DeepSeek: Estimating the Total Historical Energy Cost of Bitcoin

Okay, so I need to estimate the total historical energy cost of 1 Bitcoin. Hmm, where do I start? I know that Bitcoin mining uses a lot of energy because of the Proof of Work mechanism. Miners use powerful computers to solve complex mathematical problems, and this process consumes electricity. But how do I calculate the total energy cost over the entire history of Bitcoin?

First, I think I need to find out how much energy has been consumed by the Bitcoin network since its inception. Then, multiply that by the average cost of electricity over time to get the total energy cost. But wait, how do I get the energy consumption data? I remember there are some estimates like the Cambridge Bitcoin Electricity Consumption Index (CBECI) that tracks this. Maybe I can use their data or similar sources.

Also, the energy consumption isn’t constant over time. In the early days, when Bitcoin was new, there were fewer miners and less powerful hardware. As Bitcoin gained popularity, more miners joined the network, and ASICs (Application-Specific Integrated Circuits) became prevalent, which are more energy-efficient but still consume a lot because the network’s total hashrate increases. So the energy consumption has probably increased exponentially over time.

I need to break this down into manageable parts. Let’s outline the steps:

1. **Estimate total energy consumption from 2009 (Bitcoin’s launch) to present.**

– Find the annual energy consumption each year.

– Sum them up for the total energy used.

2. **Estimate the average electricity cost per kWh over time.**

– Electricity prices vary by region and over time. Miners often locate in areas with cheap electricity, like China (before crackdowns), Iceland, etc. So maybe use a global average or a weighted average based on miner locations.

3. **Multiply total energy consumed by average electricity cost to get total energy cost.**

But how detailed do I need to be? Since this is an estimate, maybe use yearly averages. Also, I should consider the changing efficiency of mining hardware over time. Early CPUs and GPUs were less efficient than ASICs. So the energy consumption per hash has decreased, but the total network hashrate has increased, leading to higher overall consumption.

Wait, another approach: The total energy consumed can be approximated by the total number of hashes performed over Bitcoin’s history divided by the efficiency (hashes per joule) of the hardware at each time. But tracking the exact hardware mix over time is complicated. Maybe use average network efficiency each year?

Alternatively, use the total network hashrate over time, convert that into energy consumption by assuming an average efficiency (J/TH). For example, if the network hashrate is X TH/s, and the average efficiency is Y J/TH, then energy consumption per second is X*Y. Multiply by seconds in a year to get annual energy.

But the efficiency (J/TH) has improved over time. So I need a timeline of average efficiency. Maybe there are studies or models that estimate this. For instance, the CBECI might use certain assumptions about miner efficiency improvements.

Alternatively, some sources provide total annual energy consumption estimates. For example, Digiconomist’s Bitcoin Energy Consumption Index. If I can get annual estimates from 2009 to 2023, sum them all up.

Once I have the total energy in TWh, convert that to kWh (1 TWh = 1 billion kWh) and multiply by the average electricity cost per kWh. But the electricity cost varies. Miners seek the cheapest electricity, so maybe the average cost is lower than residential rates. Some estimates use $0.05 per kWh as a global average for miners.

Wait, let’s check some sources. According to the CBECI, as of recent years, the annualized consumption is around 100 TWh/year. But going back, in 2017 it was around 30 TWh, and earlier years much less. For example, in 2009, it was negligible because there were few miners.

So perhaps approximate the total energy consumption by year:

– 2009: Minimal, maybe 0.01 TWh

– 2010: 0.1 TWh

– 2011: 0.5 TWh

– 2012: 1 TWh

– 2013: 5 TWh

– 2014: 10 TWh

– 2015: 15 TWh

– 2016: 20 TWh

– 2017: 30 TWh

– 2018: 50 TWh

– 2019: 60 TWh

– 2020: 80 TWh

– 2021: 100 TWh

– 2022: 120 TWh

– 2023: 130 TWh (up to present)

But these numbers are rough guesses. I need to cross-reference with actual data. For example, according to CBECI, in 2020, Bitcoin’s annual consumption was around 75 TWh. In 2021, it peaked around 100 TWh. So maybe adjust the estimates accordingly.

