Methodology

Overview

Summary

The Cambridge Network Sustainability Index (CBNSI) provides up-to-date estimates of the daily power demands of various cryptocurrency networks. Here, we describe the methodology we used to assess the Ethereum network's electricity use before it transitioned from proof-of-work (PoW) to proof-of-stake (PoS). Similar to our widely cited Cambridge Bitcoin Electricity Consumption Index (CBECI), the applied methodology is based on building a basket of real-world hardware with the underlying assumption that mining nodes (‘miners’) are rational economic agents that only use profitable hardware.

Given that the actual power demand cannot be determined due to the decentralised nature of the network, we made several assumptions, including hypothetical lower-bound (floor) and upper-bound (ceiling) estimates. These two boundaries encompass a best-guess estimate, a more accurate indication of the actual power demand.

The lower-bound estimate is the theoretical minimum total power demand based on the best-case assumption that all miners always use the most energy-efficient equipment. The upper-bound estimate is the theoretical maximum total power demand based on the worst-case assumption that all miners always use the least energy-efficient hardware as long as running the equipment remains profitable in terms of electricity costs. The best-guess estimate is based on the more realistic assumption that miners use a combination of profitable hardware.

In September 2022, the Ethereum network shifted its consensus mechanism from PoW to PoS. This unprecedented move replaced ‘miners’ with ‘validators’ as finding a valid block hash became obsolete and was replaced by other means of ensuring distributed consensus. Therefore, our last PoW estimate is one day before The Merge concluded. A fundamentally different approach is required to evaluate post-Merge Ethereum power demand; hence, the approach we describe here does not apply. Nevertheless, examining Ethereum's historical electricity consumption is necessary to better understand the network's impact on the environment before it transitioned to PoS, given that its electricity consumption was second only to Bitcoin during this period.

While the approach we used to estimate Ethereum’s post-Merge power demand is beyond the scope of this methodology, it is available in another segment on our website, as well as an estimate of Ethereum's post-Merge electricity consumption. You can find more information on The Merge in our FAQs section, and more insights about its impact from an environmental perspective here.

The Cambridge Blockchain Network Sustainability Index model

Representation

The dashboard on the index page displays Ethereum's estimated power demand and electricity consumption for all scenarios (lower bound, upper bound and the best guess) on the last day before The Merge.

The first number refers to the Ethereum network's total power demand . This measure corresponds to the electrical power the Ethereum network needs or uses at any given moment and is expressed in gigawatts (GW). The second figure refers to the network’s total electricity consumption, a metric that corresponds to the total amount of electricity used over a given period. In this case, it is an annualised value expressed in terawatt-hours (TWh) based on the assumption that the estimated power demand remains constant over an entire year.

Further, we applied a seven-day moving average to the resulting estimates to make the output values less dependent on short-term hashrate fluctuations, thereby rendering them more suitable for comparison with other electricity usage alternatives.

Model parameters

The Cambridge Blockchain Network Sustainability Index (CBNSI) model considers the parameters outlined in Table 1. The following sections specify how we calculated each estimate and what assumptions were made.

Table 1: CBNSI model parameters

Parameter	Description	Measure/unit	Source
Network hashrate, daily mean	The average rate at which miners solve hash puzzles on a given day	terahashes per second (Th/s)	Dynamic:
Mining revenue	The aggregated value of all financial incentives paid to miners	USD	Before EIP-1559: block subsidy + transaction fee + uncle reward After EIP-1559: block subsidy + miner tips + uncle reward
Block subsidy	The total value of native tokens issued	USD	Dynamic:
Transaction fee	The total financial incentives given to miners to prioritise transactions	USD	Dynamic:
Miner tips	The total financial incentives given to miners to prioritise transactions	USD	Dynamic:
Uncle reward	The total rewards for stale blocks	USD	Dynamic:
Mining equipment efficiency	The energy efficiency of a given mining hardware type	h/J	Static: hardware specs from 100+ equipment types, taken from various sources
Mining equipment memory size	The amount of data a device can store at any given moment in its memory	gigabyte (GB)	Static: hardware specs from 100+ equipment types, taken from various sources
Electricity cost	The cost of electricity	USD per kilowatt-hour (USD/kWh)	Static: estimate (assumption)
Power usage effectiveness (PUE)	A measure of how efficiently energy is used in a data centre	/	Static: estimate (assumption)

It is worth noting that a change in protocol rules implemented by Ethereum Improvement Proposal (EIP) 1559 required us to change the input variables for calculating mining revenue. Before EIP-1559 was implemented, mining revenue was calculated as the sum of block subsidies, transaction fees and uncle reward. After EIP-1559, miner tips replaced transaction fees as an additional incentive for prioritising transactions.

