📊 Constant Product Formula: x * y = k
Understand the mathematical formula powering all AMM swaps
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0 / 5 completed🔢 The Constant Product Formula
The constant product formula (x × y = k) is the mathematical foundation of AMMs. It ensures that the product of the two token reserves remains constant during trades, automatically adjusting prices based on supply and demand.
How the Formula Works
The Equation: x × y = k
x and y are the reserves of two tokens in the pool. k is a constant that never changes (except when liquidity is added/removed).
Automatic Pricing
When someone trades, they add one token and remove another. The formula maintains the constant k, causing the price to adjust automatically.
Self-Balancing
Large trades have bigger price impact. This incentivizes arbitrageurs to balance the pool when it deviates from market prices.
🎮 Interactive: Trade Simulator
Execute trades and watch how the constant product formula maintains equilibrium:
Why This Formula?
Infinite Liquidity
The pool never runs out of either token. As reserves decrease, the price increases exponentially, making it prohibitively expensive to drain the pool.
Price Impact
Larger trades have exponentially larger price impact. This naturally limits manipulation and incentivizes splitting large trades.
Mathematical Properties
The constant product formula creates a hyperbolic curve. This means the price curve is smooth and continuous, but the rate of price change accelerates as reserves deplete.