or exceed that gap over time. This is why pool evaluation often considers both metrics together rather than in isolation.

The concept also overlaps with drawdown analysis. During periods of strong divergence between paired assets, LP value can lag a simple spot hold even when the overall position remains positive in dollar terms. That relative lag is one reason traders track impermanent loss alongside broader portfolio performance. Volatility matters as well, since larger relative price swings increase the rebalancing effect and can deepen LP underperformance. In more advanced pool designs, the picture becomes more complex. Concentrated liquidity, alternative weightings, and custom rebalancing rules can materially change the risk profile compared with a classic 50/50 constant-product AMM. For that reason, impermanent loss in this calculator is best understood as the standard reference case from which more specialized pool mechanics can be compared.