# Bitcoin Miner Equations You Need to Know

Gain insights about Bitcoin ASIC performance, mining profitability, ROI, and breakeven.

A bitcoin miner uses calculations to gain knowledge about machine performance, profit, and ROI. Thus, it is important to get to grasps with some of the basic mathematics of mining. Don’t worry, most equations are pretty straight forward. Here are a few common ones to help you mine like a pro.

The first section of this guide discusses ways to analyze ASIC performance, the second section introduces operational cost equations, lastly, coin earning and profit estimations are described.

## Miner Performance and Purchase

### ASIC Efficiency

Canaan Creative released the first application specific computers for bitcoin mining in 2013. Since then, over 20 companies have created ASICs. Hundreds of different bitcoin miner models have entered the market (Bitcoin Wiki). But, not all perform the same. Which one do you choose?

Depending on operating costs individual ASIC models earn different margins of profit. One way to gauge ASIC performance is to calculate machine efficiency. The most common efficiency ratio is:

``efficiency = watt / terahash``

This equation shows how many watts are required to hash one trillion times a second with a particular bitcoin miner model. The greater the number, the less the machine earns. The lower the number, the more profit it nets.

For example, a Whatsminer M20S 68 TH/s, which entered the market in 2019, runs at 3360 W. So,

``efficiency = 3360 W / 68 TH = 49.``

The M20S has an efficiency rating of 49. In comparison an AvalonMiner 1166 Pro, which appeared in 2020, has an efficiency rating of 42. And, the newly released S-19, 95 TH/s has an efficiency ratio of 34.

This means, that at today’s BTC value and \$0.06 electricity per kWh, the M20S earns a 53% margin, whilst the 1166 Pro nets 60% profit, and the S19 wins over 66%. The S19 is the most profitable of these three ASICs as it has the lowest efficiency ratio value. Profit margins explained a bit further on.

Note: Many manufacturers list efficiency ratios in J/s / TH/s. One kWh = 3.6 megajoules. We neglect Joules to limit complexity as most independent and home miners pay power in kWh and not Joules.

### ASIC Sales Price in Asia

It is sometimes difficult to get ahold of mining machines from manufacturers in China. Due to high demand machines are sold out for months in advance. Many a bitcoin miner, therefore, purchase ASICs through resellers. But, buyer beware, scammers on social media, fake websites, and marketplaces do exist.

Asian vendors market their sales price in Chinese Renminbi (RMB), or Yuan (Y) per TH. For example, a S-19 PRO 110 TH/s is listed at Y 235/TH, or RMB 235/TH. Note, RMB and Y are of equal value. So, in order to get the total sale price of this machine you need to multiply the fiat value advertised, by the terahash.

``````buy cost = price * terahash
so,
S-19 Pro = Y 235 * 110 TH = 25,850 Yuan (or RMB) total price.``````

As one RMB currently equals around \$0.153 USD, we will multiply to convert currencies:

``25,850 RMB * \$0.153 = \$3955.05. ``

Thus, in this example, the total price for the S19 is just under four-thousand dollars. Remember, the RMB currency value, and hardware prices constantly fluctuate, so look them up on the day.

## Bitcoin Miner Costs

### Electricity Costs in kWh

A bitcoin miner is normally charged monthly for the amount of kilowatt hours (kWh) their machines have consumed. To find the price paid per month to run a S-19 95 TH/s, at 3.25 kW, we need to first compute the monthly kWh as follows:

``````3.25 kW * hours per day * days per month =
3.25 * 24 * 30 =
2340 kWh/month``````

Thus, the monthly kWh are 2,340. So, if we assume the miner pays 6¢ power per kWh, this means the estimated monthly electricity bill is:

``2340 kWh * \$0.06/kWh = \$140.40 in electricity costs for the month.``

Note that, this calculation does not account for fluctuations in power consumption, line loss, or down time. Inspect your electricity bill.

