Hash Price Explained

Learn how to calculate hash price, how it changes in relation to bitcoin’s price and the network’s hash rate, and apply it in practice.

Learning Objectives:

• Defining hash price
• Calculating hash price and its respective variables
• The directional impact of bitcoin's price and the network's hash rate on hash price
• Estimating mining profitability and comparing the effectiveness of mining rigs using hash price

Table of Contents

• What Is Hash Price?
• But First, What Is a Hash?
• Hash Price Calculation
  • Estimating the Bitcoin Network’s Daily Revenue
  • Estimating the Bitcoin Network’s Hash Rate
  • Solving for Hash Price
• How Do Changes in Bitcoin’s Price and the Network’s Hash Rate Impact Hash Price?
• Applying Hash Price to Estimate Profitability and Effectiveness of Mining Rigssome text
  • Calculating the Value Creation of Bitcoin Mining
  • Comparing the Effectiveness of Mining Rigs
• Closing Remarks

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Disclaimer

This report is provided for general informational purposes only. The opinions expressed in the report may differ from those expressed by Marathon Digital Holdings ("MDH"), its officers, employees, directors or advisors or their affiliates. The information on this report does not constitute investment, legal, accounting or other advice or information by MDH or its officers, employees, directors or advisors or their affiliates. Information has been obtained from sources believed to be reliable, but MDH or its affiliates do not warrant its completeness or accuracy. Outlooks and past performance are not guarantees of future results. The information in the report may be changed without notice and is not guaranteed to be complete, correct or up-to-date, and may not reflect the most current developments.

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What Is Hash Price?

Hash price measures the daily revenue Bitcoin miners can expect to earn per unit of computational power and is typically measured in dollars per terahash per second per day ($/TH/s/day). Hash price can be viewed as the market value of converting electricity into hashes for bitcoin.

Three variables drive hash price:

• Bitcoin’s exchange rate to dollars (bitcoin's price)
• The Bitcoin block reward (block subsidy + fees)
• The Bitcoin network’s hash rate

In the volatile world of Bitcoin mining, predicting miner performance and profitability can be challenging. Bitcoin mining relies heavily on two crucial yet unknown variables: bitcoin’s price and the network’s hash rate. However, there is a way to simplify these variables into a single number using hash price. Hash price measures the daily revenue Bitcoin miners can expect to earn per unit of computational power. This metric is essential for not only miners, but also investors and analysts in estimating the profitability of ASIC mining rigs and gauging the effectiveness of their ability to convert electricity into revenue.‍

‍By understanding hash price, one can simplify the logic of Bitcoin mining, as it expresses in a single number, the dollar value of one unit of computational power or hash.

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But First, What Is a Hash?

As it relates to Bitcoin, a hash is an encrypted, fixed-length string of bits that serves as a digital fingerprint for authenticating and identifying blocks on the Bitcoin blockchain. Miners generate hashes using the SHA-256D hashing algorithm to transform transaction data into 256 bits (64 characters) through the mining process. While specialized computers (ASICs) are predominately used for mining today, it is important to note that any computing device capable of executing the calculation can be used to generate hashes, such as a general-purpose computer, albeit inefficiently and ineffectually.

At its core, the mining process involves converting electricity into hashes using ASICs. Miners race against other miners to create as many hashes as possible to guess the correct hash of the block header – a data structure containing essential information about the block, such as the block height, the previous block's hash, the Merkle root of the transactions, and a timestamp. The objective for a miner is to generate the correct hash that matches a specific number with a certain number of leading zeros (at the time of writing, this is a number with 20 leading zeros), which is determined by the Bitcoin protocol's difficulty adjustment. The "solution" cannot be determined in advance, nor can miners alter the algorithm to produce a specific hash value. This feature of Bitcoin's proof-of-work algorithm means that the only way to produce a hash result that satisfies the hash function is to try again and again, randomly modifying one parameter, known as the nonce, until the desired hash result appears by chance.

So, what motivates miners to consume electricity and expend real-world resources to mine blocks? For their efforts, the first miner to produce the correct hash is rewarded with newly minted bitcoin (block subsidy) and transaction fees; this continual process repeats approximately every 10 minutes. As such, hashes can be viewed as a digital commodity, similar to electricity, unable to be stored or held. The value of a hash fluctuates based on bitcoin's price, the block reward, and network's hash rate. And since bitcoin has a dollar- denominated market price, the value of a single hash can be calculated using a simple formula.

NOTE: For a more in-depth understanding of a hash, the mining process, and other terminology, please visit the Bitcoin Wiki.

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Figure 1: High-Level Overview of the Electricity to Hash Conversion Process

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Hash Price Calculation

Three primary variables are needed to calculate hash price – bitcoin’s price, the Bitcoin block reward, and the total aggregated hashing power of all active mining rigs (Bitcoin network’s hash rate). The equation for hash price is:

Or simply...

Estimating the Bitcoin Network’s Daily Revenue

Estimating the network’s daily revenue is relatively simple, thanks to Bitcoin’s transparent ledger and predictable supply schedule.

