What is impermanent loss and how is it calculated?
Impermanent loss is the gap between what a liquidity pool position is worth and what the same deposit would be worth if you had simply held the two assets. It appears whenever the prices of the two assets move apart, because the pool rebalances as they move: it ends up holding less of the asset that rose and more of the one that fell.
For a 50/50 constant-product pool, the formula needs only the change in the price ratio, r: impermanent loss = 2 x sqrt(r) / (1 + r) - 1. If asset A doubles while B stays flat, r = 2, and the loss is 2 x 1.4142 / 3 - 1 = -5.72%.
With the default inputs, a $10,000 deposit split evenly would be worth $15,000 if held: $10,000 in A and $5,000 in B. In the pool it is worth $14,142.14, which is $857.86 less. The pool now holds 70.71% as many units of A as you deposited and 141.42% as many units of B; that shift is where the gap comes from.
Where does the 50/50 formula come from?
A constant-product pool holds qA units of A and qB units of B and keeps their product fixed, qA * qB = k, when trades go through it (fees aside). The pool's price of A in units of B is qB / qA, and because the pool starts 50/50 by value, the A side is worth exactly qB measured in B. Traders who spot a gap between the pool's price and the wider market trade against the pool until the two match.
Suppose the market price of A relative to B changes by a factor r. For the pool to show the new price while qA * qB stays at k, the balances must become qA / sqrt(r) and qB * sqrt(r). Measured in B, the pool is then worth 2 * qB * sqrt(r), while the original balances held untouched are worth qB * (1 + r). Divide one by the other and qB cancels: pool / held = 2 * sqrt(r) / (1 + r).
Two things follow. The loss depends only on the ratio of the price changes, not on the size of the deposit or on which way the move went. And r and 1 / r give the same loss: A halving against B costs the same 5.72% as A doubling.
Impermanent loss at different price changes
The loss is small for small moves and grows quickly for large ones. For a 50/50 pool, with A's price change measured against B:
| A's price against B | Ratio r | Impermanent loss |
|---|---|---|
| -90% | 0.1 | -42.50% |
| -75% | 0.25 | -20.00% |
| -50% | 0.5 | -5.72% |
| -25% | 0.75 | -1.03% |
| -10% | 0.9 | -0.14% |
| +10% | 1.1 | -0.11% |
| +25% | 1.25 | -0.62% |
| +50% | 1.5 | -2.02% |
| +100% | 2 | -5.72% |
| +200% | 3 | -13.40% |
| +300% | 4 | -20.00% |
| +400% | 5 | -25.46% |
A fourfold rise and a 75% fall both cost 20.00%, because 4 and 0.25 are reciprocals. The chart under the calculator draws this curve for your weighting, with the 50/50 curve beside it when the two differ.
How do weighted pools change impermanent loss?
Some pools hold the two assets in a fixed proportion of value other than half and half, such as 80/20. The document A non-custodial portfolio manager, liquidity provider, and price sensor, a whitepaper dated 19 September 2019, sets out the rule they follow: the product of each balance raised to its normalized weight, with the weights summing to 1, is held constant, and it proves that each asset's share of the pool's value then stays equal to its weight.
From that rule, if A has weight w and the price ratio changes by r, the pool is worth r^w times its starting value, measured in B, while holding is worth w x r + (1 - w). So impermanent loss = r^w / (w x r + 1 - w) - 1. With w = 0.5 this is exactly the 50/50 formula above. A $10,000 deposit when A doubles:
| Weight of A / B | Pool value | Value if held | Loss if A doubles | Loss if A halves |
|---|---|---|---|---|
| 20/80 | $11,486.98 | $12,000.00 | -4.28% | -3.27% |
| 50/50 | $14,142.14 | $15,000.00 | -5.72% | -5.72% |
| 60/40 | $15,157.17 | $16,000.00 | -5.27% | -5.75% |
| 80/20 | $17,411.01 | $18,000.00 | -3.27% | -4.28% |
| 95/5 | $19,318.73 | $19,500.00 | -0.93% | -1.40% |
A weighted pool is not simply a gentler version of 50/50: the loss is no longer the same for a rise and a fall. An 80/20 pool loses less than 50/50 when A doubles, but at a 90% fall in A it loses 43.40% against 42.50%. The result panel shows the 50/50 figure for your moves whenever you choose another weighting.
What if both assets change in price?
Only the ratio matters, so the calculator takes a price change for each asset and works out r = (1 + change in A) / (1 + change in B). If A rises 50% while B falls 20%, r = 1.5 / 0.8 = 1.875. A $10,000 deposit in a 50/50 pool is then worth $10,954.45, against $11,500.00 if held, an impermanent loss of 4.74%.
The flip side is that when both assets move by the same proportion, r stays at 1 and there is no impermanent loss at all, even if both doubled or both halved. The pool still rises or falls with the market; it just does not fall behind holding. When B is a stablecoin that kept its peg, its change is zero and r is simply A's move.
Can trading fees offset impermanent loss?
Pools charge a fee on each trade and share it with the liquidity providers, so the full comparison is pool value + fees earned - value if held. Enter the fees under Fees earned as a percentage of your starting deposit. The calculator also shows the fees that would exactly cover the loss: (value if held - pool value) / deposit.
On the default inputs, fees of 8.58% of the deposit would cover the $857.86 gap. Fees of 3%, or $300, leave the pool at $14,442.14, still $557.86 behind holding. In a larger move the hurdle rises fast: in a 50/50 pool of £2,000 where A quadruples, the pool is worth £4,000 against £5,000 held, and it would take fees of 50% of the deposit to close the gap.
