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Impermanent loss calculator
For a Uniswap v3 or v4 range, and for a full-range v2 position. Divergence against simply holding, with the fee income that has to beat it.
How to read it
Divergence is what the pool costs you by rebalancing as the price ratio moves – it is arithmetic, not a fee anyone charges, and it becomes a realised loss only when you withdraw. Fee income is the other side, and it is paid out of volume rather than out of the price going your way. A position is worth holding when the second beats the first over the period you were in.
The fee figure here assumes the position stays in range for the whole period. It will not. Treat it as the ceiling rather than the estimate, and discount it by however much of the time you expect price to be outside your band.
The maths it runs
While price sits inside a range, a position holds x = L(1/√p − 1/√pb) of one token and y = L(√p − √pa) of the other, so its value in units of the second token is L(2√p − p/√pb − √pa). Holding instead means keeping the amounts you deposited, whose value moves linearly with price. Divergence is the gap between the two.
Written that way there is no separate formula for a full-range position. Widen the range far enough and the expression collapses to 2√r/(1+r) − 1, the closed form usually quoted for v2 – which is why the full-range checkbox here is one setting rather than a different calculator.
What the same move costs at different widths
A price that doubles against an entry of 100, with the fee side left out:
| Range | Divergence vs holding | Capital efficiency |
|---|---|---|
| Full range (v2) | −5.72% | ×1.0 |
| 50 – 200 | −19.53% | ×3.4 |
| 80 – 125 | −29.40% | ×9.5 |
| 95 – 105 | −31.97% | ×40.5 |
Both columns move together, and that is the whole trade. A narrow band earns many times more per dollar while price is inside it, loses far more when price travels, and earns nothing at all once price is out. Nothing in a placement tool changes any of that – what tooling changes is how precisely you place the band and how quickly you can move it.
What this cannot tell you
- How much of the period price actually spent inside the range, which decides the fee income and depends on the path rather than on the two prices you entered.
- Whether the pool's volume holds. The fee side is an extrapolation from one day's trading, and a token's volume is the least stable number attached to it.
- The gas of opening, rebalancing and closing, which on a ladder of positions is paid per position in both directions.
- Anything about the token itself. A pool paying enormous fees is often paying them because the asset is about to make the divergence column look optimistic.
Frequently asked
How is impermanent loss calculated?
For a full-range position the closed form is 2√r/(1+r) − 1, where r is the ratio by which the price changed. For a concentrated range the position value is L(2√p − p/√pb − √pa) while price is inside the band, compared against the value of simply holding what you deposited. The second reduces to the first once the range is wide enough.
How much is impermanent loss at a 2x move?
About 5.72% behind holding for a full-range position. Inside a concentrated range it is far larger – roughly 29% for a band of 80 to 125 around an entry of 100, and roughly 32% for 95 to 105, because the same move takes price out of the band entirely.
Does impermanent loss apply to Uniswap v3 and v4?
Yes, and more sharply than to v2. Concentrating liquidity into a range multiplies both fee income and divergence, and outside the range the position stops earning while holding entirely the token that fell.
Is impermanent loss permanent?
It reverses if the price ratio returns to where you entered, and it becomes a realised loss the moment you withdraw. Withdrawing during the move locks it in at its widest point.
Do fees make up for impermanent loss?
Sometimes, and it is the only thing that can. Fee income is a function of the pool's volume against its liquidity and of the fee tier; divergence is a function of how far the price ratio travels. A position is worth holding when the first beats the second over the period, which is what the calculator above compares.
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