Selecting mining equipment

The mining equipment included in this methodology are graphics processing units (GPUs) and, to some extent, application-specific integrated circuits (ASICs), as these were the hardware types predominantly used to mine ether (ETH). We did not consider other hardware that would have been technically capable of mining ether but not economically.¹ GPUs have distinguished themselves by their versatility in mining; however, ASCIs are designed for a single purpose (which is mining a specific algorithm) and are usually more efficient than GPUs.

Due to the criticism that non-ASIC-resistant protocol designs pose the risk of centralisation,² Ethereum was initially designed to be ASIC-resistant. This was to prevent computing power from becoming concentrated in dedicated data centres (‘mining farms’) and ensure fairer competition between regular (at-home) miners and those with far more financial resources. Nevertheless, ASICs started to appear, sparking a discussion about a hard fork to keep Ethereum ASIC-resistant.³ In the end, however, the hashing algorithm did not change, paving the way for further ASIC development. However, unlike Bitcoin, the ASICs introduced specifically for Ethereum mining were not significantly more efficient than GPUs. Only recently have ASICs emerged with significantly higher efficiency.

We compiled a list of almost 100 different Ethereum mining hardware devices for this study from several public resources of distinct types of mining equipment and their specifications.⁴ Each day, we create a subset of eligible hardware from this list based on profitability and the three constraints listed below.

Avoiding double counting. GPU models are often available in various memory sizes. However, we included only one memory size for each GPU model in calculating our best-guess estimate, as incorporating the full range of memory sizes available for a GPU model could overstate the actual use of that model. We followed the same approach for the light hashrate (LHR) versions of GPU models, excluding them to avoid double counting.⁵ LHR versions are specifically built to provide less mining performance.
Consolidating ASIC manufacturers to exclude ‘exotic’ devices. In our Bitcoin methodology, we consolidated hardware manufacturers to exclude ‘exotic’ devices by only considering ASIC hardware from the three major manufacturers, Bitmain, MicroBT and Canaan, which are estimated to have a combined market share of at least 85%.⁶ We used a similar constraint in this methodology. However, since we have not found a similar study for Ethereum regarding the market share of ASIC manufacturers, we used the study conducted for Bitcoin as a basis. We also added the manufacturer Innosilicon based on research conducted by McDonald (2021).
Considering GPU memory capacity and Ethereum DAG file size. This constraint relates to the directed acyclic graph (DAG) file size. If Ethereum's DAG file size exceeds the memory capacity of a GPU or ASIC, that device can no longer mine. Therefore, we did not consider GPU or ASIC models with a memory capacity less than Ethereum's DAG file size, even if it would be profitable to mine with these devices. Table 2 shows the dates on which key DAG file sizes were exceeded.

Table 2: DAG file size

DAG file size (GB)	Block height	Date
2	3,840,000	08/06/2017
3	7,680,000	02/05/2019
4	11,520,000	25/12/2020
5	15,360,000	17/08/2022

The complete list of all devices found is open to comments and suggestions. This list also includes the devices we excluded based on the abovementioned constraints to ensure comprehensive disclosure and transparency. Figure 1 shows the evolution of Ethereum mining hardware (expressed in mega hash per joule (Mh/J)) from late 2014.

Figure 1: Evolution of Ethereum mining hardware efficiency

The profitability threshold

Similar to the CBECI, our model for Ethereum assumes that miners are rational economic agents that only operate their devices for as long as they are profitable. To determine whether a particular mining device from our list can be included in the group of profitable hardware, the miner's total revenue must be equal to or greater than the cost of operating the hardware on a given day, as shown in Equation 1. The operating cost for each hardware model in the list is calculated by dividing the cost of electricity per joule (P) by the device’s energy efficiency (η). In addition to the profitability condition, all the requirements outlined in the previous section must be satisfied.

Assumption 1: The average electricity price for Ethereum mining globally is constant over time and is 0.1 USD/kWh.

$\frac{P}{\eta} \leq R\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [1]\\$ $where,\\ P\ =\ electricity\ cost\ per\ joule\ [USD/J] \\ \eta =\ energy\ efficiency\ of\ mining\ hardware\ in\ [h/J] \\ R\ =\ mining\ revenue\ per\ hash\ [USD/h]\\$
In this context, profitability only refers to electricity costs incurred from operating the hardware. Other costs, such as capital expenditures (for example, acquisition and amortisation costs) or other operational expenditures (for example, cooling, maintenance and labour costs), are not considered.

