Find a maximum trade size for a stated price-impact budget

For a fee-free constant-product pool, an average output-rate shortfall limit can be translated into an input-size limit. The result is a model calculation, not a universal sizing rule for every AMM.

Define the exact limit

Let x be the starting input reserve and a the trade input. Assume x > 0, a ≥ 0 and a permitted shortfall fraction 0 ≤ b < 1. Relative to the initial output-per-input spot rate, the average-rate shortfall is a / (x + a). To keep that shortfall at or below b, solve:

a / (x + a) ≤ b

a ≤ b × x / (1 − b)

With a hypothetical x of 100,000 and b of 0.01, maximum modeled input is approximately 1,010.10101 tokens. That corresponds to a 1% average output-rate shortfall, not merely a trade equal to 1% of the reserve.

Validate the substitution

Putting 1,010.10101 back into a / (100,000 + a) yields 0.01. The initial output reserve affects how many output tokens are received, but cancels from this relative shortfall measure under the stated model. A 100% shortfall ceiling provides no finite input-size bound in this idealized model, so the displayed inversion does not apply at b = 1.

The underlying invariant comes from the constant-product pool design. This inversion is an illustrative derivation with fees excluded.

Know when to stop using the shortcut

A total execution-cost ceiling must also consider fees and separate payments. A final marginal-price movement limit needs a different formula. Concentrated liquidity can cross range boundaries, and a stable-asset pool follows another curve.

For a real route, obtain quotes near the calculated threshold using the actual state and fee rule. If the selected path changes, the original single-pool formula no longer describes the entire trade.

Never infer an acceptable personal risk level from b. The calculation takes a chosen constraint as input and states the maximum size under assumptions; it does not recommend that constraint or promise execution at the resulting size.