- Kingdoms in the real world varied in size a great deal.
- The sizes you get following the guides in the DMG are perfectly reasonable
- You can (and probably should for the sake of interest) vary them a lot
- The suggestion in the DMG that their scale matches the size of Great Britain is dependent on switching context from distance to area.
A single sheet of hex paper with 5 hexes to the inch is ideal for most maps.
Since D&D is published by Americans, I'm going to assume they are talking about Letter sized paper.
- Letter paper is 11" tall.
- Therefore Letter paper is 55 hexes tall
(Province Scale) each hex represents 1 mile
- Letter paper is 55 miles tall at Province Scale
(Province Scale) an area that can be covered in one day’s travel in any direction from the center of the map
So that assumes a party can cover 27.5 miles in a day.
normal travel speed is 3 miles per hour (source)
This maps onto real-world values:
most hikers will average about 2-3 miles per hour. (source)
So this assumes that a little under 10 hours per day will be spent walking. Given breaks for food and setting up camp, this is feasible given a day dedicated to travelling.
On a kingdom-scale map, each hex represents 6 miles
We can therefore just multiply everything by 6
- Letter paper is 330 miles tall
- 330 miles / 27.5 miles per day = 12 days
A map at [Kingdom] scale covers a large region, about the size of Great Britain
Now D&D is directly relating it to the real world. Great Britain is about 700 miles long and about half that wide.
If we want to detour via area (even though it is counter-intuitive as the context in the DMG is firmly geared towards distance).
Letter paper is 8.5" wide. So that is 255 miles.
That gives us an area of 84,150 square miles which is about the size of Great Britain (80,823).
The implication that Great Britain will fit on a sheet of Letter paper at Kingdom Scale is just wrong though. GB isn't the right shape (over double the length and not remotely rectangular).
That said: a 330×255 mile kingdom is perfectly reasonable:
So, you’re writing your story or building your campaign world. How many villages does that give us in a kingdom? Choose your kingdom size, and go with the above. A kingdom could be huge, but some were little more than a region the size of a small county. The defining factor isn’t the size, but the independence—a king does’t owe feudal allegiance to a higher secular authority. (source).
… it just isn't the size of Great Britain.
Since that source mentions "the size of a small county".
[Runtland's] greatest length north to south is only 18 miles (29 km) and its greatest breadth east to west is 17 miles (27 km). (source).
This is significantly smaller than 330×255!
And you can go larger if you like, it is (presumably) your campaign world that you are mapping and having uniformly sized kingdoms would look rather odd!
And as a fun aside:
Land's End to John o' Groats is the traversal of the whole length of the island of Great Britain between two extremities, in the southwest and northeast. The traditional distance by road is 874 miles (1,407 km) and takes most cyclists 10 to 14 days; the record for running the route is nine days. Off-road walkers typically walk about 1,200 miles (1,900 km) and take two or three months for the expedition. (source)