Miners' electricity costs vary significantly, and therefore determining it is a complex task. There is a vast array of factors, including variations in pricing between and within countries, as well as fluctuations in pricing over time. Electricity costs also depend on whether consumers are retail or wholesale, and if wholesale, whether they have signed Power Purchase Agreements (PPAs) with rates that deviate from local pricing schemes. Additionally, some miners generated their own electricity, further complicating the calculation of costs. In light of these complexities, it is assumed that, on average, miners pay 0.10 USD per kilowatt-hour (0.10 USD/kWh).⁷

Note: The Ethereum 1.0 index page allows visitors to choose different values for the electricity cost parameter to explore how electricity prices influence hardware selection and total electricity consumption.

Further, the gathered data and assumption allowed us to compute a profitability threshold (Equation 2) over time, showing the minimum efficiency required for the hardware to be profitable (Figure 2). As can be seen, the profitability threshold has increased over time, suggesting that miners gradually had to invest in more efficient hardware to stay competitive as older and less efficient hardware became uneconomical.

Figure 2: Profitability threshold

The profitability threshold θ is calculated using Equation 2:

$\theta = \frac{P}{R} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [2]\\$ $where,\\ \theta =\ profitability\ threshold,\ measured\ in\ [h/J]\\ R\ =\ mining\ revenue\ per\ hash\ [USD/h]\\ P\ =\ electricity\ cost\ per\ joule\ [USD/J] \\$
The profitability threshold is used to compile a set of efficiencies of profitable mining hardware Ŝ(P) given electricity price (Equation 3). Ŝ(P) is created each day and contains all mining hardware with energy efficiency greater than the profitability threshold θ(P) (Equation 4).

$\hat{S}(P) =\{{\eta }_1,\ {\eta }_2,\dots, {\eta }_n \}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [3] \\$ $where,\\ \hat{S}(P) = set\ of\ energy\ efficiencies\ of\ profitable\ hardware\ devices\ given\ electricity\ price\ P\\ \eta_i = energy\ efficiency\ of\ mining\ hardware\ satisfying\ \eta_i\ > \theta(P),\ measured\ in\ [h/J]\ with\ \{{1},\dots, {n} \}$

$\theta(P) < \eta_{i}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [4]\\$ $where,\\ \theta(P) = profitability\ threshold\ given\ electricity\ price\ P,\ measured\ in\ [h/J]\\ \eta_i = energy\ efficiency\ of\ mining\ hardware\ i\ in\ set\ \hat{S}\ = \eta_{i,asic}\ \cup\ \hat\eta_{i,gpu},\ measured\ in\ [h/J]\\$
Before introducing the profitability condition, we create an updated set of mining hardware, denoted by Ŝ, by adjusting the power data of all GPUs in the original set S. This set contains all hardware devices that fulfil all non-profitability-related conditions (such as sufficient memory size), and the adjustments are made based on research conducted by McDonald (2021), who identified inefficiencies associated with the following factors:

Power supply units (PSU). Power loss in a PSU refers to the inefficiencies in converting AC voltage to DC voltage, resulting in a difference between the power draw and actual power supplied to system components. This can be caused by inefficient conversion, oversizing, inadequate cooling, ageing components, and poor design. Given that electricity costs are a significant component of mining, miners likely tended to use highly efficient (Gold rated or above) PSUs.⁸
Power requirements of additional hardware components. Mining rigs, which are purpose-built systems designed to mine cryptocurrencies with GPUs, contain additional hardware components such as CPU, motherboard, RAM, storage, and fans that constitute additional power requirements.

To ensure a comprehensive measurement of energy efficiency, we adjust the power data of all GPUs in set S to account for inefficiencies associated with PSU power loss and consumption of additional hardware components, as identified by McDonald (2021). Specifically, we adopt a factor of 1.03 for overhead_gpu and a divisor of 0.90 for efficiency_gpu. This adjustment is only applied to GPUs in our model, as ASIC manufacturers already consider inefficiencies in the stated power data of their hardware.⁹

Assumption 2: GPU power data need to be adjusted to account for inefficiencies related to PSU power loss and additional hardware components that are part of a mining rig. To capture both instances, a divisor of 0.9 is assumed for the former and a factor of 1.03 for the latter.

