Methodology

Overview

Summary

The Cambridge Bitcoin Electricity Consumption Index (CBECI) provides a real-time estimate of the total electricity load and consumption of the Bitcoin network. The model is based on a bottom-up approach initially developed by Marc Bevand in 2017 that takes different types of available mining hardware as the starting point.

Given that the exact electricity consumption cannot be determined, the CBECI provides a range of possibilities consisting of a lower bound (floor) and an upper bound (ceiling) estimate. Within the boundaries of this range, a best-guess estimate is calculated to provide a more realistic figure that we believe comes closest to Bitcoin’s real annual electricity consumption.

The lower bound estimate corresponds to the absolute minimum total electricity expenditure based on the best case assumption that all miners always use the most energy-efficient equipment available on the market. The upper bound estimate specifies the absolute maximum total electricity expenditure based on the worst case assumption that all miners always use the least energy-efficient hardware available on the market as long as running the equipment is still profitable in electricity terms. The best-guess estimate is based on the assumption that miners use a basket of profitable hardware rather than a single model.

Representation

The CBECI landing page displays two numbers for each type of estimate.

The first number refers to the total electrical power consumed by the Bitcoin network and is expressed in gigawatts (GW). This figure is updated every 30 seconds and corresponds to the rate at which Bitcoin uses electricity.

The second number refers to the total yearly electricity consumption of the Bitcoin network and is expressed in terawatt-hours (TWh). We annualise Bitcoin’s electricity consumption assuming continuous power usage at the aforementioned rate over the period of one year. We apply a 7-day moving average to the resulting data point in order to make the output value less dependent of short-term hashrate movements, and thus more suitable for comparisons with alternative uses of electricity.

Model parameters

The model takes into account the parameters outlined in Table 1 below. The following sections will specify how each estimate is calculated and what assumptions have been used.

ParameterDescriptionMeasure/UnitSource
Network hashrate Total number of hashes produced by miners Exahashes per second (Eh/s) Dynamic: Blockchain.info
Miner revenues Total value of block rewards and transaction fees paid to miners USD Dynamic: Blockchain.info
Mining equipment efficiency Measures the energy efficiency of a given mining hardware type Joules per Gigahash (J/Gh) Static: hardware specs from 60+ equipment types, taken from various sources
Electricity cost Average electricity cost incurred by miners USD per kilowatt-hour ($/kWh) Static: estimate (assumption)
Data centre efficiency Measures how efficiently energy is used in a data centre: expressed via power usage effectiveness (PUE) Static: estimate (assumption)

CBECI Model

Selecting mining equipment

In the first years of Bitcoin, mining was mainly performed using general-purpose graphics processing units (GPUs) and field-programmable gate arrays (FPGAs). This changed considerably when in 2012 the first application-specific integrated circuits (ASICs) started to emerge. ASICs are specialised hardware specifically optimised for Bitcoin mining that are orders of magnitude more efficient than previous devices used for mining: it didn’t take long for ASICs to become popular and displace GPU and FPGA mining.

We have compiled a list of more than 60 different Bitcoin ASIC models designed for SHA-256 operations that have been brought to market since October 2014, which serves as the starting date of the CBECI. The list is based on a combination of public resources that list various types of mining equipment and their specifications. 1

Mining efficiency of each machine type is expressed in Joules per Gigahash (J/Gh): given that real power usage can vary significantly depending on several parameters (e.g. usage conditions, overclocking), the manufacturer specifications have been refined with the help of experts to more accurately reflect real power usage. The full list is available at http://sha256.cbeci.org and is open to comments and suggestions. Figure 1 shows the evolution of Bitcoin mining equipment efficiency since late 2014.

Note: a 1000W mining device that generates 10,000 Gigahashes per second (Gh/s) has an efficiency of 0.1 Joules per Gh (J/Gh). This chart is based on a list of 60+ SHA-256 mining equipment available at http://sha256.cbeci.org.

The profitability threshold

The key idea underlying the CBECI model is that miners will run the equipment as long as it remains profitable in electricity terms. In order to determine the time periods during which a given hardware type is profitable, we model the economic lifetime of each machine by taking into account total miner revenues, total network hashrate, the energy efficiency of the hardware in question, and the average electricity price per kWh that miners have to pay.

