Formula & Calculator
AMM Constant Product Price Impact
Estimates how much a trade will move the price in a constant-product automated market maker (like Uniswap) pool, based on trade size relative to pool depth.
Interpretation
Price Impact (%) = (Δy / y) × 100, where x×y=k. The change in price caused by a trade on an AMM. Used to assess slippage.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Price Impact | Estimated price impact | % |
| Δy | Change in output token reserve | |
| y | Output token reserve before trade |
What it means
In AMMs (like Uniswap), trades change the reserves, affecting the price. Price impact is the percentage change in price caused by a trade. A larger trade has more impact. This is used to estimate slippage and to decide optimal trade sizes. Understanding price impact is essential for traders to minimise costs and for LPs to understand their risk.
Worked example
AMM Constant Product Price Impact – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Pool Reserve (token Y) | 1,000,000 |
| Trade Output Amount | 10,000 |
| Parameter | Value |
|---|---|
| Reserve | 50,000 |
| Output | 5,000 |
Common mistakes
- AMM constant product: x*y = k, where x and y are token reserves.
- Δy: The change in token y reserve after a swap.
- Price impact: The percentage change in price due to the trade.
- Larger trades: Cause higher price impact.
Applications
AMM constant product price impact measures the percentage price change caused by a trade in a liquidity pool, based on the constant product formula (x*y=k). This is used to estimate slippage before executing a trade. Traders use it to assess the cost of larger trades and to choose pools with sufficient liquidity. Understanding price impact is critical for efficient trading on DEXs.
- Estimating slippage for trades on AMMs
- Choosing optimal pools for minimal price impact
- Managing trade size relative to pool liquidity
- Evaluating the efficiency of a trading route
- Educational understanding of AMM mechanics
Frequently Asked Questions
Price Impact = (Δy / y) × 100, where Δy is the amount of output token taken from the pool, and y is the pool's reserve of that token. For example, removing 10,000 from a 1,000,000 token reserve gives a 1% price impact.
The constant product formula (x*y=k) means that as you take more of one token, the price moves to maintain the product. Larger trades consume a larger proportion of the pool, causing higher slippage.
Price impact is the change in the spot price caused by your trade. Slippage is the difference between the expected price and the actual execution price, which includes price impact plus any other market movements.
Use a pool with deeper liquidity (higher reserves), split your trade into smaller parts, or use a DEX aggregator that routes through multiple pools to minimise impact.
Yes, it is symmetric. Buying a token increases its price (positive impact), selling decreases it (negative impact). The magnitude depends on the trade size relative to reserves.
Price impact reduces the profit margin, especially for large trades. Arbitrageurs must factor in price impact to determine if an opportunity is still profitable after execution.
For a multi-hop swap, you need to calculate the impact at each step. The total impact is the product (or sum) of each step's impact, depending on the route.
Stable pools (e.g., stablecoins) have low price impact because reserves are large relative to normal trade sizes. Volatile pools have higher impact due to lower liquidity.