In recent times, there have been several debates on whether Bitcoin's energy consumption will reach inconceivable amounts of electricity and resources in future years.

The figure (1) below indicates an exponential growth function highlighting the possibility it may consume the world's entire electrical energy by February 2020.

Can it be true that the Bitcoin network has such a huge environmental footprint? It is a media-effective story picked up by a large number of media outlets, but one cannot expect continuous, exponential growth. Let's look at how to calculate the power consumption of the Bitcoin-block-chain and if there is any reason this voracious energy consumption will continue endlessly.

Power Consumption Formula

The proof-of-work process makes Bitcoin a very secure, decentralized network. Due to it's decentralized nature, nobody knows exactly how much power is required by the network. There have been many sophisticated attempts to directly determine the energy demand. However, these results cannot be used due to the many uncertain assumptions and apparently unrealistic results, (e.g. Figure 1).

This is why an indirect calculation approach makes sense here, by calculating miners' income and deducing the energy costs and energy consumption as a percentage. Based on the assumptions on (bitcoinenergyconsumption.com), I have derived the following formula.

On average, the power consumption of all Bitcoin miners in ten minutes is: 

where

E = Average total hashing electricity consumption of all miners (not others nodes) to get a new block in the block-chain (kWh, not included is power needed for ASIC production, for Miner's office, light etc...)

f = Total fees paid for all transactions in the block in $USD

r = Coinbase block reward for winning miner (50 BTC, 25 BTC. currently 12.5 BTC, ...)

p = Bitcoin (average) exchange price in $USD/BTC

k = Average price to buy a kWh ($USD/kWh). If assuming a price of $0.05/kWh, formula is E = 12kWh (f+rp)

This formula helps us to answer many questions regarding Bitcoin's energy consumption. Let's investigate them one by one. Does this formula include any variables capable of causing an exponential growth in E with a monthly rate of 29.98% corresponding to an annual rate of 2225.5%?

• k might grow exponentially with inflation, if at all then this works against the exponential growth of E. If k would drop exponentially, then this would promote the exponential growth of E, at least partially. Therefore, this is a very unlikely scenario. 
• r definitely goes exponentially in the other direction and is not helping E in any way to reach stratospheric growth.
• f might increase, but if exponentially and at an extraordinary rate, it would stand in the way of this growth itself (auto-cannibalization). Users would therefore avoid transactions and switch to other currencies wherever possible, which would drive fee's down again.
• p is getting less important for the energy consumption over time (due to an exponential decrease of r). Currently, given that we are in Bitcoin's early years, it still has a significant impact. In case p would grow exponentially, the formula shows that this may drive E into growth at a similar rate. The p factor is driven by demand. What would be Bitcoin's price in February 2020 assuming the monthly energy consumption growth is 29.98% (k=0.05$, r=12.5 BTC and f=$9160.50USD)?

21,776,000,000 kWh = 21,776 TWh = e = 12kWh (f+rp) ⇒ p = $145.2m

This again would have auto-cannibalization effects. The $ price for all 18.6m Bitcoin's ($2.637 Trillion) would by far exceed existing supply, so this would require huge inflation. This amount is more than twelve times higher than the estimated value of all developed real estate in the world. The inflation in this scenario would raise the price per kWh significantly, which would cause energy consumption to decrease according to our formula.

Example

Calculation of 2017 Bitcoin average power consumption for one block (10 minutes time-frame) with the formula (numbers extracted from above):

Average price (p) = $3524

Block reward (r) = 12.5 BTC

Average no. of transactions/block: 1970

Average transaction fee: $4.65 ⇒ Total fee's per block (f) = $9160.50

With k = $0.05 follows

E = 637,526 kWh

⇒ Energy consumption per transaction = 324 kWh

⇒ Electricity costs per average transaction = $16.20

⇒ Total power consumption of the Bitcoin network 2017: 33,56 TWh or 3831 MW permanent average

Questions & Answers

Will the power consumption of the Bitcoin network continue to increase in the future?

Not necessarily. Factors influencing electricity consumption are:

• f total fee's paid. This is market driven. If demand goes down, fee's go down.
• r Coinbase reward. It is dropping exponentially (halving every four years) which is a reduction factor
• p the higher the exchange price, the higher the consumption in the early years, later on the price has no influence anymore because it is multiplied by a value tending to zero.
• k assumed as stable. If going up, power consumption goes down.

For example, if Bitcoin's price under the current protocol and hashing power would be $100,000 in year the 2049. This causes 'only' 0.6*0.0244140625*$100,000/$0.05 = 150 MWh per block where $10,000 would cause 0.6*12.5*$10,000/$0.05 = 1500 MWh per block. On the other hand, if people hold their Bitcoin's and there is low demand for trade, then fee's are close to zero.

Will miners' power consumption fall because more efficient power-saving ASICs are being invented and less power is needed to calculate a hash?

No, technical progress is not helping here (and if so only in the short term). If miners use more efficient tools, then the difficulty of the hashing puzzle will increase accordingly. Each single hash would then be calculated consuming less power, but this is compensated by the fact that more hashes have to be calculated. The bottom line is that 60% of miners' income goes into electricity bills, if they can now calculate more hashes, then competitors can too, and all of them coincide with the same percentage of success at a higher level.

Will bitcoin transaction fees increase when miners can no longer generate revenue from the Coinbase rewards?

