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I need to calculate the price impact on Uniswap V3 to further compute the bid-ask spreads. What would be the mathematical formula and which data do I need?

Thank you in advance for the help I'll keep the post updated with my research

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It is not possible to have a single mathematical formula as a swap Uniswap v3 may cross tick range boundaries. Each tick range may have different liquidity and needs to be considered separately. The multi-step swapping algorithm is given in the whitepaper, Figure 4.

For a single step, the computeSwapStep logic may be used. Alternatively, look at formulas 6.9 to 6.16 in the whitepaper and implement the logic yourself.

Edit: If access to on-chain data is an option, the best solution may be to call the QuoterV2 contract using a static call, as it returns not only the amount, but also the sqrtPriceX96After, which can be compared with the pool's previous sqrtPriceX96 to directly get the price impact.

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