24″ FullHD to 31.5″ UHD DPI (Mouse) Conversion – Invoice

I switched from my 24″ FHD 1920x1080p to 31.5″ UHD 3840x2160p (GIGABYTE M32U) monitor two days ago.
My mouse is a DeathAdder Elite and I had a DPI of 1000 on a 24″ FHD monitor.

These 1000 DPI, which I set on the Razer Synapse, now definitely feel too slow on a UHD monitor.
I only swapped the monitor, otherwise all Windows settings etc have remained the same (except for user-defined text size, i.e. scaling, I set it to 150% in Windows, otherwise I’d get a magnifying glass to see the symbols) will need and text ,

So now I thought I would have to adjust the dpi of my mouse and increase the value to 3000. It works quite well in desktop mode, but in all my games, which now run at UHD resolution, it feels wrong and completely unrecognizable.

Then I thought there must be a simple calculator on the internet where I enter my current values ​​and the DPI of the mouse and then the new values ​​from the UHD monitor and then I get my adjusted DPI spit.
Unfortunately I couldn’t find anything like this, but I came across this link: DPI Basics

I also found that I calculated the PPI of my FullHD and UHD:
24″ FHD = 91,787ppi ~ 92ppi
31.5″ UHD = 139,867ppi ~ 140ppi

But if I stick to his calculation example (based on my 1000 dpi starting value), I get a low dpi value for a UHD monitor

1000 x 92/140 = 657 dpi

Have I perhaps misunderstood something or just calculated completely wrong? Could it be that his example is related to staying at the same resolution but switching to a bigger monitor? So from 24″ FHD to 27″ FHD? Then I don’t think my calculations matter much.
Maybe someone of you know an easier way to calculate this I’m slowly getting frustrated

There’s also an example of that on the website at the end:
“If you play at Full HD with 800 dpi, for example, you should set your mouse to 1,067 dpi in WQHD to keep par here.”
Unfortunately there is no invoice for this

kind regards