Impermanent Loss Calculator: What the Formula Hides

An impermanent loss calculator takes two prices, the one at deposit and the one now, and returns how far a liquidity position trails simply holding the same tokens. Under the hood it runs one line of algebra: Uniswap's docs give the constant-product loss formula as 2 times the square root of the price ratio, divided by 1 plus that ratio, minus 1. Plug in a 3x move and you get roughly 13.4% behind holding, before fees.

That one number is where most calculator pages stop. The useful part is what it leaves out: fees, range choices and the path the price took.

Impermanent loss calculator crypto: how the pool math works

Every crypto calculator of this kind reduces your inputs to a single price ratio, r, and evaluates the same formula. Token amounts, dollar values and pool size drop out, because the loss is a percentage of what holding would be worth.

Worked example, desk style. Say ETH triples against USDC, so r is 3:

• The square root of 3 is about 1.732.
• Twice that is about 3.464.
• Divide by 1 plus r, which is 4, and you get about 0.866.
• Subtract 1 and the result is about minus 0.134.

So the position sits 13.4% behind a wallet that held the original ETH and USDC. That matches the figure Uniswap publishes: a 3x price change costs 13.4% relative to holding.

Two things fall out of the algebra that calculators rarely spell out. Direction does not matter: a token that falls to one third of its price produces the same loss as one that triples, because swapping r for 1 over r leaves the formula unchanged. And the loss depends only on where the price ends, not on the route it took, as long as you ignore fees.

Using a liquidity pool impermanent loss calculator with fees

A liquidity pool calculator that shows only the formula output is reporting half the trade. On Uniswap v2, 0.3% of all trade volume is distributed proportionally to liquidity providers (fee level per the v2 docs, as of October 2026).

So the real comparison is impermanent loss against accumulated fees. A pair that chops sideways inside a band can generate plenty of volume while r stays close to 1, which is the good case for an LP. A pair that trends hard in one direction does the opposite: r runs away, the loss grows, and fees have to come from volume you cannot see in advance.

This is also where price path matters again. The formula ignores the route, but fees do not. Two positions with the same start and end price can finish far apart depending on how much the price swung through the pool in between.

Building an impermanent loss calculator in Excel

You do not need a web tool. With the price ratio in cell A2, one cell does the work:

=2*SQRT(A2)/(1+A2)-1

Format the result as a percentage. For the ratio, divide the current price by the deposit price in a neighbouring cell and point the formula at it. Add a fee column (volume share times the fee tier) next to it and you have a better tool than most calculator pages, because it shows both sides of the ledger.

Check your sheet against Uniswap's published points: a 1.25x move costs 0.6%, 3x costs 13.4%, and a 5x price change costs 25.5% versus holding.

Impermanent loss calculator for concentrated liquidity

The plain formula assumes liquidity is spread across every possible price. Concentrated liquidity changes that: on Uniswap it is liquidity allocated within a custom price range.

The range also caps the upside. Per Uniswap, once the price exits your interval, the position stops earning fees because its liquidity is no longer active.

Academic work points the same way. A study of Uniswap v3 LPs by Heimbach, Schertenleib and Wattenhofer concluded that significant returns require accepting more financial risk. Narrow ranges are not free yield.

Reading an impermanent loss chart

An impermanent loss chart plots the formula output against the price ratio. It sits at zero when r equals 1 and bends down on both sides, slowly at first and then faster.

The shape is the whole lesson. Small moves cost almost nothing, which is why stable or correlated pairs suit passive LPs. Large moves cost a lot, and the curve keeps falling, so a pair you expect to trend is a pair where holding usually beats providing liquidity unless fees are heavy.

Pool questions

How do you calculate impermanent loss by hand?

Divide the new price by the price at deposit to get the price ratio r, then compute 2 times the square root of r, divided by 1 plus r, minus 1. The result is your position versus simply holding, before fees.

Is impermanent loss actually a loss?

Only against the hold benchmark. If the price returns to the deposit ratio, the gap closes, which is where the name comes from. If you withdraw while the ratio is away from where you started, the gap becomes real.

Can trading fees cover impermanent loss?

Sometimes. A v2 pool pays LPs a share of every trade, so heavy volume on a calm pair can outrun a small loss. A large one-way move needs a lot of volume to catch up, and a calculator will not tell you whether that volume arrives.

Does impermanent loss hit stablecoin pairs?

Far less. Two assets pegged to the same dollar keep a price ratio near 1, and the formula returns close to zero there. The risk shows up only if one side breaks its peg.

Chain and source links

• Uniswap Labs, Understanding Returns (Uniswap v2 docs), undated, accessed 2026-10-16
• Uniswap Labs, Concentrated Liquidity (Uniswap docs), undated, accessed 2026-10-16
• arXiv (Heimbach, Schertenleib, Wattenhofer), Risks and Returns of Uniswap V3 Liquidity Providers, 2022-05-18