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Can anyone explain me in the plain English how difficulty is calculated. I have a very approximate understanding that it is calculated based on the amount of hash power in all the bitcoin community over a specific period of time. But this is very vague.

Also I understand it can change very rapidly. Can it only increase? Is there any formula how to calculate it or predict it?

Thanks for a detailed answer, Meni Rosenfeld. Just to make sure I got everything right. I am summing up all the time, it took to generate the last 2016 blocks. And then apply the formula.

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I think follow up questions are better as comments to the answer. Basically yes, but no summing is actually needed - you can just take the timestamps of the last block and of the one 2016 blocks before, and subtract. – Meni Rosenfeld Dec 19 '12 at 14:18

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The Bitcoin difficulty started at 1 (and can never go below that). Then for every 2016 blocks that are found, the timestamps of the blocks are compared to find out how much time it took to find 2016 blocks, call it T. We want 2016 blocks to take 2 weeks, so if T is different, we multiply the difficulty by (2 weeks / T) - this way, if the hashrate continues the way it was, it will now take 2 weeks to find 2016 blocks.

For example, if it took only 10 days it means difficulty is too low and thus will be increased by 40%.

The difficulty can increase or decrease depending on whether it took less or more than 2 weeks to find 2016 blocks. Generally, the difficulty will decrease after the network hashrate drops.

If the correction factor is greater than 4 (or less than 1/4), then 4 or 1/4 are used instead, to prevent the change to be too abrupt.

There is a bug in the implementation, due to which the calculation is based on the time to find the last 2015 blocks rather than 2016. Fixing it would require a hard fork and is thus deferred for now.

It is possible to give a rough estimate for the next difficulty change, based on the time to find the recent blocks. Nobody can make longer-term predictions for the future difficulty reliably, but anyone is free to speculate based on exchange rate trends, Moore's law and other hardware advances.

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Stellar answer. – Colin Dean Dec 19 '12 at 17:02
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the answer is really amazing and precise. I wish all answers were the same – Salvador Dali Dec 19 '12 at 17:46
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@SalvadorDali: Thank you, it helps that the question is good :). – Meni Rosenfeld Dec 19 '12 at 17:55
Is that bug still there? Shouldn't there be a GitHub issue for that so that people can keep track of the status... With such bugs in the protocol, it will be hard for the Bitcoin ecosystem to move away from the situation in which the Satoshi client devs set all the rules. – Steven Roose Jun 11 at 22:23
@StevenRoose: AFAIK it is, but I will leave it to people who are more involved with the core code to comment... This is adequate for a separate SE question. – Meni Rosenfeld Jun 12 at 15:19

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