Bitcoin is often criticized for the electricity it consumes. However, few discussions on this topic present a detailed method to arrive at an estimate. This article shows how to use some simple math to draw your own conclusions about Bitcoin’s electricity consumption and the effects it may have on the world.

Methods

Estimating Bitcoin’s energy consumption requires a model. Built into any model are certain assumptions. Provided that assumptions are clearly stated and all calculations are given, imperfections in the model can be corrected to arrive at a more accurate estimate.

Two models have been proposed to estimate Bitcoin’s energy consumption: top-down and bottom-up. These two models were presented in the Princeton Bitcoin Video Course.

A variation on the methods presented here has also appeared in a recent paper.

Top-Down

The top-down approach asks the question: how much electricity would the current block subsidy buy? In this model, miners take no profit and have no expenses. They use all of the block reward proceeds to fund power consumption.

We begin the calculation by determining the block subsidy rate in US dollars (USD) per hour. Each block produces 12.5 BTC and there are six block per hour on average. The current exchange rate is $6,700 USD/BTC. We therefore calculate the subsidy rate of:

12.5 BTC/block × 6700 USD/BTC × 6 blocks/h

or 500,000 USD/h. Every hour, the Bitcoin network pays miners the equivalent of US $500,000.

Next, we compute how much electricity the block subsidy rate could buy. Rates vary across the world, but a range of $0.05 to $0.10 per kilowatt hour (kWh) is typical. Picking the pessimistic case of 0.05 USD/kWh, we can compute the energy that can be bought from the block subsidy:

500,000 USD/h ÷ 0.05 USD/kWh

or 1.0×10⁷ kW (10 million kW). To make this number easier to work with, it can also be expressed as 10 GW (gigawatts), where one gigawatt equals 1 million kilowatts.

Under this model, the Bitcoin network consumes electrical energy at a rate of 10 GW. We can think of this figure as an upper bound because the assumption of no profit or other expenses is unrealistic. The real number is likely to be lower because less money is actually available to buy electricity.

Bottom-Up

We can also arrive at a lower limit for power consumption by assuming that all miners use modern, efficient hardware. Combining the technical specifications for a specific unit with Bitcoin’s implied hash rate would yield an estimate of the power required to generate sufficient hashes to maintain a 10-minute block interval. For simplicity, this model assumes that no electricity will be used for cooling or hardware manufacture.

The Antminer S9i is a popular unit we’ll use for this estimate. Antminer reports the following specifications:

• 14 terahash/second (1.4x10¹³ H/s)
• 1320 watts (W)

Using this information allows us to calculate the amount of energy required for a single hash (1 watt = 1 joule/s, or 1 J/s):

1.3x10^3 J/s ÷ 1.4x10^13 H/s = 9.2x10^-11 J/H

According to Blockchain.info the current implied network hash rate is 3.9x10⁷ terahashes/second (TH/s). We can express this rate in terms of hashes per second with:

3.9x10^7 TH/s × 1x10^12 H/TH = 3.9x10^19 H/s

In other words, the Bitcoin network generates 3.9x10¹⁹ hashes per second.

Given the energy cost for each hash using the S9i, we can compute the amount of energy used by a Bitcoin network composed only of these units:

3.9x10^19 H/s × 9.2x10^-11 J/H

or 3.6x10⁹ J/s (3.6x10⁹ W). In other words, a Bitcoin network made of only Antminer S9i units would consume 3.6 GW of energy in this model (1 GW = 1 billion watts).

Summary

The two models, bottom-up and top-down, give results within a factor of 10 of each other:

• bottom-up: 3.6 GW
• top-down: 10 GW

The actual figure is likely to lie somewhere between these two extremes.

Comparison

A network-wide energy consumption of 3.6-10 GW only makes sense if it can be compared to the output of power plants and consumption around the world. What does several gigawatts of energy consumption actually mean?

The world’s largest power plants offer a convenient frame of reference for power production. The largest plant, Three Gorges Dam in China, produces 23 GW. The largest plant in the US, Grand Coulee, produces 6.5 GW. It’s clear that the power consumed by the Bitcoin network is on par with the output of the world’s largest electric power plants.

How does Bitcoin’s energy consumption compare with that of the world’s countries?

We know Bitcoin’s bottom-up power consumption (3.6 GW). Therefore, Bitcoin’s annual power consumption equals this rate times the number of hours in a year. Given that 1,000 kW = 1 GW, we find:

3.6x10^9 W × 8760 h

or 3.2x10¹⁰ kWh. We can compare this energy with the energy used by the world’s countries. At rank 59 on the list, Denmark uses 3.2x10¹⁰ kWh. In other words, the Bitcoin network consumes as much electrical energy as the country of Denmark under the bottom-up model.

Recall that the top-down model yielded power consumption of 10 GW. Using this as a base, we get:

10x10^9 W × 8760 h

or 8.8x10¹⁰ kWh. At rank 35 on the list, Pakistan consumes 8.2x10¹⁰ kWh, and rank 34 Philippines consumes 9.1x10¹⁰ kWh. In other words, the Bitcoin network consumes about as much electrical energy as the countries of Philippines and Pakistan under the top-down model.

Conclusions

Some simple math and reference data are all it takes to estimate Bitcoin’s energy use and put it into context:

• 3.6-10 GW
• equivalent to one of the world’s largest electrical plants
• roughly equal to the countries of Denmark, Philippines and Pakistan