$\hat\eta_{i,gpu} = \frac{\eta_{i,gpu}\ *\ overhead_{gpu}}{efficiency_{gpu}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [5]\\$ $where,\\ \hat\eta_{i,gpu} = energy\ efficiency\ of\ GPU\ mining\ hardware\ i,\ measured\ in\ [h/J]\\ \eta_{i,gpu} = unadjusted\ energy\ efficiency\ of\ GPU\ mining\ hardware\ i\ in\ set\ {S}\ =\ {\eta_{i, asic}} \cup {{\eta}_{i,gpu}},\ measured\ in\ [h/J] \\ overhead_{gpu} = inefficiency\ factor\ based\ on\ additional\ hardware\ components\ required\ in\ GPU\ mining\ \\ efficiency_{gpu} = percentage\ of\ actual\ power\ delivered\ by\ PSU\ versus\ power\ drawn$

Occasionally, there might be a period during which there is no profitable hardware, resulting in an empty set Ŝ(P). In this case, Assumption 3 applies.

Assumption 3: During a period when no mining equipment is profitable, the last known non-empty set of profitable mining hardware is assumed to power the entire network.

It is reasonable to assume miners will not immediately switch off unprofitable hardware unless unfavourable market conditions persist for an extended period. To account for this, we applied a 14-day moving average to the profitability threshold to smooth the process of rebalancing Ŝ(P) and avoid it being subject to short-term fluctuations in mining profitability.

Constructing lower-bound estimates

In the best-case scenario, we assumed all miners always use the most energy-efficient equipment to maximise the expected profit. Therefore, we based the lower-bound estimates (D_lower and E_lower) on Assumptions 4 and 5.

Assumption 4 (lower bound): All miners always operate the most efficient hardware available. This assumption also implies that miners will immediately upgrade their equipment as soon as more energy-efficient hardware becomes available.

Power usage effectiveness (PUE) measures data centre energy efficiency. Data centres typically consume more energy than is needed to operate the servers because of factors such as cooling and supporting IT equipment. The higher the PUE ratio, the less efficient the energy use. Data centres with a PUE below 1.2 are typically considered efficient. For reference, Google's average PUE is 1.10, while the average PUE of most data centres is 1.8 or higher.

In bitcoin mining, electricity costs account for most operational expenditures.¹⁰ As a result, mining operators have a clear incentive to optimise cooling systems to reduce overall costs. Conversations with bitcoin miners support the assumption that mining facilities typically have much lower PUEs than traditional data centres. Given the lack of data in this respect for Ethereum, but the activity being similar in nature, we assumed that this is also true for Ethereum.

Assumption 5 (lower bound): In the lower-bound estimate scenario, the mining facility has optimised the data centre operations to have nearly zero overhead costs. In this case, a PUE_l of 1.01 is assumed.

The lower-bound estimates are calculated using Equations 6 and 7:

$D_{lower} = \frac{H}{max(\hat{S}(P))}\ *\ PUE_{l}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [6]$

$where,\\ D_{lower} = lower\ bound\ power\ demand\ [W]\\ max(\hat{S}(P)) = energy\ efficiency\ of\ the\ most\ efficient\ mining\ hardware\ [h/J]\\ H = Ethereum\ network\ hashrate\ [h/s]\\ PUE_{l} = power\ usage\ effectiveness\\$
$E_{lower}(P) = \frac{H}{max(\hat{S}(P))}\ *\ PUE_{l}\ *\ 60\ *\ 60\ *\ 24\ *\ 365.25\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [7]\\$ $where,\\ E_{lower} = lower\ bound\ electricity\ consumption\ [Ws]\\ max(\hat{S})) = energy\ efficiency\ of\ the\ most\ efficient\ mining\ hardware [h/J]\\ H = Ethereum\ network\ hashrate\ [h/s]\\ PUE_{l} = power\ usage\ effectiveness\\$
The lower-bound estimate corresponds to the absolute minimum power demand of the Ethereum network. While this is useful for providing a quantifiable minimum, it is a purely hypothetical value that is non-viable for various reasons, such as the following:

Not all miners use the most efficient hardware: A miner will likely continue operating less efficient equipment as long as mining revenue is somewhat higher than costs.
Long delivery and installation times: Delivery and installation of new equipment can take several months after release.
Hardware supply shortage: The most efficient hardware may not be available in sufficient quantities that could reasonably be responsible for the total Ethereum network hashrate.
Optimistic PUE: Not all mining facilities have an optimal PUE.

Constructing upper-bound estimates

For computing the upper-bound estimates (D_upper and E_upper), we followed a similar logic, except in this case, we assumed that the least efficient but still profitable hardware model powers the network.

