Impermanent Loss Calculator

The Impermanent Loss Calculator helps liquidity providers compare potential impermanent loss against simply holding their crypto assets in volatile markets.

About the Impermanent Loss Calculator

The Impermanent Loss Calculator estimates how much value you give up by providing liquidity instead of simply holding your tokens. It models common AMM scenarios where token prices move in different directions and the pool continually rebalances your position. The result is shown as a percentage loss or gain relative to holding.

Impermanent loss is called “impermanent” because it can shrink or disappear if prices return to their original levels. But if you withdraw your liquidity while prices are far from your entry levels, that loss becomes permanent. The calculator helps you see that trade-off ahead of time rather than after the fact.

This tool focuses on constant product AMMs such as Uniswap v2–style pools with 50/50 asset weighting. It assumes no slippage from your own trades and that the pool is large enough that your position does not move the price by itself. You can still use it for other pools, but treat those results as rough guidance rather than precise forecasts.

How to Use Impermanent Loss (Step by Step)

Use impermanent loss estimates as a planning tool, not a single number you blindly follow. Think of the loss as the “hidden cost” of earning trading fees or farming rewards in a liquidity pool. By walking through structured steps, you can judge whether that cost is acceptable for your strategy and risk tolerance.

• Define the pool: which two tokens you will deposit, and the initial price between them.
• Set realistic price ranges for both tokens, including best-case, base-case, and worst-case scenarios.
• Run the Calculator for several target price outcomes, not just one, to see a range of potential impermanent loss values.
• Compare the estimated loss against expected trading fees and any token rewards under the same assumptions.
• Decide whether to proceed, size down, or skip the pool based on the trade-off between potential returns and possible loss.

Repeat this process each time market conditions change or incentives shift. Over time you will treat impermanent loss like any other cost, such as volatility or gas fees, and factor it into your overall portfolio plan.

Impermanent Loss Formulas & Derivations

Impermanent loss in a simple 50/50 constant-product AMM can be expressed with a compact formula. The key idea is that your pool position automatically rebalances as prices move, so you end up holding a different mix of tokens compared with just holding your original amounts. The formula compares those two outcomes at the same final price.

• Let the initial price of token A in terms of token B be ( P_0 ), and the final price be ( P_1 ). Define the price ratio ( r = frac{P_1}{P_0} ).
• In a 50/50 constant-product pool, your position value after the price move is proportional to ( sqrt{r} times frac{2}{1 + r} ) relative to holding.
• The standard impermanent loss formula (as a fraction of simply holding) becomes: ( text{IL} = 1 – frac{2sqrt{r}}{1 + r} ).
• To express this as a percentage, multiply by 100: ( text{IL%} = left(1 – frac{2sqrt{r}}{1 + r}right) times 100% ).
• If both tokens move in the same direction versus a third asset like USD but keep their ratio constant, then ( r = 1 ) and ( text{IL} = 0 ). The loss appears only when the relative price between the two assets changes.

The Calculator hides the math but uses these relationships under the hood. It can also extend them for custom weightings, like 80/20 pools, by using generalized formulas for constant-product AMMs. When you understand how the ratio ( r ) drives results, you can quickly estimate rough impermanent loss even without detailed calculations.

Inputs and Assumptions for Impermanent Loss

The Impermanent Loss Calculator depends on clear input choices and explicit assumptions. To get meaningful results, you should enter numbers that match your realistic expectations, not just perfect scenarios. Most inputs are in simple units you probably already track, such as prices in dollars or token ratios.

• Initial price ratio: the starting exchange rate between the two tokens when you add liquidity.
• Final price ratio or target prices: your projected future prices, either relative to each other or in a common unit like USD.
• Pool type and weight: whether the AMM is 50/50, 80/20, or another ratio that affects how your position rebalances.
• Investment size: the total value you plan to supply, so the calculator can show absolute dollar losses, not just percentages.
• Fees and rewards (optional): estimated trading fee APR and incentive yields, used to compare against the modeled impermanent loss.

Be careful with extreme ranges, such as 90% price crashes or 10x rallies, because they can push the simple formulas to edge cases. The math still works, but your real-world outcome may differ due to slippage, liquidity depth, or protocol-specific rules. Use wide-range scenarios to test sensitivity, then focus on the middle band where prices are more likely to end up.

Step-by-Step: Use the Impermanent Loss Calculator

Here’s a concise overview before we dive into the key points:

1. Select the pair of tokens and the AMM pool type that most closely matches where you plan to provide liquidity.
2. Enter the initial prices or the initial price ratio at the time you expect to deposit your tokens.
3. Input your projected future prices or the target final price ratio you want to test.
4. Specify your investment size and, if available, the expected fee APR and any liquidity mining rewards.
5. Run the Calculator to generate estimated impermanent loss, both as a percentage and as an absolute value.
6. Review the results alongside your expected fees and rewards to gauge net potential gain or loss.

These points provide quick orientation—use them alongside the full explanations in this page.

