Impermanent Loss Calculator
Compare a weighted liquidity position with holding the same two assets as their prices change. See the modeled pool value and relative underperformance before fees.
How the model works
Enter the percentage price change for each asset from a shared starting point, Asset A’s pool weight, and a starting position value. The remaining pool weight belongs to Asset B.
The holding comparison applies the two price factors to the starting weights without rebalancing. The modeled pool factor is the weighted geometric mean of those price factors, as in an ideal weighted product pool with arbitrage keeping the target weights in balance.
The displayed underperformance compares the modeled pool factor with the holding factor. It is a relative difference, not a claim that either position lost money. Both modeled values can rise or fall from the starting value.
The calculation uses the ending price changes only. It does not model the route prices took between the start and end, trading fees, rewards, gas, or a specific protocol’s implementation.
Step by step
- Enter both assets’ price changes from the same starting point.
- Set Asset A’s starting pool weight and the starting position value.
- Compare the holding value, modeled pool value, and relative difference.
Worked example
Start with a position valued at 1,000 in the displayed currency. Set the pool weights to 50% Asset A and 50% Asset B, then enter a 100% price increase for Asset A and no change for Asset B. The holding factor is 1.5, so the holding value is 1,500.
The weighted product factor is √2, about 1.414214, so the modeled pool value is about 1,414.21. Relative underperformance is about 5.7191%. With an 80% Asset A weight under the same price changes, the factors are 1.8 held and 2^0.8 ≈ 1.741101 pooled, for about 3.2722% relative underperformance.
When to use this calculator
Use it to compare an ideal weighted pool position with holding the same two assets under specified endpoint price changes and weights.
Change one assumption at a time to see how the modeled relative difference changes. Check the pool’s actual design and fee terms separately before applying this simplified model.
Common interpretation errors
Do not treat the output as the percentage decline of the pool or as a forecast. It measures pool value relative to the specified holding comparison; either value may be above or below the starting value.
Do not add fee or reward income to the result. Those amounts are not modeled. A return of prices toward their starting ratio does not guarantee that a real liquidity position will recover its costs or value.
Formula and assumptions
a = 1 + Asset A price change / 100
b = 1 + Asset B price change / 100
w = Asset A pool weight / 100
Hold factor = w × a + (1 − w) × b
Pool factor = a^w × b^(1 − w)
Relative underperformance = (1 − Pool factor / Hold factor) × 100%
This is an ideal full range weighted product model. The pool factor uses the weighted geometric mean; the hold factor uses the weighted arithmetic mean. Position values equal each factor multiplied by the starting value.
Scope and limitations
This ideal full range weighted product model assumes positive ending price factors and arbitrage that maintains the selected pool weights. It does not represent concentrated liquidity, fees, rewards, gas, taxes, slippage, deposits, withdrawals, or a particular protocol. Impermanent loss describes relative underperformance against holding in this model and does not guarantee recovery. The calculation has no intermediate price path, so real pool results can differ.
Key terms
- Price factor
- The ending asset price divided by its starting price, written as one plus the entered percentage change.
- Pool weight
- The share of the modeled pool assigned to an asset at the starting point. Asset B receives one minus Asset A’s weight.
- Relative underperformance
- The modeled pool factor compared with the value factor from holding the starting weighted asset mix, expressed as a percentage of that holding value.
Compare related calculations
This calculator isolates the effect of the two endpoint price changes and the selected pool weights. It does not estimate fee income or total liquidity provider returns.
For a broader comparison, model token prices, fees, and other costs with separate inputs from the relevant pool or protocol. Do not assume another calculator’s yield estimate applies to this position.
FAQ
What does the percentage compare?
It compares the modeled weighted product pool value with the value of holding the same starting asset mix at the entered ending prices. It is not the pool’s percentage loss from its starting value.
How does the pool weight affect the result?
Asset A’s weight sets its exponent in the weighted product factor and its share in the holding factor. Asset B receives the remaining weight. The model requires both weights to be above zero.
Why is the 50/50 example about 5.7191%?
When Asset A doubles and Asset B is unchanged, the 50/50 holding factor is 1.5 and the pool factor is √2. The pool factor is about 5.7191% below the holding factor, before fees and other costs.
Does the result include trading fees or rewards?
No. The comparison models price factors and pool weights only. Fees, incentives, gas, and other costs or income are excluded.
Does this model cover concentrated liquidity?
No. It models an ideal full range weighted product position. Concentrated liquidity changes exposure when prices move through or outside a selected range.
Related tools
This calculator compares two modeled position values under endpoint price changes. Analyze protocol fees, token rewards, and other costs separately using inputs for the pool you are evaluating.