Liquidity Pool Math

At the heart of every AMM is a simple equation: x · y = k. When someone swaps token X for token Y, the product of reserves must stay constant (ignoring fees). This creates a price curve that automatically adjusts to supply and demand. Understanding this math is key to evaluating LP positions.

📐 Constant Product Curve (x · y = k)

Reserve X (ETH) 100 Reserve Y (USDC) 200000 Swap Size (ETH) 5

k (constant)

20,000,000

Spot Price

$2,000

Effective Price

$1,905

Price Impact

-4.76%

Output (USDC)

9,524

🏊 Pool Share & Fee Calculator

Your Deposit ($) 10000 Total Pool TVL ($) 10000000 Daily Volume ($) 5000000 Fee Tier (%) 0.30

Pool Share

Daily Fees

$1.50

Monthly Fees

$45

Fee APR

5.48%

📚 How x·y=k Creates Prices

PRICE DISCOVERY

The spot price at any point = Y/X. As X decreases (someone buys ETH), the price of ETH rises along the curve.

SLIPPAGE

Larger swaps move further along the curve, getting worse prices. The difference between spot and effective price is slippage.

ARBITRAGE

If the AMM price diverges from the market, arbitrageurs swap until it realigns — keeping the pool price accurate.