Worked Examples

Imagine you deposit $5,000 of ETH and $5,000 of USDC into a 50/50 ETH/USDC pool when ETH trades at $2,000. After some time, ETH doubles to $4,000 while USDC stays at $1. The price ratio between ETH and USDC has moved from 2,000 to 4,000, so ( r = 2 ). Plugging into the formula, impermanent loss is about 5.72%, meaning your LP position is worth roughly 5.72% less than if you had simply held ETH and USDC in your wallet at the new prices. What this means

Now consider a more volatile case: you deposit equal values of a blue-chip token and a highly volatile governance token in a 50/50 pool. Suppose the governance token falls by 60% relative to the blue-chip token over the period you are in the pool. The price ratio might shift such that ( r = 0.4 ), leading to an impermanent loss of around 13.4%. Even if you earn trading fees, your final outcome may still trail simple holding unless volume and fee rates are very high. What this means

Accuracy & Limitations

The Impermanent Loss Calculator is built to simplify complex AMM behavior into manageable scenarios. It uses stable formulas and clear assumptions, but it cannot reflect every detail of live markets. Treat it as a planning and comparison tool rather than an exact predictor of your future portfolio value.

• It assumes constant-product AMMs and may not accurately model concentrated liquidity or dynamic fee structures.
• It ignores slippage from your own deposits and withdrawals, which can matter in small or illiquid pools.
• It uses point estimates for prices and does not simulate full price paths or intraday volatility.
• It does not include smart contract risk, oracle failures, or protocol-specific quirks like withdrawal fees.

Because of these limits, always cross-check Calculator outputs with other risk tools and your own judgment. Use conservative assumptions, especially for volatile tokens or experimental pools, and avoid committing funds you cannot afford to see fluctuate. The Calculator helps you ask better questions; it does not remove uncertainty.

Units & Conversions

Units matter when you measure impermanent loss because AMM pools often quote prices in ratios rather than in dollars. You might think in terms of USD, while the pool rebalances based on token-to-token exchange rates. Understanding how to move between these units keeps your scenarios consistent and prevents misreading the Calculator’s ranges.

Use the table as a quick reference when setting up inputs. Keep all your prices in the same base currency, such as USD, before converting to ratios. When you read results, remember that a small percentage loss on a large position size can still be a significant dollar amount.

Tips If Results Look Off

If the Calculator output seems strange, treat it as a signal to review your assumptions and units. Many surprising results come from mixing price bases, entering ratios backward, or testing unrealistic ranges without noticing. A short checklist can help you catch these issues early.

• Check that your initial and final prices both use the same base currency.
• Confirm that the price ratio is entered as “final divided by initial,” not the other way around.
• Review your pool type and weighting to ensure it matches the actual protocol.
• Run a milder scenario first, such as a 20% price move, and see if the result behaves as expected.

If results still look inconsistent, test a known example from a trusted article or documentation and compare numbers. That helps you see whether the issue is with your input choices or your understanding of how the AMM behaves. When in doubt, err on the side of assuming higher risk and lower net yield.

FAQ about Impermanent Loss Calculator

Is impermanent loss always bad?

Impermanent loss is a cost, but it is not always a deal-breaker. If trading volume is high and fees or rewards are strong, your net outcome can still beat simple holding even after accounting for impermanent loss.

Can the calculator show negative impermanent loss?

In some unusual scenarios, especially with non-50/50 weightings or asymmetric moves, your liquidity position can outperform holding, leading to what looks like “negative” impermanent loss, though it is better thought of as an excess gain.

How often should I rerun my scenarios?

Rerun the Calculator whenever market conditions change significantly, such as large price swings, new reward programs, or updated fee structures, so your assumptions stay aligned with reality.

Does the calculator work for concentrated liquidity like Uniswap v3?

The basic formulas were designed for full-range pools, so you can use them as a rough guide, but concentrated liquidity requires more advanced modeling and may give very different real-world outcomes.

Glossary for Impermanent Loss

Automated Market Maker (AMM)

An AMM is a type of decentralized exchange that uses liquidity pools and formulas, rather than traditional order books, to set token prices and execute trades.

Liquidity Pool

A liquidity pool is a shared pot of two or more tokens locked in a smart contract, which traders use to swap between assets while paying fees to liquidity providers.

Liquidity Provider (LP) Token

An LP token represents your share of a liquidity pool, including both your initial deposit and your portion of accumulated trading fees.

Impermanent Loss

Impermanent loss is the difference in value between providing liquidity to a pool and simply holding the same tokens, measured at the same final prices.

Constant-Product Formula

The constant-product formula, often written as x·y = k, keeps the product of token reserves fixed and determines how AMM pools rebalance as trades happen.

Price Ratio

The price ratio is the relative price of one token against another, used to calculate how much the pool must rebalance and how much impermanent loss occurs.

Slippage

Slippage is the difference between the expected trade price and the actual execution price, often caused by limited liquidity or large order sizes.

APR (Annual Percentage Rate)

APR is the yearly interest or yield rate, without compounding, used to compare expected rewards from fees and incentives against potential impermanent loss.

Sources & Further Reading

Here’s a concise overview before we dive into the key points:

• Uniswap v2 whitepaper – Original description of constant-product AMMs and liquidity provision mechanics.
• Bancor: Impermanent Loss Explained – Detailed walkthrough of how impermanent loss arises and why it matters.
• Binance Academy: Impermanent Loss Explained – Beginner-friendly explanation with clear examples and diagrams.
• Balancer Docs: Impermanent Loss – Technical notes on impermanent loss in multi-asset and weighted pools.
• Paradigm Research on AMM Price Impact – Deeper mathematical treatment of AMM behavior and price dynamics.

These points provide quick orientation—use them alongside the full explanations in this page.