I have heard that the maximum block size means that the Bitcoin network has a maximum throughput. What is this maximum?

The current block size limit is 1MB, but this is likely to be changed in the future.

Transactions are about 500B, so the current limit is 2000 transactions per block, or about 3 per second.

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    Wow, that's slow. If Bitcoin keeps growing, they'll definitely have to increase the block size – Casebash Jun 13 '12 at 12:08
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    Is this actually a current limitation regardless of the client implementation? Do you have a reference for that assertion? – barrymac Sep 27 '13 at 0:00
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    @barrymac github.com/bitcoin/bitcoin/blob/… – theymos Sep 27 '13 at 1:41
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    IMO it's not so certain that the max block size will be increased in the near future. There's likely to be a lot of controversy about it. See keepbitcoinfree.org – theymos Sep 27 '13 at 1:43
  • @theymos We found the same thing from via different paths! +1 for linking to the line of code responsible! – barrymac Sep 27 '13 at 11:03

From the Scalability on the wiki page

Today the Bitcoin network is restricted to a sustained rate of 7 tps by some artificial limits. These were put in place to stop people from ballooning the size of the block chain before the network and community was ready for it. Once those limits are lifted, the maximum transaction rate will go up significantly.

I also found this talk by Peter Todd from keepbitcoinfree.org on using off blockchain transactions to avoid hitting the main block chain with the full transaction load which was followed by good Q&A

There's also some charts comparing to other payment networks

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