This results in the following mathematical inequality:

It is worth noting that profitability in this context exclusively considers electricity costs incurred for running the machines: it does not take into account capital expenditures (e.g. acquisition and amortisation costs) nor other operational expenditures (e.g. cooling, maintenance, and labour costs).

The profitability threshold (θ) is then calculated as follows:

Assumption 1: the global average electricity price is constant over time and corresponds to 0.05 USD/kWh.

Electricity prices available to miners vary significantly from one region to another for a variety of reasons. We assume that on average, miners face a constant electricity price of 5 USD cents per kilowatt-hour (0.05 USD/kWh). This default value is based on in-depth conversations with miners worldwide and is consistent with estimates used in previous research. 2

Note: The CBECI landing page allows visitors to choose different values for the average electricity cost in order to explore how electricity prices influence hardware selection and total electricity consumption.

Assuming a fixed electricity price of 0.05 USD/kWh, we can model the evolution of the profitability threshold over time (Figure 2). While mining equipment with an energy efficiency below 2 J/Gh remained profitable in early 2015, the threshold has substantially decreased over time as a result of the introduction of newer ASIC generations and a continuous increase in hashrate. Large price spikes occasionally lead to a sharp increase of the profitability threshold (e.g. bull run in late 2017), which tends to correct relatively soon as effects are cancelled out by growing total hashrate.


Sometimes, it is possible that no mining equipment is profitable during a certain period. In this case, we use the following assumption:

Assumption 2: during time periods where no mining equipment is profitable, the model uses the last known profitable equipment.

It is reasonable to assume that miners will not immediately switch off unprofitable equipment as long as the time periods are acceptably short and infrequent.

The model applies a 14-day moving average to the profitability threshold in order to smoothen the switch from one equipment type to another as a result of short-term hashrate variations and price volatility.

Constructing the lower bound estimate

In a best case scenario, every single miner would always use the most energy-efficient equipment that maximises expected profits. The lower bound estimate (Elower) is thus based on the following best-case assumption:

Assumption 3a (lower bound): all miners always run the most efficient hardware available.

This assumption also implies that miners will rapidly upgrade mining gear as soon as more energy-efficient hardware becomes available on the market.

Assumption 4a (lower bound): all mining facilities have a PUE of 1.01.

Power usage effectiveness (PUE) is a measure of data centre energy efficiency: data centres generally consume more energy than is required to simply run servers, mostly because of cooling, supporting IT equipment, and other overheads. The higher the ratio, the less efficiently energy is used. Data centres with PUE below 1.2 are generally considered efficient. For reference, Google’s average PUE is 1.11, whereas the average PUE of most data centres corresponds to 1.8 or more.

In the case of Bitcoin mining, however, electricity costs account for the vast majority of operational expenditures: mining farm operators have a clear incentive to optimise cooling systems in order to reduce overall costs. Conversations with miners support the hypothesis that mining facilities generally have significantly lower PUE than traditional data centres.

In a best case scenario, mining facilities have optimised data centre operations to a point where there is nearly zero overhead. This scenario is represented by assuming a PUE of 1.01.

The lower bound estimate can be mathematically expressed as follows:


The lower bound estimate corresponds to the absolute minimum electricity consumption of the Bitcoin network. While useful for providing a quantifiable floor, it is unrealistic for a variety of reasons:

  • Not all miners use the most efficient hardware: old equipment can remain profitable for a considerable time when miners have access to cheap electricity and Bitcoin prices remain high.
  • Long delivery and installation times: the delivery and installation of newly released equipment can take up to 3 months.
  • Hardware supply shortage: the most efficient hardware may not be available in all regions in sufficient quantities.
  • Optimistic PUE: not all mining facilities have an optimal PUE.

Constructing the upper bound estimate

Calculating the upper bound estimate (Eupper) is a more difficult task.