Fees earned in the past say nothing certain about fees in the future, which depend on trading volume, the fee rate and how many others provide liquidity. The calculator only adds the figure you type.
Worked examples in pounds and euros
The formulas work on percentages, so any of the 24 currencies gives the same loss; only the money figures change. Nothing is converted.
| Example | Inputs | Pool value | Value if held | Impermanent loss |
|---|---|---|---|---|
| Pounds, 50/50 | £2,000; A +300%, B unchanged; fees 12% | £4,000.00, or £4,240.00 with fees | £5,000.00 | -20.00% |
| Euros, 80/20 | €5,000; A -40%, B unchanged | €3,322.70 | €3,400.00 | -2.27% |
In the pound example, 12% fees add £240 but the pool still ends £760 behind holding. In the euro example, the same 40% fall in A would cost 3.18% in a 50/50 pool; at 80/20 it costs 2.27%, or €77.30.
How to calculate impermanent loss in Excel or Google Sheets
Put A's price change in B1 and B's in B2, as decimals, so +100% is 1. The ratio in B3 is =(1+B1)/(1+B2). The 50/50 impermanent loss is then =2*SQRT(B3)/(1+B3)-1; with B1 = 1 and B2 = 0 it returns -0.0572.
For a weighted pool with A's weight in B4, use =B3^B4/(B4*B3+1-B4)-1. With 0.8 in B4 and the same moves it returns -0.0327. To turn either into money, multiply the value if held, deposit x (B4 x (1+B1) + (1-B4) x (1+B2)), by the loss.
What this calculator leaves out
The loss is called impermanent because it shrinks back if the prices return to their starting ratio; it is locked in when you withdraw at a different ratio. The calculator measures it at the prices you enter and makes no assumption about where they go next.
It models full-range two-asset pools only. Pools that concentrate liquidity in a price range magnify the effect inside that range and stop earning fees outside it, which these formulas do not capture. Pools of three or more assets, network fees for depositing and withdrawing, reward tokens paid on top of fees, and the risk of a fault in the pool's code or a stablecoin losing its peg are all outside it. Crypto rules differ from country to country; for tax on a gain once the tokens are withdrawn and sold, see the capital gains tax calculator.
Glossary
Liquidity pool: a smart contract holding two or more assets that traders swap against. Liquidity provider: someone who deposits assets into a pool and receives a share of its fees. Constant-product pool: a pool that keeps the product of its two balances fixed, which holds them 50/50 by value. Weighted pool: a pool that holds assets in fixed value shares other than equal. Price ratio (r): the change in A's price divided by the change in B's. Impermanent loss: the shortfall of a pool position against holding the same deposit. Arbitrage: trading to close a gap between the pool's price and the market price.
Frequently asked questions
How do you calculate impermanent loss?
Divide the change in A's price by the change in B's to get the ratio r, then use 2 x sqrt(r) / (1 + r) - 1 for a 50/50 pool. If A doubles against B, r = 2 and the impermanent loss is 5.72% of the value you would have had by holding.
What is the impermanent loss if one token doubles?
In a 50/50 pool, 5.72%. A $10,000 deposit is worth $14,142.14 in the pool against $15,000 if held, a gap of $857.86. In an 80/20 pool weighted toward the token that doubled, the loss is 3.27%.
Is impermanent loss the same for a rise and a fall?
In a 50/50 pool, the same ratio either way gives the same loss: A doubling against B and A halving against B both cost 5.72%. In a weighted pool they differ; an 80/20 pool loses 3.27% when A doubles and 4.28% when it halves.
How do weighted pools change impermanent loss?
With weight w on asset A, the loss is r^w / (w x r + 1 - w) - 1. Moving the weight toward the asset that moves reduces the loss for that move, but the loss for a move the other way can be larger than in a 50/50 pool.
Do I have impermanent loss if both prices go up?
Only if they rise by different proportions. If A rises 50% and B falls 20%, the ratio is 1.875 and a 50/50 pool loses 4.74% against holding. If both double, the ratio stays at 1 and there is no impermanent loss.
Can fees make up for impermanent loss?
They can reduce or exceed it, depending on how much the pool earns. On the default inputs, fees of 8.58% of the deposit would cover the gap; fees of 3% leave the pool $557.86 behind holding. The calculator adds only the fee figure you enter.
Why is it called impermanent?
Because the shortfall disappears if the two prices return to their starting ratio. It becomes a realized loss when you withdraw while the ratio is different from when you deposited.
Is impermanent loss the same as losing money?
No. It compares the pool with holding, not with your original deposit. In the default example the pool is worth $14,142.14, more than the $10,000 deposited, yet $857.86 less than holding. A pool can also fall in value and show an impermanent loss on top.
Does the calculator use live token prices?
No. You enter the percentage change of each asset's price yourself, so the result works for a past period or a move you want to test. Nothing is fetched.
Does this work for concentrated liquidity pools?
No. The formulas here are for full-range pools. Concentrated positions amplify the effect while the price stays in range and change behavior outside it, which needs a different calculation.
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Last reviewed 13 November 2026 by the NIFM Academy editorial team. Next review by 13 May 2027.
- A non-custodial portfolio manager, liquidity provider, and price sensor (whitepaper, version dated 19 September 2019), value function of balances raised to normalized weights summing to 1, held constant across trades; spot price from balances divided by weights; each token's share of pool value equals its weight. Read 13 November 2026. Checked 13 November 2026.
- Impermanent loss arithmetic, 50/50 constant-product pool: 2 x sqrt(r) / (1 + r) - 1, derived on the page from x x y = k; weighted pool: r^w / (w x r + 1 - w) - 1, shown in the working under every result. Checked 13 November 2026.