Impermanent Loss Explained: The LP vs HODL Gap

Why Providing Liquidity Can Underperform Just Holding

You deposit two tokens into a 50/50 liquidity pool, you earn a slice of every trade’s fees, and you assume that’s pure upside on top of holding the coins. Then one of the tokens doubles, you withdraw, and you have less value than if you had simply left both tokens sitting in your wallet. That gap has a name: impermanent loss. It is not a bug or a hack — it is the built-in cost of the automated rebalancing that makes a constant-product pool work.

This guide explains what impermanent loss actually is for a standard 50/50 constant-product pool (Uniswap v2 style), how the loss scales as the price ratio between the two tokens moves, and the crucial honest caveat: the loss is measured before the trading fees you earn as a liquidity provider, which in an active pool can offset some or all of it. If you want to put numbers on a specific price scenario, the impermanent loss calculator does the arithmetic below instantly.

What Impermanent Loss Really Is

A constant-product automated market maker keeps the product of the two token balances constant (the familiar x × y = k). To hold that product fixed as the market price moves, the pool automatically sells the token that is rising and buys the token that is falling. Arbitrage traders do this rebalancing for you, and they keep the difference.

The consequence: when you withdraw, you own less of the token that went up and more of the token that went down than if you had just held both. Compared with holding, you gave away part of the winner. That difference in value — value as liquidity minus value if held — is impermanent loss.

It is called “impermanent” because it only exists on paper while the price ratio has diverged from where you deposited. If the ratio returns to its starting point, the loss disappears completely. It becomes a permanent, realized loss only if you withdraw while the prices are still diverged.

The IL Curve: Loss vs Price Ratio

For a 50/50 constant-product pool, impermanent loss depends only on the price ratio k — the exit price divided by the entry price of the volatile token relative to the other. The closed-form formula is:

• IL = 2√k ÷ (1 + k) − 1

Two things fall out of this formula that every liquidity provider should internalize:

• The loss is symmetric. A token that doubles (k = 2) and a token that halves (k = 0.5) produce the exact same impermanent loss. What matters is how far the ratio moves, not the direction.
• The loss accelerates, then flattens. Small moves cost almost nothing; large moves cost a lot, but the percentage grows more slowly than the price. A 2× move costs about 5.7%; a 4× move costs 20%.

The table below reads straight off the formula. This is the “IL curve” every LP is exposed to, regardless of the token pair:

Price change	Price ratio (k)	Impermanent loss
+25%	1.25	−0.62%
+50%	1.50	−2.02%
+100%	2.00	−5.72%
+200%	3.00	−13.40%
+300%	4.00	−20.00%
+400%	5.00	−25.46%
−50%	0.50	−5.72%

Notice the last row: a token halving (−50%, k = 0.5) gives the same −5.72% as a token doubling (+100%, k = 2). This is why highly correlated pairs (two stablecoins, or a token and its staked derivative) suffer almost no impermanent loss — their ratio barely moves — while a volatile token paired against a stablecoin carries the full curve.

Worked Example

Suppose you deposit $10,000 into an ETH/USDC pool when ETH is $100, so half ($5,000) is ETH and half ($5,000) is USDC. ETH then rises 50% to $150, a price ratio of k = 1.5.

• Value if held = deposit × (1 + k) ÷ 2 = $10,000 × 2.5 ÷ 2 = $12,500
• Value as liquidity = deposit × √k = $10,000 × 1.2247 = $12,247.45
• Impermanent loss ($) = $12,247.45 − $12,500 = −$252.55
• Impermanent loss (%) = −2.02%

Both positions gained value — the pool did not lose money in absolute terms. The point is that holding would have gained more. That $252.55 gap is your impermanent loss, and it is the number you must weigh against the fees the pool earned you over the same period.

The Honest Caveat: Fees Are Not in This Number

The single most important thing to understand about any impermanent loss figure — including the one this calculator produces — is what it leaves out. It assumes a standard 50/50 constant-product pool with no trading fees earned. Real liquidity providing has a second, opposing force: every trade routed through the pool pays fees to LPs.

Your real return as a liquidity provider is the combination of two effects that pull in opposite directions:

• Impermanent loss — a drag that grows with how far the price ratio moves. This guide’s number.
• Fee income — a gain that grows with trading volume relative to pool size. In pools with high volume relative to their TVL, fee income can outweigh impermanent loss, especially when the two tokens are correlated and the ratio barely moves.

Because the two effects depend on completely different inputs, it makes sense to estimate them separately and then net them. Use this calculator for the loss side of a specific price scenario, and the liquidity pool APR guide and its calculator for the fee side. A position is only worth providing if the projected fee APR over your holding period comfortably exceeds the impermanent loss you expect from the price move you anticipate.

How to Use the Impermanent Loss Calculator

The tool needs three inputs and returns the full LP-versus-HODL comparison:

1. Price at Deposit — the price of the volatile token (relative to the other) when you entered the pool. In the example above, $100.
2. Current / Exit Price — the price now, or the price at which you plan to withdraw. The ratio between this and the deposit price is all that drives the loss. In the example, $150.
3. Total Amount Deposited — the full dollar value you put into the pool (both tokens combined). This scales the dollar figures; it does not change the percentage.

The results give you the whole picture: Price Change (how far the ratio moved), Value if Held, Value as Liquidity, Impermanent Loss as a percentage, and Impermanent Loss ($) in dollars. Read the percentage to judge the severity of the price move, and the dollar figure to compare directly against the fees you have earned.

How This Fits Your Workflow

Impermanent loss is a planning tool, not an afterthought. Before committing capital to a pool, model the price scenario you actually expect — not the worst case, the realistic one — and read the loss off the curve. Then ask whether the pool’s fee yield over your intended holding period covers it. A few practical rules:

• Correlated pairs minimize IL. Two stablecoins or a token and its liquid-staking derivative keep k near 1, so the loss stays tiny.
• Volatile-vs-stable pairs carry the full curve. These need meaningful fee income to be worthwhile.
• The loss is only realized on withdrawal. If you believe the ratio will revert, waiting can erase a paper loss entirely.
• Always net it against fees. The calculator’s number ignores fee income by design — real LP returns can offset some or all of this loss.