Calculate Bitcoins Mined Per Day

[jonnybravo0311]

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.

Code:

25 / (18736441558 * 2**32 / 29650000000000 / 86400) = 0.79585047[btc] per day

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

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[ukzerosniper]

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.

[ukzerosniper]

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

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

[jonnybravo0311]

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

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)

[cp1]

Column A:

Code:

mining start date:
Difficulty
Hash Rate / GHsec^-1
BTC / hour
days at this difficulty
hours at this difficulty
Total BTC at this difficulty

Column B:

Code:

=NOW()
18736441558
29650
=25/((B2/(B3*1000000000))*2^32/3600)
=6.8/24
=B5*24
=B4*B6

Column C:

Code:

=B1+B5
=B2*(1+0.1)
=B3
=25/((C2/(C3*1000000000))*2^32/3600)
13
=C5*24
=C4*C6

[ukzerosniper]

Column A:

Code:

mining start date:
Difficulty
Hash Rate / GHsec^-1
BTC / hour
days at this difficulty
hours at this difficulty
Total BTC at this difficulty

Column B:

Code:

=NOW()
18736441558
29650
=25/((B2/(B3*1000000000))*2^32/3600)
=6.8/24
=B5*24
=B4*B6

Column C:

Code:

=B1+B5
=B2*(1+0.1)
=B3
=25/((C2/(C3*1000000000))*2^32/3600)
13
=C5*24
=C4*C6

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

[hazenyc]

The formula is very simple:

Code:

BTC earned per day = Block Reward / (Difficulty * 2**32 / hash rate / seconds in a day)

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?

[jonnybravo0311]

The formula is very simple:

Code:

BTC earned per day = Block Reward / (Difficulty * 2**32 / hash rate / seconds in a day)

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:

Code:

40007470271 * 2^32 / 1000000000000 / 86400 = 1988.78 days

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:

Code:

25 / 1988.78 = 0.01257052

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.

[Mabsark]

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

[jonnybravo0311]

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:

Code:

Reward = hash rate * block reward * time period / (2^32 * difficulty)

Precisely the same as:

Code:

block reward / (difficulty * 2^32 / hash rate / time period)

Using your 1GH/s miner:

Code:

25 / (40007470271 * 2^32 / 10^9 / 86400) = 0.00001257

[Mabsark]

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.

[jonnybravo0311]

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!

[Mabsark]

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

The expected number of hashes we need to calculate to find a block with difficulty D is therefore

D * 2**256 / (0xffff * 2**208)

Yeah, the meaning is the same.

[jonnybravo0311]

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

The expected number of hashes we need to calculate to find a block with difficulty D is therefore

D * 2**256 / (0xffff * 2**208)

Yeah, the meaning is the same.

Thanks for the clarification!

[Mabsark]

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

The expected number of hashes we need to calculate to find a block with difficulty D is therefore

D * 2**256 / (0xffff * 2**208)

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.