• On average, the Bitcoin blockchain adds a block every 10 minutes, which equates to 144 blocks per day.
• Each block produced and added to the blockchain rewards miners with the block subsidy and transaction fees. Currently, miners earn 6.25 BTC per block, excluding fees.
• Approximately every four years, the block subsidy is automatically reduced by 50% (Halving). The next Halving is expected to occur in the spring of 2024, at which point the block subsidy will be 3.125 BTC.
• So, approximately 900 BTC will enter the market every day until the next halving.

Multiplying the daily bitcoin production by the dollar exchange rate of bitcoin (BTC USD), we get the total revenue generated by miners on a given day.

If the price of bitcoin as of February 24, 2023, is $23,000 and the network produced 144 blocks, then the Bitcoin network’s daily revenue is approximately $20.7 million, exclusive of fees.

Estimating the Bitcoin Network’s Daily Hash Rate

Determining the network’s hash rate is more complex. The true hashing power of the Bitcoin network is unknown because miners on the network can keep their hash rate private. However, it is possible to infer an estimate of the hash rate using the actual number of blocks produced on a given day and the difficulty rate (a measurement of how challenging it is to find the correct hash). The equation for the network’s hash rate is:

Or simply...

Anyone can source the network’s difficulty rate using a Bitcoin node by running the “getmininginfo” command. Alternatively, a web-based application, such as BRAIINS Insights or mempool.space, can provide the difficulty rate.

Figure 2: Publicly Sourced Difficulty Rate (2/24/2023)¹

Furthermore, this equation factors in the average number of unique hashes required to produce a new block, approximately 2³². By multiplying this variable by the difficulty rate, we solve for the “work” or computational effort required by miners to produce one block. Dividing the result by 600 seconds (10 minutes) outputs the estimated hash rate.

For simplicity, let us assume that the number of blocks found and the number of blocks expected as of February 24 are the same. Lastly, with a difficulty rate of approximately 39.2 trillion, the network’s hash rate is approximately 280 quintillion hashes per second, which is equivalent to 280 million terahashes per second (TH/s) or 280 exahashes per second (EH/s).

NOTE: Hash rate is a reverse-engineered metric estimated from block production and mining difficulty, and it does not precisely measure the true hashing power of the Bitcoin network. Using a moving average for the hash rate is the best approach to minimize the margin of error.

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Solving for Hash Price

Now that we have the network’s daily revenue ($20.7 million) and the network’s hash rate (280 million TH/s), we can fill in our equation for hash price.

Fundamentally, the calculated hash price informs us that a miner can expect to earn $0.07 per day in revenue for every 1 TH/s of computational power deployed. In other words, it represents the market value of converting electricity into 1 TH/s for bitcoin.

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How Do Changes in Bitcoin’s Price and the Network’s Hash Rate Impact Hash Price?

As shown above, hash price results from the dynamic between bitcoin’s price and the network’s hash rate.

But how do these variables influence hash price?

• Hash price is positively correlated with bitcoin’s price and transaction fees. As bitcoin’s price or transaction fee volume increases, the dollar value of the block reward increases, and hash price rises in tandem.
• Hash price is negatively correlated with the network’s hash rate. As the total computing power of the network increases, the Bitcoin protocol’s difficulty adjustment kicks in, making it more challenging for miners to find blocks. As a result, the hash price decreases.

NOTE: Even though the hash rate increases as new mining rigs come online, the number of bitcoin produced daily remains steady. This is achieved through Bitcoin’s difficulty adjustment.

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Applying Hash Price to Estimate Profitability and Effectiveness of Mining Rigs

Hash price can be augmented by incorporating the cost of electricity and efficiency to help determine the following:

• The incremental value created (or destroyed) through the mining process, also referred to as profitability.
• The effectiveness of a mining rig’s ability to convert electricity into revenue.

Calculating the Value Creation of Bitcoin Mining

Hash price is a helpful metric for estimating mining profitability. To get a better understanding, let us run through an example using Bitmain’s S19 XP mining rig – the most efficient Bitcoin ASIC on the market today.

• The S19 XP can produce 140 TH/s. Assuming a hash price of $0.07 and an uptime of 100%, this translates to approximately $9.80 per day in revenue (140 TH/s * $0.07).
• The S19 XP consumes about 3,010 watts or roughly 72.24 kilowatt-hours (kWh) over a 24-hour period.

Based on this information, we can determine the “net” incremental value created through the electricity conversion function of an S19 XP on a given day at various levels of hash price and electricity costs.

Figure 3: Daily Net Value ($USD) Created by an S19 XP Mining Rig (2/24/2023)

NOTE: Net value created is defined as revenue less electricity costs and does not consider other expenses. The value added or destroyed is at a point in time. The future value of converting electricity into hashes could differ as bitcoin’s price and the network’s hash rate fluctuate.

Figure 3 above shows the daily profitability (revenue minus electricity costs) of an S19 XP running nonstop. At a hash price of $0.07:

• The machine is adding value up to $0.13 per kWh, indicating that it is profitable to convert electricity into hashes at or below $0.13 per kWh.
• The machine is “destroying” value at or above $0.14 per kWh; it might make sense to power off the mining rig and use the electricity for something else.

