Impermanent Loss Calculator

Impermanent loss (IL) is one of the most important concepts for anyone participating in decentralized finance (DeFi) as a liquidity provider (LP). When you deposit assets into an automated market maker (AMM) pool, such as those on Uniswap, SushiSwap, or Curve, you are exposed to a specific type of risk: your portfolio value inside the pool may be lower than it would have been if you had simply held the same assets in your wallet. This difference is called impermanent loss.

How AMMs Work

Automated market makers use mathematical formulas to price assets and facilitate trades without a traditional order book. The most common model, popularized by Uniswap v2, uses the constant product formula: x times y = k, where x and y are the quantities of two tokens in a pool, and k is a constant. When traders buy one token, they add the other token to the pool, adjusting prices until equilibrium is restored.

As a liquidity provider, you deposit an equal value of both tokens into the pool and receive LP tokens representing your share. In exchange, you earn a portion of the trading fees generated by the pool. However, every time the price ratio between the two tokens changes, arbitrageurs rebalance the pool, which changes the quantities of each token you hold, and this is where impermanent loss arises.

The Impermanent Loss Formula

The impermanent loss for a standard constant product AMM pool is calculated using the formula: IL = 2 times the square root of r, divided by (1 + r), minus 1, where r is the price ratio (current price divided by initial price). This formula captures the divergence loss that occurs purely from price movement, regardless of which direction the price moves.

Importantly, impermanent loss is symmetric with respect to direction. Whether the price doubles or halves, the IL is the same magnitude. A 2x price increase produces approximately 5.7% IL. A 4x increase produces approximately 20% IL. A 5x move results in roughly 25.5% IL.

Why Is It Called Impermanent?

The loss is described as impermanent because it only crystallizes when you withdraw your liquidity from the pool. If the price of the token returns to its original value relative to the paired asset, the impermanent loss disappears entirely. This is why some liquidity providers choose to wait out price volatility rather than withdrawing during unfavorable price moves.

However, if you withdraw at any point when the price ratio differs from when you deposited, the loss becomes permanent. This is a key distinction that many new DeFi participants overlook.

Fee Income vs. Impermanent Loss

Impermanent loss is not the only factor determining whether providing liquidity is profitable. Every trade through the pool generates fees, which are distributed proportionally to LPs. On pools with high trading volume, fee income can more than compensate for impermanent loss.

For example, a pool charging a 0.3% fee on every trade may generate substantial returns for LPs if the pool sees millions of dollars in daily volume. The profitability of LP positions depends on the balance between fee APR and the magnitude of impermanent loss from price divergence. Stablecoin-to-stablecoin pools tend to have low IL (since prices rarely diverge significantly) but also lower fee income. Volatile token pairs have higher potential fee income but also higher IL risk.

Impermanent Loss in Different AMM Designs

While the standard constant product formula is the most common, different AMM designs handle impermanent loss differently. Curve Finance uses a hybrid formula designed to minimize IL for assets that are expected to trade at near-equal prices, such as stablecoins or wrapped versions of the same asset. Balancer allows pools with more than two assets and different weightings, which changes the IL profile. Uniswap v3 introduced concentrated liquidity, allowing LPs to provide liquidity within specific price ranges, which can increase fee efficiency but also creates new complexity around managing positions.

Some protocols have attempted to mitigate IL through divergence loss protection or single-sided liquidity mechanisms. These designs often introduce other trade-offs and risks, so it is important to understand the specific mechanics of any pool before committing funds.

DeFi Risks Beyond Impermanent Loss

Impermanent loss is just one of many risks in DeFi liquidity provision. Smart contract risk is significant: bugs or exploits in the AMM code can result in the loss of all deposited funds. Several major DeFi protocols have been drained by hackers exploiting vulnerabilities in their smart contracts. Rug pulls, where project developers abandon a protocol and take user funds, have cost investors billions of dollars.

Token price risk is compounded in DeFi because you hold two assets simultaneously. If both tokens decline in value, your portfolio loses value from both the price decline and impermanent loss. Always research thoroughly and only commit funds you can afford to lose.

Using the Calculator

This calculator uses the standard constant product formula to estimate impermanent loss for a 50/50 AMM pool. Enter the initial token price when you deposited, the current token price, and the total value of your initial investment. The calculator then shows your estimated IL percentage, what your portfolio would be worth if you had simply held the tokens, what it is currently worth inside the LP pool, and the dollar difference between the two.

The results assume a simple 50/50 pool and do not account for fees earned, gas costs, or other protocol-specific mechanics. Use the results as a directional estimate to understand the magnitude of your IL exposure, not as a precise accounting of your actual returns.