### Other Service Costs

In order to charge for exact power consumed, bitcoin mines meter each ASIC. An ASIC’s power consumption has about a +/- 5% margin from the manufacturer machine specs. For example, a S-19, listed at 3.25 kW, may actually run between 3.08 kW and 3.41 kW. See the following, for how such kW margins are counted:

``````3.25 * 0.05 = 0.1625 kW margins
lower kW bracket = 3.25 - 0.1625 = 3.0875 kW
upper kW bracket = 3.25 + 0.1625 = 3.4125 kW ``````

When it comes the monthly bill, the rate per kWh charged to the bitcoin miner often includes service fees for things like, data center management, security, and climate control. Upon setting up mining rigs for the first time, mines may charge for installation, PSUs, and/or electricity deposits.

Additionally, line loss, if stated on the bill, can bump up total power costs by around +5%. Further, downtime hours are usually experienced and deducted from the monthly fees. Farms should provide downtime reporting systems which can be compared to mining pool records for accurate machine running time. Line loss and down time equations may look something like this on a monthly bill, with a subtotal of \$140.40 for base kilowatt hours:

``````Line loss 5%:
\$140.40 * 0.05 = \$7.02
\$140.40 +\$7.02 = \$147.42 due for the month, readjusted for line loss

Down time:
2340 kWh/month - 10 hours down time = 2330 kWh consumed
2330 kWh * \$0.06/kWh = \$139.80 due for the month, readjusted for down time``````

## Bitcoin Miner Profits

### Profit Margin

A basic calculation of a miner’s profit margin is:

``net profit margin = ((revenue - costs) / revenue) * 100``

Revenue is the total earnings for the time period. Costs include electricity, management fees, cooling and heating. Sometimes repairs, freight, and deposits are also due.

The first part of the equation results in a ratio, which is multiplied by 100 to get a percent value. This percent value is the profit margin for the machine.

Let’s do on example together, shall we? Assume we are running a Whatsminer 30S 86 TH/s, at 3268 W. Power is 6¢ per kWh. For the past month earnings have averaged \$0.14 per TH. We are lucky and have had no repairs or extra costs. Here goes, our monthly profit margin is…

``````revenue = \$0.14/TH * 86 TH * 30 days = \$361.20
costs = 3.268kW * 24 hours * 30 days = 2352.96 kWh consumed =
2352.96 kWh * \$0.06/kWh = \$141.18

profit margin = ((361.20-141.18)/361.20) * 100 = 61%
cost margin = 100% - 61% = 39%``````

For this machine our profit margin was a healthy 61%, and 39% of our coin rewards went towards running costs. See How-to convert W to kW for further clarification of units.

### Coin Earnings

Whilst running costs are fairly static, coin earnings are not. This is because variables in the Bitcoin network are dynamic, meaning they always change value.

Finding a block is a probability not a guarantee. Pools have different payout structures, rejection rates, luck in mining blocks, and fees. Additionally, some pools may sync BTC price and network size every block, or ten minutes. Others may update their systems every six blocks, or each hour. Therefore, the best way to examine your earnings is to make and update your own spread sheet with exact mining payouts to your wallet.

With so many variables to consider, the bitcoin miner most often refers to their mining pool for earnings per TH. Earnings are provided in BTC/TH or USD/TH. Yet, if you are yearning to know what is behind the screen we will cover a simplified bitcoin miner reward equation.

To approximate earnings from bitcoin mining the following formula is the most straight forward. Although, it does not take into account operating costs. Note that the constant 2^32, refers to a normalized probability of one hash per second solving a block, using the SHA-256 algorithm’s 256-bit encryption (BitcoinWiki).

``````daily bitcoin miner earnings =
(6.25 block reward * Hash/second * 86,400 seconds per day) / (difficulty * 2^32)``````

Let’s do an example together. Assume we have 20 machines, at 1 petahash, and 63 kW. Remember, 1 petahash is a quadrillion, or 1,000,000,000,000,000 hashes per second. The current difficulty is about 19 trillion, or 19,000,000,000,000. The block reward is 6.25 (this halves every four years). And, of course, 86,400 seconds are in a 24 hour period, which is required so that the units of measurement match.

``````(6.25 * 1,000,000,000,000,000 H/s * 86,400 / (19,000,000,000,000 * 2^32) =
0.00661729 BTC, which at today's value is \$127 per day``````

We found that daily earnings are about 0.0066 BTC, or \$127/day. If we multiply the daily amount by 30 days, \$127 * 30 = \$3,810, earnings are just under four-thousand a month.

But, this equation is not suitable for estimates longer than a month. This is because network size, difficulty, and BTC price experience nonlinear rates of change. For instance, over the last two years network difficulty, which updates every two weeks or 2016 blocks, has grown 30-60% per annum. Furthermore, network size jumped up by 66%, and the BTC price increased by 79% between the years 2018 and 2020.

### Return of Investment (ROI)

Normally, machine ROI is around one year. But, this amount of time depends on how much it costs to buy and to operate the ASIC. This following ratio provides a bitcoin miner projected ROI in months:

