What is impermanent loss?
Impermanent loss (IL) is the gap between holding two tokens inside a liquidity pool and simply holding them in your wallet. When you provide liquidity to an automated market maker (AMM) such as Uniswap, your deposit is split across the two tokens and the protocol constantly rebalances it as prices move — quietly selling whichever token is rising and buying whichever is falling to keep the pool balanced. When the two prices diverge, that automatic rebalancing leaves you with less total value than if you had never deposited. It is called "impermanent" because the loss only becomes real when you withdraw; if prices drift back to where you entered, it shrinks back toward zero.
One point that trips people up: impermanent loss is measured relative to holding, not relative to your starting dollars. Your LP position can still be up in absolute terms during a bull market and also show impermanent loss, because holding the tokens outright would have made you even more. By definition IL is always zero or negative — it is a comparison, not your total profit and loss.
The impermanent loss formula (Uniswap V2 / 50-50 pools)
For a standard constant-product pool the loss depends only on the relative price change between the two tokens:
IL = 2 · √k / (1 + k) − 1
where k is the ratio of how much one token's price moved relative to the other (for a token paired with a stablecoin, k is just the token's price multiple). Some reference points computed by this tool:
| Relative price change | Impermanent loss |
|---|---|
| 1.25× | −0.62% |
| 1.5× | −2.02% |
| 2× | −5.72% |
| 3× | −13.40% |
| 5× | −25.46% |
The loss is symmetric: a token halving (0.5×) produces the same −5.72% as a doubling (2×), because only the ratio matters, not the direction.
Worked example: ETH/USDC on Uniswap V2
Suppose you deposit $2,000 into an ETH/USDC V2 pool: $1,000 of ETH at $1,000 (1 ETH) and $1,000 of USDC. ETH then doubles to $2,000 — a 2× relative move against USDC. If you had simply held, your bag would be worth 1 × $2,000 + $1,000 = $3,000. Inside the pool, the constant-product formula rebalances you to roughly 0.707 ETH and $1,414 USDC, worth about $2,828. That $172 shortfall is −5.72% of the HODL value — exactly what the formula predicts. Enter these numbers above (deposit $2,000, ETH +100%, USDC 0%) and you will see the same result.
Why Uniswap V3 impermanent loss is worse
Uniswap V3 lets you concentrate your liquidity into a chosen price range instead of spreading it across all prices from zero to infinity. Inside that range your capital is far more efficient, so you earn many times more fees per dollar. The trade-off is that impermanent loss is amplified — typically around 2 to 4× the V2 loss for a moderate range, and much higher for a tight range. Rather than quote a fixed multiple, this calculator computes your exact multiplier for the range you set, and shows it next to the result.
There is a second effect V2 never has: if price moves outside your range, your position converts entirely into the losing asset and stops earning fees altogether until price comes back. On the chart above you can see this as the flat "tails" beyond your range bounds.
Worked example: ETH/USDC ±50% range on Uniswap V3
Take an ETH/USDC V3 position with a range of roughly ±50% around entry (about a [0.5×, 2×] band). If ETH doubles — reaching the top of your range — the impermanent loss is about −19.5%, roughly 3.4× the −5.72% a V2 position would suffer for the same move. Tighten the range and the loss grows further; widen it and the loss falls back toward the V2 curve. Switch to the Concentrated (V3) tab, set the bounds to −50% and +100%, and the tool reproduces this figure along with the dollar impact.
Do trading fees offset impermanent loss?
This is the question that actually decides whether providing liquidity was worth it — and most calculators ignore it. You come out ahead only if the fees and rewards you earn exceed your impermanent loss. Enter your pool's fee/reward APR and how long you stayed in, and the tool shows the net result plus the break-even APR: the annualized fee yield that would exactly cancel the IL over that period. If the pool's real APR is comfortably above the break-even, liquidity provision made sense; if not, holding would have beaten it.
Fees here are estimated on your position's value (the HODL benchmark), and the break-even APR is the annualized fee yield that exactly offsets this IL over the period you entered. It is scale-invariant, so the percentage is the same whether you deposit $100 or $100,000.
Uniswap V2 vs V3: which should an LP choose?
Neither is universally better — it depends on how much you expect the pair to move and how actively you can manage the position. V2 (or a very wide V3 range) is lower-maintenance and lower-IL, suited to volatile or unpredictable pairs you would be happy holding anyway. A tighter V3 range multiplies both your fee income and your impermanent loss, and demands active management — you must re-center the range when price drifts, or accept sitting one-sided and fee-less. The sweet spot for most LPs is a range wide enough to stay in most of the time, on a high-volume pair whose fee APR clears the break-even shown above.
How to choose a Uniswap V3 price range
- Match the range to the pair's volatility. Stable or highly-correlated pairs (USDC/DAI, ETH/stETH) can use very tight ranges safely; volatile pairs need wider ranges to avoid constantly falling out.
- Wider ranges = lower IL, fewer fees per dollar. Narrow ranges = more fees while in range, but larger IL and a real risk of going one-sided.
