I'm trying to assess how they can be compared. Bitcoin can process 7 trans/sec, is there some equivalent on the Ethereum side? How should I think about this and what quantitative info should I use?

Let me try to explain.

Bitcoin Block Size Limit

The Bitcoin side is pretty simple to understand. The bitcoin blockchain has a hardcoded block size limit of 1 MiB. With an average transaction size of around 600 B and a target block time of 10 minutes, you get

1024 * 1024 / 600 B = 1747.7 transactions per block,

which translates down to

1747.7 / 600 s = 2.9127 transactions per second.

Here we are at around 3 transactions per second in practice, however, if you reduce the average transaction size, it's possible in theory to reach higher rates, maybe 7 transactions per second? That said, there is nothing that scales in Bitcoin unless the network finds consensus on a solution to increase the blocksize or any other scalability fix.

Ethereum Block Gas Limit

Ethereum introduces a new concept which has no transaction or block size limit but a gas limit. Gas is a unit which basicly calculates fee costs. Every transaction, every contract execution and every data storage operation on the blockchain costs gas. Every block has a block gas limit of default 4,712,388 gas which can be spent on every block.

Let's assume an average transaction size of 21,000 gas per transaction which is required for a default value transfer and a target block time of 15 seconds, we have by default the following:

4712388 / 21000 = 224.4 transactions per block

which translates down to

224.4 / 15 = 14.96 transactions per second.

So, at the current level of gas block limit and block time, there is a default possible throughput of 15 transactions per second. If you increase the required gas per transaction, it's probably a little bit lower.

But since you asked about scalability, the yellow paper specifies in equations 44-46 how the block gas limit scales:

yellow paper screenshot

Which basicly means the block gas limit can increase by 1+1/1024 each block, or:

(1+1/1024)^5760 = 276.51227240329152144804

which is a scalability factor for 276 per day. Ethereum scales indefinitely. In theory, in practice, the early olympic testnet was able to stress the network to levels at around 25 transactions per second. And this is only the status quo. See also this post about transaction size.

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