No, at least not for this reason. There is no relation between transaction fees and the Coinbase reward, but fees are directly related to the demand for transactions. Obviously, transaction fee changes have no influence on the hard-coded Coinbase reward and vice-versa. For quicker processing of transactions, fees are purely determined by market demand (transactions with the highest fees get into the next block until the block is full) and the Coinbase reward is defined by the Bitcoin protocol. For example, if the Bitcoin price (p) is $100,000 (or $1) and only five people buy and sell every 10 minutes, then transaction fees are very low, if tens of thousands of transactions compete under current circumstances then fees are very high. Fees may increase, but there is no connection to the reward.

Does a lower Coinbase reward reduce the power consumption of the Bitcoin network?

Yes. Coinbase reward reduction takes place on the so called halving days (estimated next halving day is on June 8, 2020: http://www.bitcoinblockhalf.com/, before halving years were 2016 and 2012). What happens when comparing the halving day with the day before? Miners get only half the Coinbase reward in Bitcoin, but the demand for Bitcoins, thus also the fees and the price (p) are not influenced by this reward reduction. The effect is that large numbers of miners leave the business until the remaining make a profit again. Hashing power goes down and therefore electric consumption drops. This means that over the hard-coded exponential drop in the Coinbase reward reduces the power consumption of the Bitcoin network.

Is a rising Bitcoin demand causing higher electricity consumption?

Yes. If demand goes up above a certain level, the unspent transactions don't fit into the next block, so only the ones with highest fees (top down) are selected. In the formula, you see that higher fees (f) cause higher consumption of kWh. The same happens when a lot of people sell their Bitcoins (which is actually the same, because with a Bitcoin transfer, one person is usually selling and another person at the same time is buying).

Does a high (low) Bitcoin price cause high (low) power consumption?

Not necessarily. As time moves on from Bitcoin's beginning in 2009, the less impact the price of Bitcoin has on power consumption. Today the impact is 25% of the initial impact (reward is now only 25% of 2009 value) which is still strong, in 2140 there is no impact anymore (under current rules). However, should there be a remarkable and verifiable correlation between the Bitcoin price and the number of transactions, then this statement would have to be put into perspective.

Is an energy consumption close to zero conceivable for the Bitcoin network?

This could theoretically be the case in the future with a sophisticated new consensus algorithm introduced by fork. With today's proof-of-work algorithm, this would only work in theory, according to our formula, if the electricity price (k) goes against infinity or if the Bitcoin price or fees would be negative, namely (p=-f/r). However, this scenario can be disregarded because the protocol doesn't allow for it. In any case, everyone would keep their Bitcoins if the price were negative (miners would stop adding transactions into their blocks if the fees were negative) and incidentally the security of transaction would no longer be guaranteed. Future layer two technologies such as the lightning network (side-chains, atomic swap...) could have a very positive influence on this energy balance.

Do Altcoins have an effect on the Bitcoin power consumption?

Mining is a highly competitive business with a low entry threshold. Miners must therefore work as efficiently as possible and will switch, often automatically, to other coins if there is a higher turnover with the same hashing power. Any switch, of course, results in a lower power consumption of the Bitcoin block-chain. However, this power is redirected to another coin. This shows that the power consumption of the Bitcoin network should not be seen in total isolation from the rest of the proof-of-work Cryptoworld.

Conclusion

There is no risk that the Bitcoin network consumes the entire world's electrical energy. If one is to calculate the future power consumption of the Bitcoin network, they need to take into account several factors. The first being the Coinbase halving reduction, which lowers power consumption. Additionally, power consumption costs are lower than miners' total revenue and fees do not increase when block rewards reduces. One needs to bear in mind that power costs might increase, which would reduce power consumption. A further limiting factor for fees (and thus also the electricity consumption) is that with very high fees, transactions would be shifted to other currencies (fiat or altcoins). Hashing puzzles with useful side effects for more efficient energy use does not improve the energy balance. Instead of comparing the power consumption of the Bitcoin network with that of countries, it would make more sense to choose other payment systems as a comparison point. 

It is neither a given or is it likely that the power consumption of the Bitcoin network will continue to increase in the long term. However, if the built-in mechanisms interacting with users and the rest of the cryptographic world would lead to a very low power consumption, the security of the decentralized block-chain could suffer. All this applies under the current rules. I am sure that there will be future developments that can solve the scalability problem and handle a large number of transactions without significant additional resources. We are just at the beginning of this great technology.

"Bitcoin is a remarkable cryptographic achievement and the ability to create something that is not duplicable in the digital world has enormous value."

Appendix

Resources

(1) Bitcoin mining now consuming more electricity than 159 countries including Ireland & most countries in Africa

https://powercompare.co.uk/bitcoin

(2) Sustainability of bitcoin and blockchains (Vranken, Harald), October 2017

http://www.sciencedirect.com/science/article/pii/S1877343517300015?via%3Dihub

(3) Bitcoin price stats and information (data extracted on December 22,2017)

https://bitinfocharts.com/bitcoin/

(4) Blockchain Charts (data extracted on December 22,2017)

https://blockchain.info/charts/

(5) All the World’s Money and Markets in One Visualization

http://money.visualcapitalist.com/worlds-money-markets-one-visualization-2017/

(6) Harnessing Energy from Bitcoin Mining to Sequence Genetic data

https://cointelegraph.com/news/harnessing-energy-from-bitcoin-mining-to-sequence-genetic-data

(7) The Bitcoin vs Visa Electricity Consumption Fallacy

https://hackernoon.com/the-bitcoin-vs-visa-electricity-consumption-fallacy-8cf194987a50