- Factor in gas and rebalancing. A tight range that needs frequent re-centering can bleed its extra fee income to transaction costs.
- Use the break-even. If a tighter range's IL pushes the break-even APR above what the pool realistically pays, widen it.
How to reduce impermanent loss
- Correlated pairs (stablecoin/stablecoin, ETH/stETH) barely diverge, so IL stays tiny.
- Wider V3 ranges or weighted pools (e.g. Balancer 80/20) lower IL amplification. An 80/20 pool cuts a 2× move's loss from −5.72% to about −3.27%.
- High-fee, high-volume pools can out-earn the loss — always check the break-even above.
- If you would be happy just holding both tokens long term, IL matters less to you — it is only the cost of the fee income you are collecting.
Methodology — how we calculate this
Every number on this page comes from closed-form AMM math, computed in your browser. Nothing is sent to a server.
Uniswap V2 / constant-product (50-50): we use IL = 2·√k/(1+k) − 1, where k is the relative price factor of token A versus token B. This is the standard result for an x·y = constant pool.
Uniswap V3 / concentrated liquidity: for a position opened at price p₀ with range [pₐ, p_b], the token amounts follow the V3 liquidity equations x = 1/√p − 1/√p_b and y = √p − √pₐ (clamped at the range bounds). We value the position at the exit price and divide by the value of the original tokens held, giving the value-vs-HODL ratio. See the Uniswap V3 whitepaper for the derivation. Crucially, the dollar figures use the true entry weights of a V3 position (which are only 50/50 when the range is geometrically symmetric), so lopsided ranges report the correct HODL value, IL in dollars and break-even.
Balancer / weighted pools: for weights wₐ, w_b (summing to 1) and price factors rₐ, r_b, value-vs-HODL is (rₐ^wₐ · r_b^w_b) / (wₐrₐ + w_b r_b) − 1. At 50/50 this reduces exactly to the V2 formula.
Fee break-even: net result = fees − IL$, where fees = notional · APR · days/365. The break-even APR is the value of APR that makes net zero. These figures are estimates and do not model gas, price impact, rewards vesting or fee compounding.
Glossary
- Impermanent loss (IL)
- The value gap between holding tokens in an AMM pool versus holding them in your wallet, caused by price divergence.
- AMM (automated market maker)
- A smart contract that prices trades from a formula (e.g.
x·y=k) instead of an order book. - LP (liquidity provider)
- Someone who deposits token pairs into a pool to earn a share of trading fees.
- Concentrated liquidity
- Uniswap V3's model where liquidity is placed within a chosen price range for higher capital efficiency.
- Range / bounds
- The lower and upper prices between which a V3 position is active and earning fees.
- Fee tier
- The percentage a pool charges per trade (e.g. 0.05%, 0.30%, 1.00%), paid to LPs.
- HODL
- Simply holding the tokens in your wallet — the baseline IL is measured against.
- Weighted pool
- A Balancer-style pool with non-equal token weights (e.g. 80/20), which reduces IL relative to 50/50.
FAQ
What is impermanent loss?
Impermanent loss is the difference in value between holding two tokens inside a liquidity pool versus simply holding them in your wallet. An automated market maker (AMM) rebalances your position as prices move, quietly selling the token that is rising and buying the one that is falling, so when prices diverge you end up with less value than if you had just held. It is called impermanent because it only locks in if you withdraw while prices have diverged; if prices return to your entry point it disappears.
How is impermanent loss calculated?
For a standard 50/50 constant-product pool, IL = 2 times the square root of k, divided by (1 + k), minus 1 — where k is the ratio of how much one token's price changed relative to the other. A 2x relative price move gives about -5.72%, a 3x move about -13.40%, and a 5x move about -25.46%. The loss is symmetric: a token halving (0.5x) produces the same -5.72% as a doubling.
Why is impermanent loss worse on Uniswap V3?
Uniswap V3 concentrates your liquidity into a chosen price range. Inside that range your capital earns far more fees, but impermanent loss is amplified — typically about 2 to 4 times the V2 loss for a moderate range, and much higher for a tight range. This calculator computes your exact multiplier for the range you set. If price leaves your range, the position becomes 100% of one token and stops earning fees entirely.
Do trading fees offset impermanent loss?
Sometimes. You come out ahead only if the fees and rewards you earn exceed your impermanent loss. This calculator shows the break-even: the annualized fee APR needed to exactly offset the IL for the number of days you stay in the pool, plus the net result once you enter your pool's APR.
Is impermanent loss real money lost?
While you are in the pool it is an opportunity cost — the gap between your LP position and simply holding. It becomes a realized loss only if you withdraw after prices have diverged. If prices return to where you entered, the impermanent loss goes back to zero. Note that IL is measured against holding, so your position can still be up in dollar terms even while showing impermanent loss.
Does this calculator work for any AMM?
Yes. The V2 mode applies to any constant-product 50/50 AMM such as Uniswap V2, SushiSwap and PancakeSwap V2. The V3 mode models Uniswap-V3-style concentrated liquidity and its clones like PancakeSwap V3. The weighted mode covers Balancer-style pools such as 80/20 weightings.