Impermanent Loss Calculator

Enter the initial and current prices of two assets in a liquidity pool to estimate impermanent loss (relative to simply holding the assets outside the pool, excluding fees/rewards). The calculator will provide the impermanent loss as a percentage.

Enter initial and current prices for both assets (same currency), and a pool weight (use 50% for a standard 50/50 pool).

Initial Price of Asset A Initial Price of Asset B Current Price of Asset A Current Price of Asset B

Pool Weight of Asset A (%)

Initial Position Value

Impermanent Loss (%)

LP Portfolio Value (same currency as Initial Position Value)

HODL Value (same currency as Initial Position Value)

Price Ratio r = (A/B)_now / (A/B)_initial

Change in price ratio (A/B) (%)

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Impermanent Loss Formula

The following formula is used to calculate impermanent loss (relative to holding), based on the change in the price ratio between the two assets and the pool weights:

\begin{aligned} r &= \frac{(P_A/P_B)_{\text{current}}}{(P_A/P_B)_{\text{initial}}} = \frac{(P_{A,1}/P_{A,0})}{(P_{B,1}/P_{B,0})} \\ IL &= \frac{r^{w}}{w\cdot r + (1-w)} - 1 \\ \text{For } w=0.5: \quad IL &= \frac{2\sqrt{r}}{1+r}-1 \end{aligned}

Variables:

IL is the impermanent loss as a decimal (e.g., −0.134 = −13.4%). Multiply by 100 to express it as a percentage.
r is the relative price change, defined as (A/B)_current ÷ (A/B)_initial.
w is the pool weight of Asset A (as a fraction from 0 to 1). For a 50/50 pool, w = 0.5.

To calculate impermanent loss, compute the initial and current price ratio P_A/P_B, take their ratio to get r, and then apply the formula above (using your pool weight).

What is an Impermanent Loss?

Impermanent loss occurs when the price of assets in a liquidity pool changes after a liquidity provider has deposited them into the pool. The loss is ‘impermanent’ because it can be recovered if the prices return to their original state at the time of deposit. It is a risk associated with providing liquidity in automated market maker (AMM) platforms.

How to Calculate Impermanent Loss?

The following steps outline how to calculate the Impermanent Loss.

First, determine the initial price of Asset A and Asset B.
Next, determine the current price of Asset A and Asset B.
Compute the initial price ratio (P_A/P_B)_initial and the current price ratio (P_A/P_B)_current.
Compute r = (P_A/P_B)_current ÷ (P_A/P_B)_initial.
Choose the pool weight w for Asset A (for a 50/50 pool, use w = 0.5) and apply the impermanent loss formula.
Use the calculator above to verify your results.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Initial Price of Asset A = $100

Initial Price of Asset B = $200

Current Price of Asset A = $150

Current Price of Asset B = $100

For a 50/50 pool: r = (150/100) ÷ (100/200) = 3, so IL = 2√3/(1+3) − 1 ≈ −0.13397 (≈ −13.40%).