Is the TV and monitor the same size?
This is pretty self-explanatory though.
3840 x 2160 pixels = 4K
1920 x 1080 pixels = HD
It's literally double the amount of pixels in each direction, meaning that everything is half the size it normally is to allow it to fit on your TV.
So simply double your DPI, 400@HD = 800@4K etc.
Most 4K TVs are 30hz anyway, I would honestly just stick to your monitor.