Assumption 6 (upper bound): All miners always use the least efficient but still profitable mining device available. This assumption also implies that miners will quickly downgrade their equipment as soon as less energy-efficient hardware becomes profitable. Conversely, it implies that miners will quickly upgrade their equipment to the current least efficient but profitable hardware model if the previous one becomes unprofitable.

We assumed, in this case, that the PUE for all mining sites is 1.20. While this is still considered valid by common data centre standards, it lies at the upper end of the PUE values reported by miners.

Assumption 7 (upper limit): The PUE_u for all mining facilities is 1.20.

Therefore, the upper-bound estimates are calculated using Equations 8 and 9:

$D_{upper}(P) = \frac{H}{min(\hat{S}(P))}\ *\ PUE_{u}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [8]$

$where,\\ D_{upper} = upper\ bound\ power\ demand\ [W]\\ min(\hat{S}(P)) = energy\ efficiency\ of\ the\ least\ efficient\ but\ still\ profitable\ hardware\ [h/J]\\ H = Ethereum\ network\ hashrate\ [h/s]\\ PUE_{u} = power\ usage\ effectiveness\\$

$E_{upper}(P) = \frac{H}{min(\hat{S}(P))}\ *\ PUE_{u}\ *\ 60\ *\ 60\ *\ 24\ *\ 365.25\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [9]\\$ $where,\\ E_{upper} = lower\ bound\ electricity\ consumption\ [Ws]\\ min(\hat{S}(P)) = energy\ efficiency\ of\ the\ least\ efficient\ but\ still\ profitable\ hardware\ [h/J]\\ H = Ethereum\ network\ hashrate\ [h/s]\\ PUE_{u} = power\ usage\ effectiveness\\$
The upper-bound estimate corresponds to the absolute maximum power demand of the Ethereum network. While useful for providing a quantifiable maximum, it is a purely hypothetical value that is non-viable for various reasons, such as the following:

Miners are interested in the most energy-efficient hardware: Large mining operators with industrial-scale data centres compete to be the first to access the most energy-efficient ASIC generations to increase operational profitability.
Old equipment is replaced: Miners will likely replace old ASIC generations that have been unprofitable for a long time with new equipment rather than store old equipment for years, hoping the profitability threshold will rise.
Bottlenecks in hosting space: Rational miners will always use the most efficient hardware if they have limited space to operate the equipment.
Impact of other operating expenses: Failure to account for additional expenses, such as maintenance costs, can artificially inflate the economic life expectancy of inefficient hardware.

Constructing best-guess estimates

Since both the lower- and upper-bound estimates are based on impractical assumptions, we provided an educated estimate that more accurately quantifies the actual power use of the Ethereum network.

In practice, miners usually use more than one type of model and do not all switch to the latest generation of hardware simultaneously. And some may not switch at all. Instead, many miners use a combination of models. It is sensible to assume that less efficient but profitable models will remain in use until the shelf space they occupy is needed for more efficient models, or their operational costs exceed the revenues.

The difficulty in constructing the best-guess estimate is continually determining an appropriate weighting approach for all profitable hardware models that considers changing market and network conditions over time. Analysing the market share evolution of the main mining manufacturers would be a good proxy; however, reliable market share data over multiple periods is unfortunately not available.

Therefore, we used Assumptions 8 and 9 in our best-guess estimation.

Assumption 8 (best guess): All miners use an equally weighted basket of hardware models that are profitable at the assumed electricity rate.

Assumption 9 (best guess): All mining facilities have a PUE_e of 1.10.

In the best-guess estimate, all mining farms are assumed to have a PUE of 1.10.¹¹ This figure is slightly more conservative than other estimates but has been repeatedly confirmed during private conversations with miners and mining experts.

The best-guess estimate is calculated using Equations 10, 11 and 12:

$D_{estimated}(P) = \frac{H}{\psi}\ *\ PUE_{e}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [10]\\$ $where,\\ D_{upper} = upper\ bound\ power\ demand\ [W]\\ \psi = average\ energy\ efficiency\ of\ profitable\ hardware\ [h/J]\\ H = Ethereum\ network\ hashrate\ [h/s]\\ PUE_{e} = power\ usage\ effectiveness\\$
$E_{estimate}(P) = \frac{H}{\psi}\ *\ PUE_{e}\ *\ 60\ *\ 60\ *\ 24\ *\ 365.25\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [11]\\$ $where,\\ E_{estimated} = best-guess\ electricity\ consumption\ [Ws]\\ \psi = average\ energy\ efficiency\ of\ profitable\ hardware [h/J]\\ H = Ethereum\ network\ hashrate\ [h/s]\\ PUE_{e} = power\ usage\ effectiveness\\$
$\psi = \frac{\sum^N_{i\ =\ 1}\eta_{i}}{N}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [12]$

$where,\\ \eta_{i} = energy\ efficiency\ of\ profitable\ mining\ hardware\ i\ in\ [h/J]\\$
We discuss the limitations of our methodology in more detail in the following section.

