Constant Product Formula: The Engine Behind DeFi Swaps

When working with Constant Product Formula, the core pricing rule that keeps the product of two token reserves unchanged (x·y = k) in many automated market makers. Also known as x*y=k, it guarantees that every trade pushes the price along a predictable curve while preserving total liquidity. Automated Market Maker, often shortened to AMM, a smart‑contract system that replaces traditional order books with liquidity pools governed by the constant product rule makes token swaps possible without a counterparty. This simple invariant constant product formula enables anyone to become a liquidity provider and lets traders execute orders instantly, 24/7.

How the Formula Shapes Pools, Fees, and Risks

Every AMM creates a Liquidity Pool, a shared reserve of two assets that users deposit to earn fees while the constant product rule determines swap prices. Because the price moves along the curve, an imbalance between the two assets generates Impermanent Loss, the temporary value gap that liquidity providers face when the market price diverges from the pool’s price. The bigger the price swing, the larger the loss, unless fees or external incentives outweigh it. Some newer designs, like Concentrated Liquidity, a feature introduced by Uniswap v3 that lets providers allocate capital to a narrow price range, effectively tweaking the constant product curve, aim to reduce impermanent loss while boosting fee earnings. Other platforms, such as Curve, replace the x·y = k invariant with a stable‑coin‑focused curve that minimizes slippage and loss for assets that trade near parity. These variations illustrate how the constant product formula serves as a baseline that can be extended, hybridized, or replaced depending on the market segment.

The articles below dive deeper into each of these pieces. You’ll find a breakdown of how under‑collateralized DeFi loans could affect borrowing demand, a guide to end‑to‑end encryption for wallet security, step‑by‑step airdrop claims, and a practical look at tax‑optimization strategies. Most importantly for this tag, we explore impermanent loss across AMM designs, compare constant‑product pools with concentrated‑liquidity models, and evaluate real‑world performance data. Whether you’re just adding funds to a pool or tweaking a smart contract, the collection gives you the context you need to decide when the constant product formula works for you and when a different invariant might be a better fit.