Automated Market Maker — Constant-Product Liquidity Pool

Swap

Swap size (input token) 100

Pool fee 0.30%

Pool seeded at 1000 A / 1000 B.

Pool State

Reserve A

1000.0

Reserve B

1000.0

Spot price (B per A)

1.000

Invariant k

1.00e6

Last-swap slippage

—

Impermanent loss

0.00%

How it works

A constant-product AMM (the mechanism behind Uniswap-style decentralized exchanges) holds two token reserves, A and B, and enforces a single invariant on every trade:

x · y = k   (constant, apart from fee accrual)

trade in Δx (after fee f):
  Δx_eff = Δx · (1 − f)
  Δy_out = y − k / (x + Δx_eff)

spot price:  P = y / x
slippage:    (executed price − spot price) / spot price

Because the curve is a hyperbola, larger trades move the price more — the pool always quotes a worse average price than the pre-trade spot price. That gap is the slippage shown after each swap, and it grows automatically as a trade drains one side of the curve.

Impermanent loss compares a liquidity provider's current pool value to simply holding the original two tokens: as the price ratio P = y/x drifts away from where the LP deposited, IL = 2√(P_ratio)/(1+P_ratio) − 1, always ≤ 0. It vanishes only if the price returns to its starting ratio.

Swap A → B / B → A — executes a trade of the chosen size against the current curve, deducting the fee first.
Fee slider — the cut taken from every trade before it hits the invariant; higher fees widen slippage but reward liquidity providers.
Reset Pool — restores the 1000/1000 starting reserves (P = 1, k = 1,000,000) for a clean run.

Reserve A Reserve B x·y=k curve

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