Adding up these would give total TWh over the years. Let’s try:

From 2009 to 2023 (15 years):

2009: 0.01 TWh

2010: 0.1

2011: 0.5

2012: 1

2013: 5

2014: 10

2015: 15

2016: 20

2017: 30

2018: 50

2019: 60

2020: 75

2021: 100

2022: 120

2023: 65 (half-year if current)

Adding these up:

0.01 + 0.1 = 0.11

+0.5 = 0.61

+1 = 1.61

+5 = 6.61

+10 = 16.61

+15 = 31.61

+20 = 51.61

+30 = 81.61

+50 = 131.61

+60 = 191.61

+75 = 266.61

+100 = 366.61

+120 = 486.61

+65 = 551.61 TWh total energy consumption.

Convert that to kWh: 551.61 TWh = 551,610,000,000 kWh.

Assuming an average electricity cost of $0.05 per kWh (this is a common estimate for industrial/mining rates), total energy cost would be:

551,610,000,000 kWh * $0.05/kWh = $27,580,500,000.

So approximately $27.58 billion.

But wait, this is the total energy cost for the entire Bitcoin network’s history. The question is about the energy cost “of 1 Bitcoin”. Does that mean per Bitcoin mined? Or the energy cost per Bitcoin in terms of transaction?

Assuming it’s per Bitcoin mined, since energy is used in mining. There have been around 19 million Bitcoins mined so far. So total energy cost per Bitcoin would be $27.58 billion / 19 million ≈ $1,452 per Bitcoin.

But this seems low. Wait, maybe the average electricity cost is higher. Some sources suggest average costs between $0.03 to $0.05 per kWh. If we use $0.05, but maybe some years it was higher. Alternatively, if the average is $0.05, then the total is as above.

But let’s check another approach. If total energy is 551.61 TWh, and total Bitcoins mined is 19 million, then energy per Bitcoin is 551,610,000,000 kWh / 19,000,000 ≈ 29,032 kWh per Bitcoin. At $0.05 per kWh, that’s 29,032 * 0.05 = $1,451.6 per Bitcoin.

But some estimates I’ve seen before suggest higher numbers. For example, in 2021, it was reported that the energy cost per Bitcoin was around $20,000, but that might be based on higher electricity costs or different efficiency assumptions.

Wait, perhaps the confusion is between energy consumed (in kWh) versus cost. If the question is asking for the total historical energy cost attributed to a single Bitcoin, considering all the energy used in the network divided by total Bitcoins mined, then the above calculation holds. But maybe the approach is different.

Alternatively, maybe the question is asking for the total energy cost to produce one Bitcoin, considering the mining difficulty over time. That is, for each block mined, energy is used, and the cost accumulates per Bitcoin.

But since Bitcoins are produced at a fixed rate (block reward), and the difficulty adjusts, the energy cost per Bitcoin increases over time. So to compute the total historical energy cost for 1 Bitcoin, you would need to sum the energy cost for each Bitcoin mined at the time it was mined.

But this is complex because each Bitcoin mined in 2009 required much less energy than one mined in 2023. So the average would be somewhere in between.

Alternatively, take the total energy cost ($27.58 billion) and divide by total Bitcoins (19 million), getting ~$1,452 per Bitcoin.

But let’s verify with another method. Suppose in 2023, the network uses 130 TWh/year, and the current block reward is 6.25 BTC per block (until halving in 2024). There are 144 blocks per day, so 144 * 6.25 = 900 BTC/day. Annual production is 900 * 365 = 328,500 BTC/year. Energy per BTC in 2023 would be 130 TWh / 328,500 BTC ≈ 395,736 kWh/BTC. At $0.05/kWh, that’s $19,786 per BTC.

But this is just for 2023. Earlier years had lower energy consumption and more BTC mined per year because the block reward was higher (e.g., 50 BTC per block initially, then 25, 12.5, etc.). So the average would be lower.

For example, in 2009, the block reward was 50 BTC, and energy consumption was negligible. So each BTC from 2009 had almost no energy cost. As time goes on, the energy per BTC increases.

Therefore, to get the historical average, we need to calculate the energy used each year, divide by the number of BTC mined that year, then sum all those and divide by total BTC. But this requires detailed data per year.

Alternatively, approximate by considering the average block reward over time and the average energy consumption.

Total BTC mined: ~19 million.

Total blocks: approximately (14 years * 365 days * 144 blocks/day) ≈ 14*365=5110; 5110*144≈736,000 blocks. Each block initially had 50 BTC, then 25, 12.5, 6.25.

The halvings occurred in 2012, 2016, and 2020. So:

From 2009-2012: 50 BTC per block.

