Impermanent Loss Calculator
Impermanent loss is the shortfall between providing liquidity to a pool and simply holding the two assets. The pool rebalances you as prices diverge, leaving more of the weaker asset and less of the stronger one, and the gap grows with the size of the move.
Pooling versus holding
Enter how far the two assets moved apart. The loss is symmetric — a halving costs the same as a doubling.
Impermanent loss is 2√k ÷ (1 + k) − 1, where k is the price ratio. It is always negative or zero, it is symmetric, and it depends on nothing except how far the two assets moved apart.
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How the number is built
A liquidity pool holds two assets and keeps them at a constant ratio of value. When one asset rises relative to the other, the pool sells some of the winner and buys the loser — automatically, on every trade that passes through it.
The result is a shortfall against simply having held both:
Impermanent loss = 2√k ÷ (1 + k) − 1
where k is how far the two prices moved apart.
Nothing else is in that formula. Not the deposit size, not the fees, not time. It depends only on the divergence, which is what makes it calculable in advance.
A worked example
Take the defaults: one asset doubles relative to the other, on a 10,000 deposit, with 3% of fees earned.
k is 2, so impermanent loss is 2 × √2 ÷ 3 − 1 = −5.72%.
Simply holding both assets would leave 15,000 — the average of one asset unchanged and one doubled.
Pooling, including the 3% of fees, leaves 14,566.
So the fees did not cover it. 3% earned against 5.72% lost is a net −2.72%, which the calculator reports because it is the number that actually decides whether pooling was worth doing.
How fast it grows
The loss accelerates as the assets diverge:
At 1.25x apart it is −0.62%. At 1.5x, −2.02%. At 2x, −5.72%. At 3x, −13.40%. At 5x, −25.46%.
Read that list and the shape is clear. Small divergences cost almost nothing, which is why pooling feels safe for a while. Large ones cost a great deal, and crypto assets diverge by 3x and 5x routinely.
And it is symmetric. A ratio of 0.5 — one asset halving relative to the other — produces exactly the same −5.72% as a doubling. The pool does not care which direction the divergence ran.
Which explains why stablecoin pools exist. Two assets designed to hold the same value barely diverge, so the loss stays near zero and the fees are close to free money — until one of them stops holding its value, which is the risk that replaced this one.
What has to pay for it
Providing liquidity is a trade: you accept this loss in exchange for a share of trading fees. The whole question is whether the fees exceed the divergence over your holding period, and only one of those two is predictable.
A pool with little trading through it earns little. High advertised yields on thin pools are frequently a large share of a small number, and the divergence risk is the same as anywhere else.
Entering and exiting both cost. On this site’s shared series a round trip is 2% of a median bar’s range; on-chain the equivalent is transaction fees, paid on the way in, the way out, and often on claiming the rewards.
How much the fees have to earn
The useful way to run this calculator is backwards: decide how far you expect the pair to diverge, then check whether the pool’s advertised yield covers it.
At 1.5x divergence the loss is 2.02%, so a pool paying 5% a year covers it comfortably over twelve months. That is the case that makes liquidity provision look attractive, and it is a real case.
At 3x the loss is 13.40%, which needs a pool paying more than that over the same period simply to match holding — and yields that high generally sit on thin pools or new assets, where a 3x divergence is exactly what is likely.
At 5x the loss is 25.46% and almost nothing pays that reliably.
Read those three together and the trade becomes visible. The pools where impermanent loss is small pay the least, and the pools that pay the most are the ones where divergence is largest. The yield and the risk are not independent — they are two descriptions of the same volatility.
Why “impermanent” is a misleading name
The loss reverses only if the two prices return to their original ratio. That is the entire basis for the word “impermanent”, and it is a condition rather than a tendency — there is no force pulling two crypto assets back to a previous relationship.
Withdraw while they are apart and the loss is realised, exactly like any other. The name describes a possibility, not a property.
The original data
Of the 24,971 unique videos in research/search-study-corpus.jsonl, zero have an
instruction-shaped title about impermanent loss. Staking appears in 6 instruction-shaped titles at a
median of 35,757 views, and crypto more broadly in 217 at 30,027. The counts come from
site/rank_tools2.py.
217 instruction-shaped crypto videos and none on the one piece of arithmetic that decides whether providing liquidity was worth doing. Yield figures are quoted constantly in this space; the offset against them is quoted nowhere in a corpus of nearly twenty-five thousand videos.
The answer to the question on that chart is that you are ahead of your deposit and behind where you would have been. Pooling returned 14,566 against 15,000 from holding — a genuine gain, and a worse outcome than doing nothing. Both statements are true and only the second one is a decision about what to do next time.
When it fails
The formula assumes an orderly divergence and a functioning pool. A sharp move in one asset produces the loss at its steepest point, and it produces it fastest in exactly the conditions where withdrawing is most expensive and most congested. The calculation is correct and it says nothing about whether you will be able to act on it at the moment you want to.
The second failure is the one the formula cannot see: the pool itself. Contract failure, a collapsing stablecoin, or an asset going to zero are not impermanent losses and are not in the arithmetic.
A third is comparing the yield to zero. The comparison is against holding the two assets, not against holding cash.
A fourth is ignoring transaction costs. On small deposits they can exceed both the fees and the loss.
A fifth is assuming reversion. Nothing pulls two prices back together.
And a sixth is treating a stablecoin pool as riskless. The divergence risk is tiny and it has been replaced by the risk that one of the two stops being stable.
Related
Crypto covers the asset class and how it differs structurally from securities. Ethereum is where most of these pools actually live. And bitcoin is usually one half of the pairs this applies to.
The name is the problem. Calling it impermanent makes it sound like something that resolves on its own, and the only thing that makes it impermanent is the prices coming back together — which is not a plan. If you withdraw while they are apart, it is exactly as permanent as any other loss.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.