The constant-product formula
The most common AMM design keeps the product of the two reserves constant: x · y = k, where x and y are the token balances and k is fixed for a given liquidity level. The spot price of token X in terms of token Y is simply the ratio of reserves, y / x (adjusted for token decimals).
When someone buys X, they remove X and add Y. To keep k constant, the pool must give out progressively less X per unit of Y — so the price of X rises as it is bought. Nobody sets that price; the curve does.
A worked example
Take a pool with 10 ETH and 20,000 USDC, so k = 200,000. To buy 1 ETH, 9 ETH remain, and USDC must rise to 200,000 / 9 ≈ 22,222. The buyer therefore pays about 2,222 USDC for 1 ETH — above the 2,000 starting price. That gap is the cost of moving the curve.
The larger the trade relative to the pool, the wider that gap. This is why the same token can show a different execution price than its quoted spot price.
Concentrated liquidity and newer designs
Uniswap V3 and V4 let LPs concentrate liquidity in a price range, which deepens the market near the current price but changes how reserves map to price. Curve uses a different curve tuned for assets that should trade near parity. The compare pages let you see how these venues differ in practice — see the DEX overview.
How CoinVerum turns this into a price
CoinVerum reconstructs each token’s USD price from indexed swaps against reference assets, taking a median over recent observations to dampen single-pool manipulation. Because it uses only on-chain swaps — never a centralized-exchange feed — the price reflects what actually traded on Ethereum.
Frequently asked questions
Why is a token’s DEX price different from its price on Binance?
On-chain and off-chain venues are separate markets with separate liquidity. Arbitrage keeps them close for liquid assets, but thin tokens can diverge. CoinVerum reports the on-chain price specifically.
What is the difference between spot price and execution price?
Spot price is the marginal price at the current reserves; execution price is the average price you actually get once your trade moves the curve. The gap is price impact.
Can DEX prices be manipulated?
A single thin pool can be pushed off-market, which is why CoinVerum medians across recent swaps and qualifying pools rather than trusting any one trade.