Impermanent Loss Calculator

Introduction

This impermanent loss calculator estimates how an automated market maker (AMM) liquidity position may perform compared with simply holding the same tokens. It supports common pool weights (50/50 like Uniswap v2 and SushiSwap, plus weighted pools like Balancer 80/20 and 95/5) and includes an optional fee/reward APR estimate. Use it to stress-test scenarios such as “Token A doubles while Token B stays flat” or “both tokens move, but at different rates.”

The output focuses on three values: (1) the HODL value at the end prices, (2) the LP value before fees after AMM rebalancing, and (3) the LP value after fees after adding a simple APR-based fee estimate. The difference between LP (before fees) and HODL is the impermanent loss (IL). IL is usually shown as a negative percentage because it represents underperformance versus holding.

How to use: How this calculator works

AMMs maintain a target composition. In a 50/50 pool, the pool continuously trades between the two assets to keep equal value on both sides. When one token outperforms the other, the pool sells some of the winner and buys more of the laggard. That rebalancing is what creates impermanent loss.

• Pool weights: Choose 50/50, 80/20, 95/5, or a custom Token A weight.
• Prices: Enter initial prices (entry) and current/future prices (exit scenario) for both tokens.
• Investment: Enter the total starting value deposited across both tokens.
• APR and time: Add an estimated APR and days in the pool to approximate fee/reward income (simple, non-compounding).

Formula and assumptions

The calculator uses the same JavaScript logic shown in the page source. Conceptually, it computes price changes for each token and compares an LP value ratio to a HODL value ratio. Definitions used in the model:

• Price ratio change for Token A: priceRatioA = currentPriceA / initialPriceA
• Price ratio change for Token B: priceRatioB = currentPriceB / initialPriceB
• Relative ratio: relativeRatio = priceRatioA / priceRatioB (used for the 50/50 closed-form IL)

50/50 pool (constant product approximation)

For a 50/50 pool, the calculator uses the standard impermanent loss relationship based on the relative price ratio R:

Here, R corresponds to the relative ratio change between Token A and Token B (Token A’s move divided by Token B’s move). If Token B is a stablecoin that stays near $1, then R is approximately Token A’s price change.

Weighted pools (constant mean approximation)

For weighted pools, the calculator compares a geometric-style LP ratio to a linear HODL ratio:

• LP value ratio: lpValueRatio = priceRatioA^wA × priceRatioB^wB
• HODL value ratio: hodlValueRatio = wA × priceRatioA + wB × priceRatioB
• Impermanent loss: IL = (lpValueRatio / hodlValueRatio) − 1

Heavier weights (e.g., 80/20 or 95/5) typically reduce IL relative to 50/50 because the pool holds more of the dominant asset and rebalances less aggressively.

Fee income estimate

Fee/reward income is estimated as simple interest (no compounding):

feeIncome ≈ initialInvestment × (APR ÷ 100) × (daysInPool ÷ 365)

Worked example (quick)

Example scenario (similar to the default inputs): you deposit $10,000 into a 50/50 pool labeled ETH/USDC. ETH moves from $2,000 to $3,000 while USDC stays at $1. You assume 25% APR for 365 days.

1. HODL: you keep the original ETH and USDC amounts; ETH’s rise fully benefits you.
2. LP before fees: the AMM sells some ETH into USDC as ETH rises, so you end with less ETH than HODLing; this underperformance is IL.
3. LP after fees: the calculator adds a simple fee estimate (about $2,500 on $10,000 at 25% for one year) to show whether fees offset IL.

Change the future prices, pool weight, APR, or time horizon to see how sensitive the outcome is to volatility and fee levels.

How to interpret results

The results panel reports impermanent loss as a percentage and in dollars, plus a net comparison after fees. A negative “Net vs HODL” means holding would have produced a higher final value under the same end prices. The “Break-Even APR” is the approximate APR required (over the chosen time period) for fees to offset the modeled IL.

Limitations

• Single start/end snapshot: the model compares entry prices to exit prices and does not simulate the path of prices in between.
• APR is assumed constant: real fee APR varies with volume, volatility, and liquidity changes.
• No costs: gas, slippage, and tax considerations are not included.
• Protocol specifics: concentrated liquidity (e.g., Uniswap v3 ranges) and dynamic fee mechanisms are not modeled here.

Practical notes for DeFi LPs

Impermanent loss is not “good” or “bad” by itself—it is the trade-off for earning fees while maintaining a target pool composition. IL tends to be smaller for correlated assets (stablecoin pairs, wrapped/pegged assets) and larger for volatile pairs with strong divergence. If you want more exposure to one asset while still earning fees, consider a weighted pool (like 80/20) or reduce time in pool during high-volatility periods.

Educational reminder: this page is a calculator and not financial advice. Always verify pool mechanics, fee tiers, and reward token risks before providing liquidity.