Discussion

Limitations of the model

Theoretical models are generally an incomplete representation of the actual situation and are based on certain assumptions, some of which may be debatable. The following is a non-exhaustive list of the main limitations of our model:

Dependence on electricity cost estimates: Electricity costs vary significantly between countries, regions and providers. Prices are generally dynamic and also vary, for example, according to the seasons and quantity of electricity consumed. Modifying the default electricity cost assumption can substantially change the model output.
Ignoring other cost factors: We did not incorporate other factors influencing miners’ decision to switch off and replace existing equipment into the model (for example, maintenance and cooling costs).
Simplistic weighting of profitable hardware: Our assumption that all profitable equipment is equally distributed among miners is unlikely, given that not all hardware is produced in equal quantities or readily available.
Hardware selection: Not counting GPUs with different memory sizes or LHR versions of the same model might lead to underestimating the number of a specific model. Moreover, the hardware list is non-exhaustive and potentially does not capture all employed GPU or ASIC models. At times, some companies might have used hardware models that were not yet available on the market. Some have argued¹² that manufacturers used proprietary equipment for their own benefit before public release.
Hardware specifications may not correspond to actual performance: GPU manufacturers usually do not provide data on the performance of their hardware for ‘cryptocurrency mining’ purposes. Therefore, we extracted the performance data from specialised third-party benchmark providers for most GPU models in our list. However, in some instances, performance data is provided by manufacturers for GPUs that have been specifically designed for cryptocurrency mining (for instance NVIDIA CMP HX series). Moreover, employed GPUs may be over- or underclocked, which might be reflected to an unknown degree in the benchmark studies of the abovementioned performance data providers.
Short switching periods: It is unlikely that miners can react quickly enough in response to short-term changes in the profitability threshold. While we attempted to smoothen the effect of short-term hashrate variations and price volatility by applying a moving average of 14 days (profitability threshold), this may not be sufficient.

Although we can safely assume that many limitations do not significantly impact the estimation results, we are aware of the imperfections. The CBNSI is an ongoing project, and we continuously refine the estimates in response to changing circumstances and transparently present all changes in the change log.

Please feel free to message us if you would like to provide suggestions on how we could improve the index.

How the CBNSI compares to other estimates

Multiple attempts have been made to analyse the annualised (ann.) electricity consumption of the Ethereum network. Table 3 lists some studies and articles. However, it is important to note that estimates may vary considerably over time and depending on the methodology used; therefore, it is essential to consider the publication date when comparing estimates from different studies.

Table 3: Overview of previous studies

Author(s)	Publication date	Title	Estimate (TWh)
Cambridge Centre for Alternative Finance	September 2022	Ethereum 1.0 Electricity Consumption Index	14/09/2022 (last day)^a
Digiconomist	September 2022	Ethereum Energy Consumption Index	14/09/2022 (last day)^a
McDonald, K.	September 2022	Ethereum Emissions: A Bottom-up Estimate	14/09/2022 (last day)^a
Crypto Carbon Ratings Institute	September 2022	Intelligence at the intersection of sustainability and crypto	14/09/2022 (last day)^a

^aThe Merge happened on 15 September, and because data was only available for part of that day, 14 September is the last day we estimate the network’s electricity consumption.

Figure 3 shows how our estimate of annualised electricity consumption compares to other estimates over time. As we can see, while the findings of some studies exhibit close proximity, there might also be considerable differences between studies.

Figure 3: Comparing Ethereum electricity consumption estimates

Every study is based on assumptions that can be called into question. As a result, the design of any study – including our analysis – has its drawbacks. We developed our Ethereum estimation with best practices in mind and followed a similar logic to that used in our techno-economic model for Bitcoin. In addition, we provide comprehensive documentation, ensure transparency by highlighting limitations, and consider the model's dependence on assumed electricity costs by allowing visitors to adjust the default value on the index page to see how changing the electricity cost assumption affects electricity consumption.

We welcome any feedback and suggestions for further improvements.