The fees for on-chain payments are independent of the payment amount, while the fees for off-chain payments are proportional to the amount sent. It is trivial to compute the amount at which it makes more sense to make an on-chain payment.
Parameters used to compute the following numbers:
- the weight of a 2 inputs, 2 outputs on-chain transaction using p2wpkh is 836 vbytes
- a route in the lightning network has roughly a median 1000ppm proportional fee
This results in the following thresholds, depending on the on-chain feerate:
| On-chain feerate | On-chain fees | Threshold |
|---|---|---|
| 1 sat/byte | 209 sat | 2 mBTC |
| 10 sat/byte | 2090 sat | 20 mBTC |
| 25 sat/byte | 5225 sat | 50 mBTC |
| 50 sat/byte | 10450 sat | 100 mBTC |
| 75 sat/byte | 15675 sat | 150 mBTC |
| 100 sat/byte | 20900 sat | 210 mBTC |
Any lightning payment above that treshold isn't economical. It does benefit from instant settlement compared to on-chain payments, so it could still make sense depending on the use-case.