Scaling of Tkinter GUI in 4k (3840*2160) resolution?

tkinter has an internal scaling factor that it uses to convert measurements such as points and inches into pixels. You can set this with the "tk scaling" command. This command takes one argument, which is the number of pixels in one "point". A point is 1/72 of an inch, so a scaling factor of 1.0 is appropriate for a 72DPI display.

root = Tk()
root.tk.call('tk', 'scaling', 2.0)

According to a comment in a similar question, this won't affect the default fonts since they are defined outside the context of tkinter. If you specify your own fonts in points, they should honor this setting.

The official documentation for the scaling command is this:

Sets and queries the current scaling factor used by Tk to convert between physical units (for example, points, inches, or millimeters) and pixels. The number argument is a floating point number that specifies the number of pixels per point on window's display. If the window argument is omitted, it defaults to the main window. If the number argument is omitted, the current value of the scaling factor is returned.

A “point” is a unit of measurement equal to 1/72 inch. A scaling factor of 1.0 corresponds to 1 pixel per point, which is equivalent to a standard 72 dpi monitor. A scaling factor of 1.25 would mean 1.25 pixels per point, which is the setting for a 90 dpi monitor; setting the scaling factor to 1.25 on a 72 dpi monitor would cause everything in the application to be displayed 1.25 times as large as normal. The initial value for the scaling factor is set when the application starts, based on properties of the installed monitor, but it can be changed at any time. Measurements made after the scaling factor is changed will use the new scaling factor, but it is undefined whether existing widgets will resize themselves dynamically to accommodate the new scaling factor.