I need an answer to this because I'm trying to figure out the distance between some of the towns for chapter 4. Now, I'm not running this chapter as it is because...well...if it's boring to read it's boring to play. So I'm modifying this HEAVILY, and I want to know the scaling for it so that I can plan and place other events around it. The map is on page 5 with the introduction if that helps any. I'm not all too familiar with the scaling thing and I'm trying to learn to better read maps and produce them in case I want to make my own. I thank anyone for just the straight answer and appreciate anyone that gives it to me, and I would also thank and appreciate anyone that could give me a few tips on how to determine this type of thing in the future!
The map has no scale
The world of Toril is a planet about the size of Earth. On this world, the Sword Coast in part of the continent of Faerûn. The link goes to an offcial map for the Sword Coast by Wizards of the Coast with distance scales, so you can measure the distance between cities directly.
For example, the distance as the bird flies between Waterdeep and Baldurs Gate is a little over 540 miles, and the entire map on page 4 is about 1,500 miles North to South, and 1,000 miles East to West.
The map does not have hexes, and the size of hexes is how the DMG defines those scales (p. 14):
For the most detailed areas of your world, use a province scale where each hex represents 1 mile. A full-page map at this scale represents an area that can be covered in one day's travel in any direction
On a kingdom-scale map, each hex represents 6 miles. A map at this scale covers a large region, about the size of Great Britain or half the size of the state of California. That's plenty of room for adventuring.
For mapping a whole continent, use a scale where 1 hex represents 60 miles. At this scale, you can't see more than the shape of coastlines, the biggest mountain ranges, major rivers, huge lakes, and political boundaries. A map at this scale is best for showing how multiple kingdom-scale maps fit together, rather than tracking the movement of adventurers day by day. While the Sword Coast is not a whole continent, and
So technically speaking, the map has no scale at all. But, one can ask what would be a useful scale to use on this map?
The adventure Lost Mines of Phandelver does have hexes of 5 miles, close to kingdom scale, but that does only cover the North of the Sword Coast, between Neverwinter and the Sword Mountains. So that is too small (you would need 250 hexes top to bottom, which would be very tiny on a typical letter sheet of paper). Somebody has made a 60-mile hex map of the Sword Coast, and you can see (as the DMG says) that this scale is likely too large to be useful for day-to-day adventuring. For practical overland travel, a map of 24 mile hexes actually would be more useful, as that matches the normal travel speed per day, so you can move one hex per day, and would only need about 60 hexes top to bottom of the map.
You do not need hexes to deternine travel times, they are just a convenient way to do so, without needing to measure distances, as you can just count hexes. Alternatively, for convenience, you may refer to this table of precalculated travel times between cities in the North.
One final note, as @Eddymage observes, the map given in Tyranny of Dragons deviates from the official Map by Mike Schley linked above, with several cities being at slighly different positions, and the y-Axis appearing to be slightly stretched. As both are published by WotC, neither one can claim primacy (and maybe the one given in the module would be the one to use specifically for the module). You need to decide which one to use. I probably would use the Mike Schley one, that has a scale attached.
Strictly following description in the DMG, such map depicts a continent.
The DMG (page 14) reports that a Kingdom scale map
[...] covers a large region, about the size of Great Britain or half the size of the state of California. That's plenty of room for adventuring.
Since the map in the Tiranny of Dragons covers an area slightly larger than 1060\$\times\$680 miles (in the 3rd paragraph below I explain how you can compute this) and the largest dimension of the Great Britain is around 590 miles1, such map should be classified as a Continent Scale map.
Follow the guidelines that best suit your needs.
These indications (Province, Kingdom, Continent) are just indications: you may put the details that best suits your style, your campaign and what you desire to tell. Indeed, in the same section the DMG tells us that you may
Use a scale for your map that's best suited to the level of detail you want.
Search for maps with scale and compare them.
One possible solution to compute distances-and hence decide which type of map employ-is to search for a map that shows the scale, find locations that appear on such map and on yours, and then compute distances in the map with scale and compare them on your map.
At this link you can find a map of Faerun (at different resolutions): for obtaining the above result, I checked the distance between Beregost and Mirabar on the y axis (around 1060 miles) and between Luskan and Citadel Adbar on the x axis (around 680 miles)2. These values are approximative, since such cities are not exactly lying on the same line.
This method could give you a rough estimation of the surface dimensions. Indeed, if you look at the two maps, they do not depict locations at the same exact position: for example, the relative positions of Baldur's Gate and Elturiel are not consistent in the maps, in Tiranny's map the former is northern with respect the latter, while in the official map Baldur's Gate is southern.
1 I used Google Map for this measurement.
2 I used a custom C++ program for computing such distances, but you can use other free software (e.g. Gimp) and/or websites (see the links in this thread).