Measure liquidity within a one-percent price band

A price-band depth measure must specify the price orientation and whether it concerns the pool's ending marginal price. That is different from limiting the average price received across the trade.

A one-percent ending-rate band

Consider a hypothetical fee-free constant-product pool with input reserve x = 10,000 and output reserve y = 10,000. Its initial marginal output rate is one. After adding a input, the ending rate relative to the initial rate is:

Ending rate / starting rate = (x / (x + a))²

To keep that rate at or above 99% of its starting value, solve a ≤ x × (1 / sqrt(0.99) − 1). The result is approximately 50.378153 input tokens.

At that size, the average output-rate shortfall is approximately 0.501256%. A 1% average-fill limit would allow a different, larger input under the same model.

Report what “one percent” means

Use a label such as “input capacity before the output-per-input marginal rate falls 1%.” A generic “1% liquidity” label leaves readers unable to reproduce the number.

Mid and execution prices have different definitions. The calculation here derives a marginal-price boundary from the constant-product model, excluding fees and integer rounding.

Use the appropriate model for other pools

For concentrated liquidity, calculate capacity across the active ranges traversed before reaching the selected price boundary. Total balances alone are insufficient. Stable-asset curves similarly require their own invariant and parameters.

Do not compare one venue's average-fill depth with another's final-price-band depth and call the difference a liquidity advantage. Align the definition, direction, state, fees and unit of account first. A precise formula cannot rescue an incompatible comparison boundary.