Liquidity Pool Math: How Pool Share and Fees Are Calculated

Liquidity pool math explained: how automated market makers calculate your pool share from LP tokens, and how trading fees accrue to that share over time.

What a liquidity pool actually holds

A liquidity pool on an automated market maker (AMM) is a pair of token reserves locked in a smart contract, plus a running total of “LP tokens” that record who owns what fraction of those reserves. Trades don’t move through an order book matching buyers and sellers; instead, a trader swaps against the pool itself, and the pool’s own formula sets the price.

Uniswap’s documentation for its constant-product design describes the core rule as x × y = k: the two reserve balances, multiplied together, must stay equal to a constant, k, before and after every trade (ignoring the fee). If a trader buys ETH from a pool, they add USDC to one reserve and remove ETH from the other, and the amount removed is whatever keeps x × y equal to k. Larger trades move the price more than smaller ones, because a bigger shift in one reserve requires a bigger offsetting shift in the other to hold the product constant.

This is the same mechanism behind impermanent loss: the pool automatically rebalances as prices move, buying the falling asset and selling the rising one relative to a simple buy-and-hold position. Pool share math, covered below, is the other half of the picture — what you actually own of that constantly rebalancing pool.

How pool share is calculated when you deposit

When you deposit into an existing pool, the contract mints new LP tokens and sends them to you. Per Uniswap’s documentation, those tokens “entitle [depositors] to a proportional share of the liquidity available in the pool,” and if other providers later add or remove liquidity, tokens are minted or burned so that “everyone’s relative percentage share of the liquidity pool remains the same.”

The minting rule itself is simple division. If you deposit an amount of token X, and the pool already holds a reserve of X with a total LP token supply outstanding, your new tokens equal:

new LP tokens = your deposit of X ÷ pool’s reserve of X × current total LP token supply

When you deposit both tokens in the pool’s exact current ratio, the same answer comes out whether you compute it from token X or token Y, and it also equals your deposit’s dollar value divided by the pool’s total value before you joined.

Example: Suppose an ETH/USDC pool holds 500 ETH and $1,000,000 USDC (ETH at $2,000), with 100,000 LP tokens outstanding. You deposit 5 ETH and $10,000 USDC, matching the pool’s 1:2,000 ratio exactly.

Computing the mint amount both ways:

Both sides agree because the deposit matched the pool’s ratio. If your two amounts don’t match, the contract can only credit you based on whichever side represents the smaller proportional contribution; most wallet front-ends handle this by swapping part of your deposit first so it arrives at the pool balanced, but the underlying math never rewards an unbalanced deposit with extra pool share.

How trading fees accrue to your share

Fees are where a pool share turns into an actual return. According to Uniswap’s documentation, a percentage of each trade, historically 0.30% on its constant-product pools, “is distributed proportionally to all liquidity providers” holding a stake in that pool. Concentrated-liquidity designs work similarly in principle but only pay fees to liquidity positions that are active at the current price, and Uniswap v3 fee tiers commonly run from 0.01% up to 1%, with stable pairs typically at the lower end.

Continuing the example above, suppose the pool’s total value after your deposit is $2,020,000 (the prior $2,000,000 plus your $20,000), and it processes $400,000 in trading volume per day at a 0.30% fee. That works out to a 21.68% fee APR on the pool’s value, and your 0.99% share earns a proportional slice of it every day.

That $356.44 assumes the ETH/USDC price ratio doesn’t move, which isolates the fee math from impermanent loss. In practice the two interact: fees add to your position continuously, while any price move between the two tokens pulls the other way. Run a full impermanent loss calculation alongside this fee math before sizing a real deposit, and see how impermanent loss is calculated for the reserve-rebalancing side of the same pool.

Why pool share dilutes even when your tokens don’t move

A subtlety worth internalizing: your LP token balance only changes when you deposit or withdraw, but your percentage share of the pool changes constantly as other people deposit and withdraw around you. If another provider adds liquidity equal to 5% of the pool’s current LP token supply, the total supply grows by that much, and every existing holder’s percentage share falls proportionally, even though the tokens they hold still represent the same underlying claim, reserves plus accrued fees, that they had a moment before.

This matters most for headline “share of pool” numbers shown in a wallet interface at the moment of deposit. That figure is a snapshot, not a fixed entitlement, and it will drift as the pool’s total LP supply changes over your holding period. Some of that pool math also underpins lending markets, where your share of a lending pool determines your share of interest paid by borrowers rather than swap fees; see our guide to DeFi lending and borrowing rates for how that side of the math differs.

Common mistakes with pool math

1. Treating “share of pool” as fixed. It moves every time total LP supply changes, not only when you personally deposit or withdraw.
2. Assuming an unbalanced deposit earns more. Minting always uses the more limiting ratio; extra value on one side buys you nothing extra.
3. Confusing the fee tier with your actual yield. A 0.30% fee tier tells you the rate charged per trade, not your annualized return, which depends on trading volume relative to pool size.
4. Ignoring that fee income and impermanent loss move independently. A pool can post a healthy fee APR and still leave you behind a simple hold if the price ratio moves far enough; check both, as covered in our yield farming guide.
5. Skipping the contract’s own risk profile. Pool math tells you what a position is worth if the contract behaves as designed; it says nothing about exploit risk, which our smart contract risk checklist covers separately.

The bottom line

Pool share is LP tokens minted divided by total LP tokens outstanding, and it dilutes as other providers come and go, independent of your own balance. Fee income is that share multiplied by the pool’s fee revenue over a period, and it has to be weighed against impermanent loss, not treated as the whole return, before the math tells you whether providing liquidity actually beat holding.

This content is for education only and is not financial, investment, tax or legal advice. Crypto assets are volatile and you can lose money. Examples use hypothetical numbers. See our disclaimer and editorial policy.