Price of Energy - Q3 2019

The exercise as we have been calculating it here is as follows: we calculate the cost of production of coin using energy, and then we calculate the cost of purchasing energy using coin.

Lets start with a quick look at the hash rate and reward so we can say how many satoshis a double SHA256 is worth. We are still in the era of 12.5 BTC coinbase, so that's 12.5*6*24=1800 BTC per day. Tack on 50 or so BTC in fees, call it 1850. That's 0.0214 BTC per second, a whopping 2.14 million satoshi every second.

What else happens in a second? No no, what else related to bitcoin mining happens every second? Well, 90 exahashes are performed by the miners. How many is that? 9.0 * 10^18 double sha256 hashes.

It works out to 2.38*10^-14 satoshis per double hash.

That's not a lot of money. Get cracking!

Next we have a tally of some of the top hardware being advertised:

Bitfury BlockBox: 14PH/S 1.1 MW 79 W/T
Ebang Ebit E12 44TH/S 57 W/T
Canaan Avalon 166-68T 68TH/S 3196W
Bitmain Antminer S17Pro 53TH/S 39 J/TH

Lets just say we are spending something like 50 W of power to keep our boxes spinning at a terahash per second. Surely some people are doing a lot better than what we can dig up in 5 minutes online, but probably some people are doing worse. So what's our global energy hit at 90 EH/s? Well 90 EH is 90 thousand PH which is 90 million TH. That's 4.5 billion Watts. It's a much lower estimate than what some report as the world bitcoin mining energy cost.

If a Watt-second, or Joule, gets us 1/50 of a TH, that's 2*10^10 hashes per Joule. We now have sats per hash, and joules per hash. Our energy cost in sats per joule works out to be about:

C_1 = 0.5 msat / Joule.

That's how much btc we can produce with a Joule of energy, minus overhead.

So our difficulty has gone up a bit, and our hardware has improved a bit, but our price of energy hasn't moved much.


How about the other direction? The range of prices of energy sources in fiat is, well as you'd expect from using fiat currency, literally all over the map: differing by factors of an order or two of magnitude. So lets take an arbitrary cost of $0.05 USD per kwh, just because this is a number used by Camilo Mora et al. in a Nature Climate Science article, and it's lower than average but that's probably what you want for this application. The price of a dollar today is 1/9350 BTC apparently, so that puts a kwh in at a whopping 535 satoshis per kwh. A kwh is 3.6*10^6 joules, so this gives us:

C_2 = 0.15 msat / Joule

That's how much it costs us to buy a Joule of energy.

The difference between those two bold figures is what drives the expansion of the bitcoin mining industry, and is something likely to remain until something like a free market in energy appears on our lovely little spaceship aka Earth.

The ratio C1/C2 calculated here for BTC is about 4 or 5. Compare that to the ratio for fiat currency: 10^20 or so.


Leave a Reply

Your email address will not be published. Required fields are marked *