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Comparing the Effectiveness of Mining Rigs

Hash price can also be used to compare how effective different models of mining rigs are at transforming electricity into value. To determine this, we must incorporate a new metric: revenue per kilowatt-hour (REV/kWh).

• REV/kWh measures the amount of revenue that a mining rig can generate for every kilowatt-hour of electricity that it consumes.
• Two variables drive REV/kWh: hash price and joules per terahash (J/TH).
• J/TH measures the energy efficiency of a mining rig. It represents the amount of energy – measured in joules – that a mining rig consumes in order to perform one terahash of computation.

The formula for REV/kWh is:

Using this formula, we can plug in the J/TH values of commonly used mining rig models at various levels of hash price to see how their efficiency impacts their ability to generate revenue. The resulting REV/kWh figure is measured in dollars per kilowatt-hours, which can help miners optimize their profitability by selecting the most efficient mining rigs and choosing the most cost-effective locations for their mining operations.

Figure 4: Efficiency of Converting Electricity into Revenue

Figure 5: Mining Rig Specifications²

Figure 4 above shows that:

• As hash price increases, REV/kWh also increases because each hash generated by a mining rig is more valuable.
• A lower J/TH value results in higher REV/kWh because a more energy-efficient mining rig requires less energy to generate hashes.

Indicatively, miners operating the latest generation of mining rigs are likely more efficient and, therefore, more effective at converting electricity into revenue, which may potentially provide a buffer to their margins when bitcoin’s price is low, the network’s hash rate is elevated, or if electricity costs are trending up.

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Closing Remarks

• Hash price measures the dollar value of daily bitcoin rewards to miners on a per terahash basis ($/TH/s/day).
• Hash price can be viewed as the market value of converting electricity into hashes for bitcoin.
• Hash price can be viewed as the market value of converting electricity into hashes for bitcoin.
• Hash price is positively correlated with bitcoin’s price and negatively correlated with the network’s hash rate.
• Hash price can be used to calculate the incremental value Bitcoin miners create by converting electricity into bitcoin.
• Hash price, when used alongside REV/kWh, provides a valuable analysis of how efficiency drives revenue when converting electricity into computing power.

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Appendix

Hash Rate Conversion Table

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Glossary of Terminology

ASIC: an application-specific integrated circuit (ASIC) is optimized to compute one function. In the case of Bitcoin mining, this is SHA-256.

Bitcoin (BTC): a decentralized digital currency created by a pseudonymous person or group of individuals going by the alias Satoshi Nakamoto in 2009. Bitcoin is issued and transacted via a peer-to-peer network, independently of a bank.

Bitcoin (The Network): a distributed, decentralized web of miners and nodes spread across the world that facilitate transactions, update the ledger (blockchain), uphold the monetary policy, and secure the network.

Blockchain: a public ledger or database maintained by nodes that stores transactions and information.

Block Header: a data structure containing essential information about a block, such as the block's height, the previous block's hash, the Merkle root of the transactions, and a timestamp.

Block Reward: the reward a miner receives for successfully mining a block. It contains the block subsidy and transaction fee.

Block Subsidy: the amount of bitcoin minted in a block and one component of the block reward.

Difficulty: a measurement of how hard it is to mine a Bitcoin block; more specifically, how challenging it is to find a hash below a given target.

Difficulty Adjustment: a key algorithm of proof-of-work that smooths the average Bitcoin block time to 10-minute intervals by adjusting the difficulty to mine a block based on fluctuations in hash rate. The difficulty is adjusted every 2,016 blocks (approximately every two weeks).

Hash: a hash or hash function is an algorithm that morphs data of any size into an encrypted fixed-sized output. Once data is hashed, the original input cannot be deciphered since the computational power required makes decryption infeasible.

Hash Price: the daily revenue (in USD) generated by miners on a per terahash basis ($/TH/s/day).

Hash Rate (Hash per second): a measure of the computational power used in mining, or the number of calculations generated per second; also referred to as hash power.

Miner: a participant who operates specialized hardware (ASICs) to secure the Bitcoin network and earn bitcoin rewards.

Mining: the process of bundling transactions into blocks, confirming them, and linking them to the previous ones, creating a chain of blocks (blockchain).

Mining Rig: a specialized computer designed to convert electricity into hash power; also. referred to as an ASIC mining rig, ASIC miner, Bitcoin miner, etc.

Node: a computer connected to the Bitcoin network that validates transactions, keeps a historical record of transactions, and dictates and enforces the proof-of-work consensus mechanism.

Nonce (“number only used once”): a 32-bit number used by miners to adjust or change the hash output to be less than or equal to the current difficulty target.

Proof-of-Work: the consensus mechanism or protocol used by Bitcoin, requiring energy to secure the network.

SHA-256: a secure hashing algorithm or function created by the NSA and used throughout the Bitcoin network.

Transaction Fee: the cost paid by a participant to incentivize a miner to include their transaction in a block (i.e., process their transaction).

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