How does difficulty is defined for block '55798'?

Question

I know that the formula for calculating the difficulty is below -

Difficulty = T (max) / T
Where T (max) = 1d00ffff in decimal it is 486604799.

As you can see in the above screenshot the difficulty of block '55798' is 12.85. I'm trying to calculate this value using formula but getting the different result.

D = T (max) / T

When I put the correct values in the formula, It becomes like -

D = (486604799 / 471067731) = 1.03

I don't know why I'm getting the different difficulty. The correct value is 12.85. Can you please let me know the reason of this?

Answer 1

How to calculate difficulty from Bits fields (which is stored in block).

1. Convert value to hex: bits=471067731 -> 0x1c13ec53
2. Split hex value, take 8 high bits (0x1c), and 24 low (0x13ec53)
3. Use formula to get 256-bit target value: T = low * 2 ^ (8 * (high - 3)). In our case it will be: T = 0x13ec53 * 2 ^ (8 * (0x1c - 3)) = 0x0000000013ec5300000000000000000000000000000000000000000000000000
4. Divide highest possible target Tmax (0x00000000ffff0000000000000000000000000000000000000000000000000000) by our T. If we truncate zeros, it will be: 0x13ec53 / 0xffff00 = 12.849

---

Network recalculates difficulty every 2016 blocks (2 weeks). This is how 12.85 is getting recalculated from block timestamps:

block -  diff - time stamp
...
52415 -  7.82 (2010-04-21 21:50:53)
52416 - 11.46 (2010-04-21 21:52:52) <- difficulty update
...
54430 - 11.46 (2010-05-04 09:39:19)
54431 - 11.46 (2010-05-04 09:40:03)
54432 - 12.85 (2010-05-04 09:46:16) <- difficulty update
...
55798 - 12.85 (2010-05-14 16:21:05) <- your block

When network recalculates difficulty, it takes time to mine the latest 2015 blocks (due to bug in code, it should take 2016). In our example, it would be:

2010-05-04 09:40:03 - 2010-04-21 21:52:52 = 12.491 days

In normal scenario 2016 block should be mined in 14 days. So, new difficulty:

11.46 * 14 / 12.491 = 12.844