Bitcoin Forum

Hi Guys,

I am trying to create an excel formula to calculate bitcoins earned per day.

I would like to incorporate the following factors.

Current Difficulty
Current Network Hash Rate
Current Block Reward
Current Block Frequency

Once I have got the base formula working for bitcoins per day, I would then like to  calculate bitcoins earned over a 12month period with a Difficulty increase which I can input.  For example, I would input 5% increase per month, I would then see the result of that.

I know this is not anything other than a vague guide, but I would like to get it worked out.

Any help on this would be fantastic.

https://blockchain.info/stats

The above stats are for each 24 hour period

You can utilize the API that Blockchain.info and other sites have to calculate this stuff in other applications. Alternatively you could just run bitcoin-d and get information from it periodically.

Thanks juju,

I would really like to sort the formula out so that I can incorporate it into my spreadsheet. 

If anyone can help, I'd be really grateful.

Thanks

Fill right with difficulty increasing by whatever you predict and you can set the days at this difficulty to be 12, 14 whatever you predict.

Do you want to calculate the bitcoins you would mine given a specific hash rate? Or do you want to calculate the bitcoins that will probably be mined in that amount of time? To calculate the latter would be really simple, since you'd only have to divide the time by 10 minutes and multiply that number by 25 (current reward). Since 25 BTC are being created every 10 minutes (mean)

yeah exactly. The amount of bitcoins that's being generated or distributed as a block reward is designed to stay the same, at least approximately. If the hash rate is rising, the amount of bitcoin that are being generated, is actually higher than 25 per 10 minutes.

The network hash rate is not known. The value is estimated based on the rate at which blocks are being found.

You must determine the rate at which bitcoins are being generated by looking at the rate in the recent past and extrapolating that into the future.

Bitcoincharts.com says that blocks have been produced at the rate of 6.7 per hour. That translates to 4020 BTC per day.

If you want to know how much a miner will mine per day at the current difficulty, use this formula:

Daily revenue = H x 25 x 600 x 65535 / 2⁴⁸ / D x 6 x 24

where H is the hash rate (H/s) and D is the difficulty

There are some online calculators for that, for example:

http://www.bitcoinx.com/profit/ (http://www.bitcoinx.com/profit/)

Not sure if it helps, or if it is wht you want

In this example, can you clarify a couple of items so that I can fully understand the calculation?

Is H = the hash rate of my miners?
25 = the number of BTC per block
600 = ?
65535 = ?
2^48 = ?
D = network difficulty
6 = ?
24 = ?

Could you clarify this for me.  If I were to use this in excel, for your formula to work, would it be as follows.

Cell B1 Mining start date
Cell B2 Difficulty
Cell B3 Hash rate of my gear
Cell B4 BTC Per Hour
Cell B5 Days at this difficulty level

In order to be as accurate and clear as possible, could you attach a sheet with the formula working?

Thanks.

Yep that's it

65535 / 2⁴⁸ / D is the probability of a single hash solving a block
600 x 6 x 24 is the number of seconds in a day

The formula is very simple:
So, if in Excel, just put each value in a cell:
25 is block reward
18,736,441,558 is difficulty
2**32 is constant
your hash rate (or whatever hash rate you want)
86400
% increase in difficulty
days between increases
total days to consider

As has been pointed out, you can fetch the difficulty from calls to blockchain.info, or you can just change it manually for when you want to do the calculation.  Then, you'd just run the formula over and over again having it change the difficulty and recalculating earnings per day for the time period you specified.

There are any number of calculators online that already provide this level of information.  For example, bitcoinwisdom.com has a mining calculator to show ROI with any number of editable inputs, including conversion from BTC->USD, pool fees, power costs, etc.  Not sure why you're looking to reinvent the wheel, but given the formula above and the values for the cells, you certainly can.

Thanks Guys,

I am working out bills for us and the best way to optimise our power usage.

It is actually to aid my father and make a bullet proof calculator that given the correct variables can provide accurate data on power usage, electricity cost, BTC earned per day, value of BTC earned in £ and so on all in one form.

It’s optimised for the information he cares most about.

Once I have the formula updated, Ill post a copy on here so you can see where I’m at and provide any input / advice on modifications I should make to increase accuracy.

Thanks again.

Be sure to explain to your father that there is no "bullet proof" calculator because there are too many changing variables.  Even the formula I posted provides nothing more than "expected" earnings per day in an ideal world under perfect circumstances.  It does not take into account pool luck, transaction fees associated to blocks, etc.  Everything is luck, and as such the best we can provide are probabilistic calculations.

The calculations become less and less accurate over time because they take more and more guesses.  For example, nobody can tell you what the next difficultly will be.  You can guess that it will increase 5% or 10% or 20%.  Do you keep that same increase for every jump from now until the last block is mined?  Do you put in variable jumps?  Whatever you do, you're just making a guess :)  What about BTC->fiat?  That changes every second.  Electricity rates are variable.  Power usage depends on the efficiency of the power supply, the power delivery, the miners themselves.  All variables.

TLDR: it's guess work.  Make sure dad gets that.

In your example my formula looks like this =29650*600*65535/2^48/18736441558*6*24

That produces a result of 7.9 BTC per day.  I am inputting my hash rate as GH/s.  What have I got completely wrong?

2⁴⁸ is 281474976710656, and not 248.

I edited. It still looks wrong :/


The stats i'm working with are as follows.  Could someone help me incorporate these stats into a working formula that results in an BTC per day estimation.