``````ROI =
initial purchase price / net monthly income
= how many months left until ROI``````

Let’s do an example. We are looking at purchasing a Whatsminer M30S, 86 TH/s, at 3268 W. Assume coin earnings are around 14¢/TH, and we expect to pay 6¢/kW power. The purchase price is \$3,000 USD. Here is an estimate of how many months we can expect the ROI to take, at the time of purchase:

``````revenue = \$0.14/TH * 86 TH * 30 days = \$361.20
costs = 3.268kW * 24 hours * 30 days = 2352.96 kWh consumed =
2352.96 kWh * \$0.06/kWh = \$141.18

net profit = revenue - costs =
\$361.20 - \$141.18 =
\$220.02 net monthly income

projected ROI = (\$3000 / \$220.02) = 13.635 months of mining until ROI``````

Take into consideration that this method neglects machine depreciation and expected lifetime. Machine depreciation follows the BTC market, and supply and demand, both of which are volatile. For instance, an S9 was \$1000 to purchase in early 2019, post-halving it was worth \$0, and late in 2020, due to recouped miner earnings prices were up to \$200. Lifetime is said to be around four years per machine, but this is individual to the make and model, as well as environmental strains – i.e. power source stability, cooling and heating, and machine handling and hygiene (dust removal).

### Breakeven Mining

A bitcoin miner feels the impact when the BTC price drops, or the network hashrate grows, or difficulty increases, or electricity prices go up. This is because miner earnings diminish as a result. Therefore, it is important to be able to approximate your breakeven to put your mind at ease. Here is one way to do a speedy breakeven calculation, in order to find the lowest BTC reward earnings per TH that your mining operation can tolerate:

``````break even =
base operating cost per day / TH =
(kWh per day * price/kWh) / TH ``````

(Note, this calculation does not take into account mining pool fees which equivocate up to 4% of daily earnings. To include mining pool fees, the equation would be: breakeven = (base operating cost per day + (coin earnings per day * pool fee)) / TH. The pool fee would be a decimal, for example 4% becomes 0.04 in this calculation.)

Let’s do two examples of simplified breakeven calculations. First, take an Innosilicon T3, 52 TH/s, at 2.80 kW. Below, we find that in order to turn a profit, Bitcoin miner rewards must be at least \$0.078 per TH:

``````breakeven =
(2.80kW * 24h * \$0.06/kWh) / 52TH =
4.032 / 52 = \$0.077753 =
7.8¢ per TH minimum bitcoin earnings to break even``````

Secondly, we will look into the breakeven earnings per TH for a Canaan Avalon miner 1246, 90 TH/s, at 3.42 kW. Assume, once again, we pay 6¢/kWh. Here goes:

``````breakeven =
(3.42 kW * 24h * \$0.06/kWh) / 90TH =
4.9248 / 90 = \$0.05472 =
5.5¢ per TH is the minimum bitcoin earnings to break even``````

The Avalon 1246 performs better than the Innosilicon T3. The Avalon can sustain profits until earnings drop under 5.5¢/TH, whereas the 1246 makes a profit until earnings go below 7.8¢/TH. Luckily, current earnings are over 10¢/TH, so we are A-okay. Phew!

### Breakeven kWh Price

Lastly, we show you how to work out the highest kWh price a machine can tolerate before breakeven. We adjust the last equation a little, and use an Antminer S9 at 14 TH/s and 1372 W. We assume that today’s earnings are 20¢/TH.

``````breakeven kWh price =
earnings per day per TH = (machine kW * 24h * x-price-kWh) / machine TH
20¢/TH = 1.372kW * 24h * x-kWh / 14TH
\$0.20 * 14TH = 1.372 * 24 * x
2.8 / 32.928 = x
x = 0.085
So, the highest kWh rate an S9 can run on at 20¢/TH earnings is about \$0.085/kWh.``````

Good luck mining! 🙂

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