<p>Double SHA 256 follows a uniform distribution that means all hashes are equally likely to occur. So, your chances of finding the block header hash that is less than the target is same for every round of hashing.</p>

<p>With the current mining difficulty of 10183488432890, the target bits are <code>0x171ba3d1</code>. This means you will need to find the block header hash that is less than or equal to <code>0x0000000000000000001ba3d10000000000000000000000000000000000000000</code>. For one round of double hash that is a probability of 2.28631x10<sup>-23</sup>. Let's call it P. So the probability of not finding a valid hash is (1-P). For N hash attempts, the probability of not finding the valid hash is (1-P)<sup>N</sup>. To be sure that you find a block we need to ensure that <code>(1-P)^N -&gt; 0</code>. Since <code>P -&gt; 0</code>,  <code>(1-P)^N = 1-N*P</code> (using Taylor expansion). Solving both equations you get N = 1/P = 4.3738x10<sup>22</sup></p>

<p>At your hash rate of 1 TH/s it will take you 4.3738x10<sup>10</sup> seconds which is 1386.91 years.</p>

CC BY-SA 4.0
2019-08-30T12:08:08.673Z
Thank you very much Ugam, so for 10 or 100 TH/s power rate, should I simply divide what you calculated for 1 TH/s to 10 or 100? Also if my TH/s is 2, should I simply divide the 1386.91 by 2? I mean is the formula linear?
user3486308
CC BY-SA 4.0
2019-08-30T12:13:57.543Z
I also like to ensure that, if a miner has 14.5 TH/s, is that mean it should work for 95.6 years 24/7 to reach 1 BTC? (I assumed that the difficulty of network won't change trough next 100 years!).
user3486308
CC BY-SA 4.0
2019-08-30T12:21:25.190Z
@user3486308 that probability is not for 1BTC but for getting the entire block rewards since it calculates the probability of successfully mining a block at the current difficulty.
Ugam Kamat
CC BY-SA 4.0
2019-08-30T12:22:24.190Z
@user3486308 With one ASIC mining machine you will not be able to mine blocks successfully. Your best chance is to join a mining pool. Bitcoin's difficulty adjusts every 2016 blocks.
Ugam Kamat
CC BY-SA 4.0
2019-08-30T12:34:00.407Z
I just want a rough estimation.
user3486308
CC BY-SA 4.0
2019-08-30T12:37:41.050Z
@user3486308 To get a fraction of the block reward, you will need to join mining pools. If you are mining solo, you will get the entire block reward. Now, coming to your point of estimation for mining pools, you will need to go on their website and find that out. It depends upon a number of factors including number of miners in the pool, the shares and the distribution rate.
Ugam Kamat
CC BY-SA 4.0
2019-08-30T12:47:56.467Z
I answered the question here: https://bitcoin.stackexchange.com/questions/90111/are-miner-builder-sellers-profitability-calculations-true. It's a pleasure if you explain more with examples there!
user3486308
CC BY-SA 4.0
2019-08-30T13:06:30.880Z
@user3486308 as i said in my previous comments, it is not 1BTC, but the entire block rewards (12.5 BTC current subsidy + tx fees)
Ugam Kamat
CC BY-SA 4.0
2019-08-30T11:46:22.337Z
2019-08-30T21:35:16.957Z
2019-08-30T21:35:16.957Z
Ugam Kamat
<p>What I am asking for is a formula and it's source of numbers to put in there and calculate how many hashes must be calculated to get 1 bitcoin today(or every other day in future)? </p>

<p>For example, if I put 1,000,000(1TH/S) in hash rate field of the table of the this site <a href="http://www.alcula.com/calculators/finance/bitcoin-mining/" rel="nofollow noreferrer">http://www.alcula.com/calculators/finance/bitcoin-mining/</a> , it gives me </p>

<blockquote>
  <p>"Average time to find one block: 1386.91 years"</p>
</blockquote>

<p>, but I am not sure if it's calculation is true? I also like to know the formula that website uses?</p>

<mining-theory><hash>
How many hash calculation is needed to reach one BTC?
user3486308
# How many hash calculation is needed to reach one BTC?

(Asked by: username_0 on 2019-08-30)

What I am asking for is a formula and it's source of numbers to put in there and calculate how many hashes must be calculated to get 1 bitcoin today(or every other day in future)?

For example, if I put 1,000,000(1TH/S) in hash rate field of the table of the this site <http://www.alcula.com/calculators/finance/bitcoin-mining/> , it gives me

> "Average time to find one block: 1386.91 years"

, but I am not sure if it's calculation is true? I also like to know the formula that website uses?

**Tags:** mining-theory, hash


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## 1 answers

### Answer by username_1 on 2019-08-30. Score: 1 | Accepted answer

Double SHA 256 follows a uniform distribution that means all hashes are equally likely to occur. So, your chances of finding the block header hash that is less than the target is same for every round of hashing.

With the current mining difficulty of 10183488432890, the target bits are `0x171ba3d1`. This means you will need to find the block header hash that is less than or equal to `0x0000000000000000001ba3d10000000000000000000000000000000000000000`. For one round of double hash that is a probability of 2.28631x10-23. Let's call it P. So the probability of not finding a valid hash is (1-P). For N hash attempts, the probability of not finding the valid hash is (1-P)N. To be sure that you find a block we need to ensure that `(1-P)^N -> 0`. Since `P -> 0`, `(1-P)^N = 1-N*P` (using Taylor expansion). Solving both equations you get N = 1/P = 4.3738x1022

At your hash rate of 1 TH/s it will take you 4.3738x1010 seconds which is 1386.91 years.

> **Comments:**
> **username_0**: Thank you very much username_1, so for 10 or 100 TH/s power rate, should I simply divide what you calculated for 1 TH/s to 10 or 100? Also if my TH/s is 2, should I simply divide the 1386.91 by 2? I mean is the formula linear?  
> **username_0**: I also like to ensure that, if a miner has 14.5 TH/s, is that mean it should work for 95.6 years 24/7 to reach 1 BTC? (I assumed that the difficulty of network won't change trough next 100 years!).  
> **username_1**: @username_0 that probability is not for 1BTC but for getting the entire block rewards since it calculates the probability of successfully mining a block at the current difficulty.  
> **username_1**: @username_0 With one ASIC mining machine you will not be able to mine blocks successfully. Your best chance is to join a mining pool. Bitcoin's difficulty adjusts every 2016 blocks.  
> **username_0**: I just want a rough estimation.  
> **username_1**: @username_0 To get a fraction of the block reward, you will need to join mining pools. If you are mining solo, you will get the entire block reward. Now, coming to your point of estimation for mining pools, you will need to go on their website and find that out. It depends upon a number of factors including number of miners in the pool, the shares and the distribution rate.  
> **username_0**: I answered the question here: https://bitcoin.stackexchange.com/questions/90111/are-miner-builder-sellers-profitability-calculations-true. It's a pleasure if you explain more with examples there!  
> **username_1**: @username_0 as i said in my previous comments, it is not 1BTC, but the entire block rewards (12.5 BTC current subsidy + tx fees)  

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