Current Difficulty  :  18736441558      
Current Network Hash Rate TH/s  :  138086.19      
Coin Reward Per Block  :  25      
Block Frequency mins  :  10      
BitCoin Value £     :  344.52      
Your Current Speed GH/s  :  29650   
Your % total of Network Hash Rate : 0.000214721  (calculated by spreadsheet from tats in putted above)      
Total BTC Released Per Day   : 3600   (calculated by spreadsheet from tats in putted above)
   

I'm anticipate a result between 0.77299547 / 0.79585047BTC Per day


Thanks guys.

Your percentage of the total hash rate, total BTC released per day and value in Pounds is not necessary to figure out your expected earnings.  Just change the difficulty and/or hash rate (which is hashes per second - not GH/s, TH/s or anything else... HASHES per second) as necessary.

When I use this exact formula Excel changes it as follows
=25/(18736441558*2E+32/29650000000000/86400)

It gives the result 1.70908E-23

What does "* 2**32" mean in this formula?  I think this may be where its going wrong :/

It means "multiply by two to the 32nd power" which means "multiply by 4,294,967,296.  Sorry about the shorthand :)

It means "multiply by two to the 32nd power" which means "multiply by 4,294,967,296.  Sorry about the shorthand :)
[/quote]

How do I enter that into an excel formula.  Can you copy and paste the formula from excel on your PC?  When I am entering it excel is changing it and breaking it.

Thanks.

How do I enter that into an excel formula.  Can you copy and paste the formula from excel on your PC?  When I am entering it excel is changing it and breaking it.

Thanks.
[/quote]
Nailed it =25 / (18736441558 * (2^32) / 29650000000000 / 86400)

needed to put 2^32 in brackets :)

How do I enter that into an excel formula.  Can you copy and paste the formula from excel on your PC?  When I am entering it excel is changing it and breaking it.

Thanks.
[/quote]
=power(2,32)

In cell A1 you put 25
In cell A2 you put 18736441558
In cell A3 you put =power(2,32)
In cell A4 you put 29650000000000
In cell A5 you put 86400
In cell A6 you put:  =A1 / (A2 * A3 / A4 / A5)

Column A:

Column B:

Column C:

Ok this looks really interesting.  I am going to play with this tonight.

Does time between blocks matter at all in this calculation? It seem that it would, but maybe I am missing something.
If BTC is 25 coins per block, once every 10 minutes (on average), how would it change if say if blocks of 25 were found say ever 1 minute?

It wouldn't.  The formula is "expected earnings per day based on a given difficulty and hash rate".  It doesn't care about how many blocks are solved in a day.  It only cares about what your expected daily earnings are.  If you were to break down the formula, the denominator is effectively solving how many days you would expect it to take to find a block.  The numerator is the block reward.  Broken down we show first "how many days should I expect to find a block given a difficulty of X and a hash rate of Y"?  I'll use 1TH/s and current difficulty of 40007470271:
Given that answer we know that with 1TH/s at the current difficulty, we would expect to find a block of 25BTC after 1988.78 days (I rounded to two decimal places).  So, if we want to find out how much we can expect to earn a day we just take the block reward and divide it by the number of days to find that block:
So, you can expect to earn 0.01257052BTC a day right now with a 1TH/s miner.

Keep in mind, this formula is only there to provide a base of what the expected earnings are given an ideal set of circumstances.  Obviously in the real world, you can earn more or less since the process of mining itself is based upon luck so time to solve varies, the payout mechanism of the pool on which you're mining varies, fees and donations vary, transaction fees on a block vary, etc.

The simplest equation is:

Reward = Hash Rate * Block Reward * Time Period * 65535 / (2^48 * Difficulty)

The hash rate is measured in hashes per second and the time period is measured in seconds. For example, at a difficulty of 40007470271, 1 Gh/s would mine:

1*10^9 * 25 * 86400 * 65535 / (2^48 * 40007470271) = 0.00001257 BTC/Day

I'm not entirely sure how that formula is the simplest one... especially with the introduction of the random 65535 constant that is offset by dividing by 2^16.  The more commonly accepted formula to calculate expected earnings per day is the one I provided, which you can get from yours by removing that unnecessary constant (65535/65536), which I don't know why you included in the first place since it makes no sense:

Precisely the same as:


Using your 1GH/s miner:

It's not precisely the same.

2^32 = 2^48/2^16 = 4294967296
2^48/(2^16-1) = 4295032833

Compare the two when using 1 Th/s:

1*10^12 * 25 * 86400 / (2^32 * 40007470271) = 0.01257051 BTC/day
1*10^12 * 25 * 86400 * 65535 / (2^48 * 40007470271) = 0.01257032 BTC/day

You can see the values starting to diverge.

I know it's not precisely the same... hence why I pointed out it was 65535/65536 :)

So... what do those two things represent in your formula?  65535 and 2^48?  I've never seen any version of that formula before in reference to calculating expected earnings per day, so I'm curious to their meanings.  For example, is the formula I posted the "lazy man's" version of yours?  In other words, did somebody take a shortcut and just say, "well, for all intents and purposes, just use 2^32 instead of 2^48/2^16-1 since it doesn't have that much effect"?

In my formula, I use 2^32 to represent a difficulty 1 share.  Is that the same meaning in yours of the 2^48/2^16-1?

Thanks!

https://en.bitcoin.it/wiki/Difficulty


Yeah, the meaning is the same.

Thanks for the clarification!

An excellent approximation for calculating BTC per Gh per day while the block reward is 25 BTC is simply 502906 / Difficulty.