Automated Market Maker (AMM)

What is Automated Market Maker (AMM)?

An Automated Market Maker (AMM) is a smart contract that sets token prices and fills swaps with math instead of matching you with another trader. It uses a formula plus a pool of tokens to quote you a trade any time you want. Think vending machine for crypto, but the buttons are equations.

How Automated Market Maker (AMM) works

Quick walkthrough. You want to swap token A for token B on a DEX. Here is what happens behind the curtain.

• Step 1: Tokens sit inside liquidity pools managed by a smart contract.
• Step 2: Those tokens were deposited by liquidity providers (LPs), who earn a share of trading fees.
• Step 3: The contract quotes a price using a formula. A common one keeps the product of token amounts near a constant, so price comes from the pool ratio.
• Step 4: You approve the swap. The contract sends you token B, takes token A, and updates the pool balances.
• Step 5: The ratio changes, so the next trade gets a slightly different rate. That is the built in price impact doing its thing.

Yep, that is the flow.

How is Automated Market Maker (AMM) calculated?

Many pools follow a constant product rule. If x is the amount of token A in the pool and y is the amount of token B, their product stays near a constant k.

x * y = k

When you add Δx of token A, the pool updates y so the product stays near k. The output is often computed as:

output_B = y - k / (x + Δx)

Instant price comes from the ratio y divided by x. Bigger swaps move the ratio more, so you feel more price impact.

Variations

Not all pools use the same math. The main flavors you will see:

• Product: The classic constant product market maker (CPMM) that keeps x times y near a constant.
• Sum: Constant sum formulas for near one to one assets like stablecoin pairs.
• Hybrid: Blends that act like sum near parity and product off parity, popular for stables.
• Concentrated: Liquidity placed in chosen price ranges, as seen in Uniswap v3, for better capital efficiency.

Example

Swapping ETH for USDC on Uniswap at 3 a.m. still clears because the pool contract gives you a live quote and fills it on the spot.

Fun Fact

The constant product idea has roots in market making research long before crypto, but it went viral after Uniswap popularized the x times y equals k meme during DeFi summer.

Wrap-Up

Automated Market Maker (AMM) in one line: code that always makes you a trade from a shared pool, no calling a broker, no waiting around.