# How many hash calculation is needed to reach one BTC?

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?

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