Execution cost is genuinely small
Running your transaction on the rollup itself costs almost nothing. The sequencer has abundant capacity relative to demand, so the execution portion of the fee is typically a rounding error.
This is why simple transfers and swaps on rollups cost cents or less while the same operation on mainnet can cost dollars.
Data cost is inherited from Ethereum
The rollup must publish enough data for anyone to reconstruct its state. That publication happens on Ethereum and is priced by Ethereum. Dedicated data space made this dramatically cheaper than it used to be, but it still moves with mainnet demand.
So when mainnet is congested, rollup fees rise too — from a much lower base, and usually by a smaller absolute amount than the saving.
Optimistic and zero-knowledge differ in withdrawal, not fees
Optimistic rollups assume validity and allow a challenge window, which is why a native withdrawal to Ethereum takes days. Zero-knowledge rollups publish a validity proof, so withdrawal can be fast once the proof is on-chain.
Both compress data the same way, so the day-to-day fee experience is similar. The difference shows up when you want your funds back on mainnet.
Choosing a network for cost
For small and medium trades, any supported rollup or low-fee chain beats mainnet by a wide margin. For large trades, depth matters more than the few dollars of gas, and mainnet often has the deepest pools.
FBT Swap supports Ethereum alongside Arbitrum, Base, Optimism, Linea, Scroll, zkSync Era and Unichain, and shows the fee and route for the network you actually selected.