Estimate impermanent loss before you add liquidity

Estimate impermanent loss by comparing what your liquidity position could be worth after a price change with what the same tokens would be worth if you simply held them. The estimate helps show the price risk before you commit funds. It does not predict future prices or count fees, gas costs or other risks.

For a standard 50/50 pool, the calculation starts with the change in one token’s price relative to the other. Byreal’s guide to choosing when to swap or supply liquidity gives more context on that decision; the estimate here focuses on the price effect.

What does impermanent loss compare?

Impermanent loss compares your share of the pool with holding the same starting tokens outside it. In a constant-product pool, a pool design that keeps the two token balances’ product roughly constant, trades change the amounts you own. When one token rises against the other, arbitrage traders buy it from the pool until its price aligns with the wider market. Your position then holds less of the rising token and more of the other one.

That shift can leave the pool position worth less than holding the original tokens. The difference is called impermanent loss. It is a comparison, not necessarily a cash loss: the gap can shrink if prices move back, and fees may offset it. The word “impermanent” does not mean the gap will disappear.

How do you estimate the price effect?

For a 50/50 constant-product pool, let r be the ending price of one token relative to the other, divided by its starting relative price. The pool’s value, compared with holding both tokens, is 2 × √r ÷ (1 + r). Subtract that result from 1 to get the estimated loss as a share of the hold value.

For example, if one token doubles against the other, r is 2. The formula gives a pool value about 94.3% of the hold value, or an estimated 5.7% loss before fees. If the token instead halves, the estimate is also about 5.7%. This symmetry applies to the relative price ratio in this pool model.

To use the estimate before adding liquidity:

• Record the current relative price of the pair.
• Choose possible ending prices, such as a rise, a fall or no change.
• Divide each possible ending price by the current price to get r.
• Apply the formula to each case and compare the result with likely fees and costs.

When does this estimate stop fitting?

This formula is a useful first check for a full-range, 50/50 constant-product pool. It does not describe every pool. A concentrated-liquidity position, where funds are assigned to a chosen price range, can hold different token proportions and may become one-sided if the price leaves that range. Use the pool’s own position details or a calculator built for its design.

The formula also leaves out trading fees. Fees depend on trading activity and your share of the pool, so they are hard to know in advance. Compare them with the estimated price gap, then include transaction costs in your own calculation. For most readers, running several price scenarios is more useful than treating one forecast as certain. Use the result to understand the trade-off: liquidity can earn fees, while a price move can make the position lag behind simply holding the tokens.