We could imagine a worst case scenario where every miner uses the least efficient computing device available on the market that is capable of generating cryptographic hashes - a central processing unit (CPU) powering for instance a computer, a tablet, or even a smartphone. However, with the exponential increase of Bitcoin’s network difficulty since 2016, this assumption would quickly lead to a consumption figure that exceeds the world’s total energy production - let alone that miners would need to operate at massive losses.

We thus adjust the assumption as follows:

Assumption 3b (upper bound): all miners always use the least efficient hardware available at each time period as long as the equipment is still profitable in terms of electricity costs.

As soon as a given equipment type is not profitable anymore, it will be retired and replaced with the next least efficient hardware model that still remains profitable.

It is worth remembering that the profitability threshold for each mining hardware type is calculated strictly in electricity terms and does not take into account capital expenditures nor other operational expenditures.

Assumption 4b (upper bound): all mining facilities have a PUE of 1.20.

We assume that in this scenario, all mining farms have a PUE of 1.20. While still considered efficient by general-purpose data centre standards, it ranges at the higher end of PUE figures reported by miners.

The upper bound equation can thus be mathematically expressed as follows:


The upper bound estimate corresponds to the absolute maximum electricity consumption of the Bitcoin network. While useful for providing a quantifiable ceiling, it is unrealistic for a variety of reasons:

  • Miners demand the most energy-efficient hardware: large miners with industrial-scale data centres compete for gaining early access to the newest ASIC generations that are more energy-efficient.
  • Old equipment gets replaced: many miners replace old ASIC generations that have remained unprofitable for a long time with new equipment rather than storing old equipment for years hoping for the profitability threshold to increase.
  • Other operational expenditures have an impact, too: ignoring additional expenditures such as cooling and maintenance costs may artificially overstate the economic lifetime of inefficient hardware.

Constructing the best-guess estimate

Given that both the lower and upper bound estimates rely on fairly unrealistic assumptions, we attempt to provide an educated guess that more accurately quantifies Bitcoin’s real electricity usage.

In reality, many miners do not run a single type of mining equipment in their data centres, and they do not all switch to the newest hardware at the same time - if they do at all. In many cases, miners operate a combination of different models as long as the equipment remains profitable in electricity terms (i.e. stay below the profitability threshold).

The difficulty lies in determining a realistic weighting approach for all profitable equipment types on a continuous basis that takes into account changing market and network conditions over time. Analysing the market share evolution of the major mining manufacturers would be a good proxy; however, reliable market share data over multiple periods is unfortunately not available.

We thus use the following assumption for our best-guess estimate:

Assumption 3c (best-guess): all miners use an equally-weighted basket of hardware types that are profitable in electricity terms.

The assumption that all profitable machines are equally distributed among miners may seem very unrealistic at first: many hardware types have not been produced and sold in equal quantities, some equipment may not have been available to everyone at the same time, and other machines may already have been fully retired despite becoming profitable again for a short period of time.

However, when comparing our best-guess estimate to a simulation that uses hardware weighting based on Stoll et al.’s (2019) market share calculations, 3

the resulting electricity consumption values do not differ substantially (Figure 3). 4
This suggests that using the current assumption of equally-weighted profitable equipment is acceptable until further research and analysis on better weighting approaches becomes available.

Assumption 4c (best-guess): all mining facilities have a PUE of 1.10.

We assume that all mining farms have a PUE of 1.10 when calculating our best-guess estimate. 5

This figure is slightly more conservative than other estimates but has been confirmed during private conversations with miners and mining experts.

Our best-guess estimate can be mathematically expressed as follows:


Limitations of this methodology will be discussed in the next section.

Discussion

Limitations of the model

Every model is an incomplete representation of reality that relies on specific assumptions, some of which may be debatable. As a result, every model has limitations that need to be discussed. In particular, the current CBECI model exhibits the following limitations (the list is non-exhaustive):

  • Strong dependence on electricity cost estimate: electricity costs can significantly vary from one country, region, and provider to another. Prices are generally dynamic and adjustable, often according to seasonal circumstances, the quantity of electricity consumed, and other factors. Modifying the default electricity cost assumption can substantially change the model output.

