How does the puzzle rating work?

I know that the normal Elo has to do with player amount, the strength of these players, and so on. But how does Elo in puzzles work? Do these puzzles get their rating based on the games they are taken from? Or is there a calculation like for the normal rating?

I'm asking for two reasons:

1. How come my puzzle rating can be easily twice as high as my normal rating?

2. How are a simple "take hanging queen" puzzle and a "mate in 4" puzzle on the same rating?

There isn't really a logical explanation about how puzzle elo works, your puzzle elo definitely doesn't reflect your skill in the game. But the main reason is that high rated puzzle don't exactly mean it must be on the difficulty level of the games itself.

For your second question I don't have a good answer but a reason might be that high rated players and up overthinking about high rated puzzles and miss super simple tactics. I've seen 2000 rated puzzles with hanging pieces and only 30%~ passage rates.

That overthinking may be a good reason. Even though it would be kinda weird as I thought better players see a problem and think "Ah, saw that a few hundred times, it's XYZ and mate".

The puzzle elo shows your upset danger sense at certain moments!! Your real elo can be calculated by dividing your puzzle elo and adding... 100 points just to go ahead

@darlihysa If being upset is part of your ELO I would be 5k. or 50. Depending on what way is good or bad.