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How can we estimate a lower bound for the electrical energy consumed by Bitcoin's Proof of Work (PoW) mechanism? Obviously there is no hard bound, but there are some market laws at work and I think it's possible to give an estimation under some assumptions, but strangely I have not been able to find much like that.

Clarification: I'm specifically looking for something that allows predictions for the future depending on bitcoin price and usage, where mining technology and other factors might have changed. Compare my own answer as an example why I think this is possible, though I feel it could be improved. (Please note that it seems the energy consumption is pretty independent of mining technology ). Of course that kind of answer needs some assumptions - that's perfectly fine.

I think it's important to also have such a lower bound to prepare for what'd happen if the bitcoin price really goes above $100000, as some think, considering that the mining reward is proportional to the bitcoin price, and since we are already (as of 10/2023) around using up 0.4% of the world electricity production (= 15GW, assuming world production is about 30000TWh/year) ... What's your take on that?

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    Hi Hans-Peter, thanks for your interesting and well-researched questions lately. While answering your own question is a great way to establish that you have "done your homework" , please focus on asking your question in the question post. "Could you please check my work"-style questions don’t work particularly well in our format. However, self-answers are explicitly welcome here, so I would propose that you round out your question post with some clear prompts and post the last four paragraphs as your own answer post below instead.
    – Murch
    Oct 14, 2023 at 21:33
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    @Murch Thank you for your feedback! I moved the answer out and updated the question accordingly, and tried to better clarify the intention of my question. Oct 15, 2023 at 9:15

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One way to estimate a lower bound for Bitcoin’s electricity usage is to assume that the current hashrate of the network is produced by the most energy efficient technology in the market. A cursory search suggests the Antminer S19 XP with (according to Bitmain's product page) 0.022 J/GH as a likely candidate. With that baseline, today’s 471 EH/s would roughly take 0.022 J/GH * 471 EH/s * 1000 EH/PH *1000 PH/TH * 1000 TH/GH = 10,362,000,000 J/s = 10.362 GW. This closely matches the "Theoretical Lower Bound" estimated by the Cambridge Bitcoin Energy Consumption Index (CBECI) today of 9.41 GW.

A reasonable lower bound would then at least add some factor for the necessary cooling. The CBECI website provides some other figures and an explanation of their methodology which may be useful in that regard

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  • Thank you very much for your answer. I did hope for an answer that better allows answering questions about the future where technology would have changed, though - sorry for not making that clear enough. I updated the question accordingly, sorry that the answer doesn't completely fit anymore. Perhaps the methodology ccaf.io/cbnsi/cbeci/methodology of the CBECI allows extracting something like that, but it's quite involved. I'll have a look on that later. Oct 15, 2023 at 9:23
  • That methodology didn't help me, since this is a technical argument all about specific machines and hashrates, while my question needs to involve economical arguments, too. :-( BTW: perhaps you could add that 10GW is about 0.3% of world electricity production assuming 30000TWh / year. I guess thats much more relatable than GW. Oct 21, 2023 at 7:28
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Let me give a shot at it as an example, hopefully you can do better or phrase it better.

While it'd be more difficult to estimate the amount of energy because of varying energy prices, we might get an estimation on the total amount of money spent on electrical energy for bitcoin POW by comparing it to the mining reward which pays for the mining (as of 2023 6.25 BTC every ten minutes, plus some transaction costs.) That is an obvious upper bound for the energy cost, but I think we can also derive a lower bound from that.

I've read that the largest expense (about 70%) in mining is energy and that mining is a thin margin business. Obviously there is mining equipment, maintenance and taxes, so let's say the actual costs are at most 3 times the costs of the electrical energy, estimating high to play safe. The margin of the miners would be the difference of the mining reward and those total costs. Assuming bitcoin prices are stable enough for a while and chip shortage levels out, new miners would come in until the margin is too low. If that would result in, e.g., a margin of 25%, we'd have:

global electrical energy costs spent on mining > mining reward / 4

And that's pretty independent of the mining technology. When I calculate with that, I currently (10/2023) get a ballpark number of 0.1% of the world electrical energy production, which is consistent with some estimations (1, 2.) Perhaps it'd be better to use the lowest mining reward rate in the last few months in that formula, to cover price spikes.

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