Deeper guide: understanding impermanent loss in real pools

Many explanations of impermanent loss stop at the headline: “LPs underperform HODL when prices diverge.” That is true, but it is not the whole story. In practice, LP outcomes depend on how prices move, how much volume the pool sees, and what kind pool you are in. This section adds context so you can use the calculator more effectively and avoid common interpretation mistakes.

First, remember what the calculator is comparing. It assumes you start with a fixed dollar investment and split it according to the pool weights. The HODL benchmark is “what if I kept those starting token quantities in my wallet until the end prices?” The LP benchmark is “what if I deposited those tokens and let the AMM rebalance me to maintain the target weights?” The difference between those two end values is the impermanent loss component. Then the calculator adds a simple fee estimate to show a net result.

Why IL happens (intuition without heavy math)

A constant-product 50/50 AMM behaves like an always-on rebalancing strategy. When Token A rises relative to Token B, the pool sells Token A into Token B. When Token A falls, the pool buys Token A using Token B. This is why LPs often say they are “selling the winner and buying the loser.” That behavior can be beneficial in sideways markets (you harvest volatility and earn fees), but it can underperform in strong trends (you reduce exposure to the trending asset).

Weighted pools change the intensity of that rebalancing. In an 80/20 pool, most of the value stays in the 80% asset, so the pool trades less aggressively away from it. That is why weighted pools typically show smaller impermanent loss for the dominant asset’s price moves, at the cost of less diversification and sometimes different fee dynamics.

Reading the break-even APR

The “Break-Even APR” shown in the results is a practical metric: it answers, “Given the modeled price move and the time horizon, what APR would I need so that fees offset the impermanent loss?” If the break-even APR is 18% and you believe the pool can realistically earn 30% APR over the same period, then LPing may outperform HODL in that scenario. If the break-even APR is 120% and the pool’s sustainable fee APR is closer to 10–20%, then the modeled divergence is likely too large for fees to compensate.

Treat break-even APR as a screening tool, not a promise. Real APR changes daily, and rewards can be paid in volatile tokens. If rewards are denominated in a token that declines, the realized return can be much lower than the headline APR.

Scenario library: common “what if” checks

To make the calculator more useful, here are several scenario patterns you can test. Each one corresponds to a real decision LPs face. You can copy these ideas by changing only the price fields, pool type, APR, and days in pool.

• Stable vs stable: Set both tokens to $1 initially and $1 at the end. IL should be near zero; net outcome depends mostly on APR and time.
• One token trends up: Keep Token B flat and increase Token A. This highlights the classic “LP underperforms in a bull run” effect.
• Both tokens rise, but one rises more: Increase both current prices, but make Token A rise faster. IL depends on the relative move, not the absolute move.
• Downtrend stress test: Decrease Token A while Token B stays flat. IL still occurs; you end up with more of the falling asset than HODL would.
• Weighted exposure: Repeat the same price move under 50/50 and 80/20 to see how weighting changes the trade-off between exposure and IL.

Assumptions (expanded, plain language)

This calculator is intentionally simple so it can run quickly in a single page and be easy to audit. That simplicity comes with assumptions that matter when you compare results to a real protocol.

• No path dependency: The model uses only start and end prices. In reality, fees depend on the path because volume and volatility vary over time.
• No compounding: Fee income is treated as simple interest. If you compound (reinvest) fees, the effective return can be higher, but compounding also has costs.
• No range liquidity: Uniswap v3 concentrated liquidity can amplify both fee APR and IL depending on your range and whether you go out of range.
• No pool share changes: The calculation assumes your share of the pool is constant. In real pools, other LPs add/remove liquidity, affecting your fee share.
• No costs or frictions: Gas, bridging, slippage, MEV, and tax are excluded. For small positions, these can dominate outcomes.

Quick checklist before you rely on the result

1. Confirm the pool type: Is it truly 50/50, or is it weighted? If it is concentrated liquidity, treat this calculator as a rough baseline only.
2. Use realistic APR: Prefer fee APR based on recent volume/TVL rather than promotional APY. If rewards are in a volatile token, discount them.
3. Match the time horizon: If you plan to LP for 14 days, do not use 365 days. Short horizons can make fees too small to matter.
4. Stress-test multiple price outcomes: Try a mild move, a strong move, and an adverse move. If the strategy only works in one narrow case, it is fragile.
5. Remember risk outside the math: Smart contract risk, depegs, and oracle issues can overwhelm any modeled IL/fee trade-off.

With those caveats in mind, the calculator is a useful way to build intuition: it shows how pool weights, relative price moves, APR, and time interact. If you want to keep the page open as a reference, consider bookmarking it and saving a few scenarios (for example, “base case,” “bull case,” and “bear case”) by writing down the inputs you used.