  • Hardware selection: we may not be aware of new and more efficient hardware that is not yet available on the market. Some have argued that manufacturers are using proprietary equipment to their own benefits before public release. 6

  • Ignoring other cost factors: other potential factors that influence the decision of miners to switch off and/or replace existing equipment have not been incorporated into the model (e.g. maintenance and cooling costs).

  • Simplistic weighting of profitable hardware: assuming that all profitable equipment is equally distributed among miners is unrealistic given that not all hardware is produced in equal quantities and readily available. The exact market share is unknown, although existing data suggests that a few large manufacturers dominate the market. The lack of reliable longitudinal market share data impacts all bottom-up approaches.

  • Hardware specifications may not correspond to real performance: hardware manufacturers often advertise the performance and energy efficiency of their products using best case scenarios. Furthermore, miners may decide to overclock or underclock their machines for various reasons, which the model does not take into account. 

  • Short switching periods: it is unlikely that miners are able to quickly react to short-term changes in the profitability thresholds: they cannot simply replace all machines of an entire data centre in such a short period of time. While we attempt to smoothen the effect of short-term hashrate variations and price volatility, applying a moving average of 7 days (annualised consumption estimate) and 14 days (profitability threshold), respectively, may not be sufficient.

While most limitations do not have a major impact on the performance of the model, we are aware of its imperfections. The CBECI is an ongoing project that is maintained on a continuous basis. The model will be refined in response to changing circumstances, with all changes being transparently highlighted.

In case you would like to provide suggestions on how we could improve the index, please feel free to send us a message using this form.

How does the CBECI compare to other estimates?

There have been multiple attempts in the past to analyse the electricity consumption of the Bitcoin network and assess its environmental footprint. A list of available studies and articles is presented in Table 2. With the exception of Alex De Vries’s “Bitcoin Electricity Consumption Index” (BECI), there is no live index tracking Bitcoin’s electricity load and consumption in real time.

AuthorDate of publicationTitleApproachSource
Stoll, C., Klaaßen, L., and Gallersdorfer, U. June 2019 The Carbon Footprint of Bitcoin Bottom-up Link
Zade, M., Myklebost, J., Tzscheutschler, P., and Wagner, U. March 2019 Is Bitcoin the Only Problem? A Scenario Model for the Power Demand of Blockchains Bottom-up Link
Krause, M. J., and Tolaymat, T. November 2018 Quantification of energy and carbon costs for mining cryptocurrencies Bottom-up Link
Mora, C., Rollins, R.L., Taladay, K., Kantar, M.B., Chock, M.K., Shimada, M., and Franklin, E.C. October 2018 Bitcoin emissions alone could push global warming above 2°C Top-down Link
McCook, H. August 2018 The cost & sustainability of Bitcoin Bottom-up Link
De Vries, A. May 2018 Bitcoin’s Growing Energy Problem Top-down Link
Vranken, H. October 2017 Sustainability of bitcoin and blockchains Bottom-up Link
Bevand, M. February 2017 Electricity consumption of Bitcoin: a market-based and technical analysis Bottom-up Link
Hayes, A. S. March 2015 A Cost Production Model for Bitcoin Top-down Link
O’Dwyer, K.L., and Malone, D. September 2014 Bitcoin Mining and its Energy Footprint Bottom-up Link

These studies tend to produce considerably diverging findings along a relatively broad range of possible estimates. This can be explained by the application of different methodologies adopted by the study authors: some use a top-down economic approach, whereas others are based on a bottom-up techno-economic approach (like the CBECI model).

Each study is based on a set of assumptions that can be put into question. As a result, the design of each study - including our own analysis - has its own pitfalls and limitations. Some papers, however, have been criticised for applying overly simplistic assumptions and containing non-trivial errors such as inappropriate averaging over time periods or simple extrapolations. For a more thorough review of previous studies, see Koomey (2019). 7

The CBECI has been designed with the aforementioned studies in mind. We have carefully reviewed the various methodologies and incorporated best practices. This website attempts to provide comprehensive documentation with transparent version control, highlight the model’s dependence on the electricity cost assumption by allowing visitors to adjust the default value, and openly present the uncertainties and limitations of the model. Feedback and suggestions for further improvements can be given here.

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