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?

1 Answer 1


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.

  • 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? Aug 30, 2019 at 12:08
  • 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!). Aug 30, 2019 at 12:13
  • @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
    Aug 30, 2019 at 12:21
  • @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
    Aug 30, 2019 at 12:22
  • I just want a rough estimation. Aug 30, 2019 at 12:34

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