4K gaming

[Googolplex]

Simply put: 4k requires two times more compared to 1080p.
1920 x 1080p x 2 = 3840 x 2160p aka 4k.
The game you barely ran at 60's will go down to 30's.

No, that's not correct.
4K requires four times more compared to 1080p.
1920 x 1080 x 4 = 3840 x 2160p aka 4K
The game you barely ran at 60's will go down to 15's.

4K has to render the four times amount of pixels compared to 1080p.