2012-2016: 25 BTC per block.

2016-2020: 12.5 BTC per block.

2020-present: 6.25 BTC per block.

Calculating total BTC per period:

First period: 2009-2012 (4 years): 4*365*144*50 = 4*365=1,460 days; 1,460*144=210,240 blocks; 210,240*50=10,512,000 BTC.

Second period: 2013-2016 (4 years): same number of blocks, 210,240*25=5,256,000 BTC.

Third period: 2017-2020 (4 years): 210,240*12.5=2,628,000 BTC.

Fourth period: 2021-2023 (3 years): 3*365*144= 1,095 days; 1,095*144=157,680 blocks; 157,680*6.25=985,500 BTC.

Total BTC: 10,512,000 + 5,256,000 + 2,628,000 + 985,500 ≈ 19,381,500 BTC. Close to the actual 19 million, so this approximation works.

Now, assign energy consumption to each period. Earlier periods had lower energy use.

Using the previous annual estimates:

First period (2009-2012):

2009: 0.01 TWh

2010: 0.1

2011: 0.5

2012: 1

Total: 0.01+0.1+0.5+1=1.61 TWh

Second period (2013-2016):

2013:5, 2014:10, 2015:15, 2016:20 → total=5+10+15+20=50 TWh

Third period (2017-2020):

2017:30, 2018:50, 2019:60, 2020:75 → total=30+50+60+75=215 TWh

Fourth period (2021-2023):

2021:100, 2022:120, 2023:65 (half year) → total=100+120+65=285 TWh

Total energy: 1.61 +50 +215 +285 = 551.61 TWh as before.

Now, calculate energy per BTC in each period:

First period: 1.61 TWh / 10,512,000 BTC ≈ 0.153 MWh/BTC = 153 kWh/BTC

Second period:50 TWh /5,256,000 BTC ≈9.51 MWh/BTC =9,510 kWh/BTC

Third period:215 TWh /2,628,000 BTC ≈81.8 MWh/BTC =81,800 kWh/BTC

Fourth period:285 TWh /985,500 BTC≈289 MWh/BTC=289,000 kWh/BTC

Then, multiply each by electricity cost and sum:

First period:153 kWh * $0.05 = $7.65 per BTC

Second period:9,510 kWh *0.05= $475.5

Third period:81,800 kWh*0.05= $4,090

Fourth period:289,000 kWh*0.05= $14,450

Now, compute the weighted average:

Total cost = (10,512,000*7.65 +5,256,000*475.5 +2,628,000*4090 +985,500*14450) /19,381,500

Calculate each term:

First term:10,512,000 *7.65 ≈80,464,800

Second term:5,256,000 *475.5 ≈2,500,068,000

Third term:2,628,000 *4090 ≈10,750,520,000

Fourth term:985,500 *14,450 ≈14,247,975,000

Total cost sum:80,464,800 +2,500,068,000 =2,580,532,800

+10,750,520,000 =13,331,052,800

+14,247,975,000 =27,579,027,800

Divide by 19,381,500 BTC ≈$27,579,027,800 /19,381,500 ≈$1,422 per BTC

So approximately $1,422 per Bitcoin when considering the varying energy costs per era.

This aligns with the earlier total estimate of ~$27.58 billion total energy cost divided by ~19 million BTC ≈$1,452 per BTC. The slight difference is due to rounding in the periods.

But wait, this assumes that the electricity cost is constant at $0.05 per kWh over the entire period. However, electricity prices might have changed over time. For example, if earlier years had cheaper electricity, and recent years more expensive, the average could be different. But without detailed data on regional miner locations and electricity costs each year, it’s hard to adjust for this. The $0.05 is a rough average often cited.

Alternatively, if electricity costs were higher, say $0.10 per kWh, the total cost would double. But miners tend to seek the cheapest sources, so $0.05 is more realistic.

Another factor is that mining hardware efficiency improves over time, so more hashes per joule, but the network difficulty increases, requiring more hashes. So energy consumption is a balance between efficiency gains and difficulty increases. However, the total energy consumption estimates from sources like CBECI already factor in these changes.

In conclusion, the total historical energy cost for the entire Bitcoin network is approximately $27.5 billion, leading to an average of around $1,400 to $1,500 per Bitcoin. However, this is a rough estimate and actual numbers could vary based on more precise data on energy consumption and electricity costs over time.