# Electricity Hash Valuation

### Creating a cyclical price floor using the electricity cost of minting one bitcoin.

Dear readers,

Bitcoin’s energy footprint monopolizes political headlines surrounding the digital asset. But without all that energy consumption, would bitcoin exist as a neutral asset, controlled by nobody? And would it have any value at all? Amidst all of the frantic fear that bitcoin mining is a danger to humanity, we assert that energy is *precisely* what gives bitcoin its value—the market ascribes worth to this energy-derived commodity asset.

Today, we are on a quest to find bitcoin’s marginal electricity cost and use it to determine a floor price for bitcoin as it goes through market cycles. Let’s dive in.

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This metric is inspired by Charles Edwards’ Bitcoin Production Cost and Energy-Value Equivalence. Please visit the linked publications and consider following Charles.

**Abstract**

We set forth a metric used to roughly approximate the $-value of bitcoin based on the average creation cost (cost to mint 1 BTC). We observe the metric to be helpful in determining cyclical price floors.

There are minimal variables by design; this sacrifices robustness for simplicity.

Variables like rent, construction, maintenance, and the manufacturer and age of mining equipment that would make the model more robust are not included for the sake of simplicity. For example, the calculation assumes the mining machine is the finest available, but we don’t factor in the cost of the machine itself nor the infrastructure required to operate it—only the electricity.

**We want to create a metric that gives investors the a-ha moment that energy consumption is what makes bitcoin valuable—this is why simplicity is at the forefront of the model.**

Bitcoin’s electricity consumption, using hash rate and miner efficiency, can be cumulated and multiplied by the average electricity cost to create bitcoin’s Electricity Hash Value (EHV), or a raw input cost to mint 1 BTC.

**We use only three variables:**

How many hashes it takes to generate one bitcoin. This is also known as bitcoin’s difficulty. (Difficulty increases through time as more miners join the network, and bitcoin’s supply algorithm adjusts accordingly every two weeks.)

Energy efficiency in J/Th (Joules/Terahash). In other words, how much power does it take to achieve hash rate? (This decreases through time as hardware gets more advanced and sees efficiency gains.)

Average electricity cost. What does it cost to keep the miners on? (The average electricity cost fluctuates independently of bitcoin fundamentals.)

**TLDR;**

## Electricity Hash Valuation (EHV) =

## (Hashes to mine 1 BTC) *

## (Energy required to hash) *

## (Price of energy)

The formula:

EHV = (Th/BTC) * (kWh/Th) * ($/kWh)

EHV = $/BTC

Easy enough? Not yet? Let’s break it down, followed by some historical price graphs.

## Derivation

#### How many hashes are required to generate one bitcoin?

Bitcoin uses the SHA-256 hash function, an algorithm that generates verifiably random numbers called *hashes*, using a predictable amount of computing power. Generating a hash value (a number) less than the current target (a small number set by the bitcoin algorithm—this is the number that “adjusts” during a “difficulty adjustment”) wins the block subsidy (mining reward, currently at 6.25 BTC every 10 minutes); therefore, hashes per second shows how much computational power is being used by miners across bitcoin; the network *hash rate*.

Miners continue to log onto the network in droves to capture the block subsidy, cranking up the total hash rate on the network, thereby increasing the number of hashes it takes to be rewarded with BTC.

Dividing the network hash rate by the current block reward, which occurs every 10 minutes, provides the amount of hashes per individual bitcoin—this will help us later.

= (network hash rate) / (block reward [6.25 BTC/10min])

= (219,000,000 Th/s) / (6.25 BTC / (600s))

= 219,000,000*600 / 6.25 * Th/BTC ← time variables cancel out

**= 21,024,000,000 Th/BTC ← this is how many hashes it takes to generate 1 BTC**

#### Energy efficiency in J/Th?

A joule is a unit of energy expended by a miner, and a watt is a measure of joules per second, which can be used to price the cost of running a miner. For simplicity, just know that we’re converting joules to watts to easily multiply through energy price.

We decided to use the most energy-efficient miner that exists today—the top-of-the-line Antminer S19 XP. Thanks to the Luxor Tech Team and the Bitcoin Mining Council for compiling all of this data; their links can be found in the footnote.1

Using the J/Th of the most energy-efficient mining hardware and converting joules to watts gives us a variable to find kWh/Th, which we can multiply against Th/BTC.

= ((Joules/Terahash) / (Seconds*Minutes/Hour)) / (1000W/kWh)

*1 watt = 1 joule per second; so, multiplying joules by the seconds in an hour converts to watt-hours, then dividing by 1000 watts converts to kilowatt-hours.*

= ((21.5 J/Th) / (3,600s)) ← conversion from joules to watt-hours

= .005972 Wh / 1000W ← conversion from watt-hours to kilowatt-hours

**= .000005972 kWh/Th ← this is how much energy it takes to perform 1 terahash**

#### Average electricity cost?

Electricity cost is measured in dollars per kilowatt-hour, 1,000 watts being a small enough unit to compare against dollars (and cents).

Keeping it simple—this input is taken directly from the average global electricity price for business as of June 2022, which is $0.127 per kWh.

**= 0.127 $/kWh**

### Calculation

The product of all three highlighted inputs gives us what we’ve dubbed the **Electricity Hash Valuation**: a method of valuing bitcoin directly from its hash rate, block subsidy, miner energy efficiency, and electricity cost.

Let’s visualize the simplicity of this metric below:

*The variables beautifully cancel each other out, and we are left with an ***EHV of $15,946.12**.

Now that we’ve constructed this value, let’s check out some historical price data and see what we can glean from its value relative to the spot price.

Mapping both **spot price** and **EHV** since 2015: spot has traded at a consistent premium, only dropping below this bedrock floor twice in the history of the metric.

Bitcoin is a pure monetary asset—its use case is being “money.” As more participants flood the network, the price is steadily driven higher on average, followed by miners who increase their output to capture the robust economic incentives of the network. *Energy footprint allows the network to thrive; and clearly serves as a fundamental economic floor for bitcoin the asset*.

Using this dataset from the Bitcoin Mining Council, the model adjusts the J/Th value over time to reflect increasingly efficient miners, allowing whichever machine is most efficient during its time to affect the time series. This makes for a model that is reflective of the reality of Moore’s Law.

**As the hash rate of the network expands and electricity costs remain more or less constant, miners must become increasingly efficient. They are intensely competing for marginal bitcoin production, so we must understand and calculate the direct impact of energy expenditure as context for the spot price.**

**Conclusion**

Bitcoin, like any commodity, has value** because of the energy expended to create it**.

We can validate that bitcoin’s historical price appreciation has risen alongside EHV, as more energy-efficient mining hardware and fierce competition drive the input cost higher.

Here at The Bitcoin Layer, we’ve posited since the beginning that bitcoin exists on the first layer money due to its superior monetary properties. The fact that we can value the underlying asset based on its production price, akin to a commodity, indicates that bitcoin somewhat functions like other commodity monies (gold, oil). Being digital in nature, however, makes bitcoin unique. A digital commodity fundamentally linked to its energy inputs—what is something like that worth to society?

Until next time,

Joe and Nik

**This post was sponsored by Voltage, provider of enterprise-grade Bitcoin infrastructure.**

Data provided by **glassnode**, **Quantaloop.io, Luxor Tech Team**, **ElectricRate**, **Bitcoin Mining Council**