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There is an exact amount at which a percentage rail overtakes a flat-fee one. Below it, flat wins; above it, percentage wins. Working it out takes one division.
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Compare a flat fee F against a percentage p. They cost the same when the amount equals F divided by p. Below that amount the flat fee is the larger share; above it the percentage is.
A flat fee of $2 against a rate of 1% crosses at $200. Send $50 and the flat fee is 4% while the percentage rail charges $0.50. Send $2,000 and the flat fee is 0.1% while the percentage rail charges $20.
Card pricing is usually a percentage plus a small fixed amount, which means it behaves like a flat fee on very small payments and like a pure percentage on large ones. The fixed component is there because authorisation costs the same whether the payment is for one unit or ten thousand.
When both rails have both components, the crossover still exists but you have to compute it rather than eyeball it. That is what a comparison priced on a specific amount is for.
If you take many small payments, hunt for the lowest fixed component, not the lowest percentage. If you take a few large ones, the percentage is nearly all of your cost and the fixed part is noise.
Averages hide this. A business with a bimodal mix of tiny and large payments can be worse off on a rail that is cheapest for its average payment than on one that is second-best for both halves.
Prices change. Everything here is explained against live fee data, so you can check any of it directly.