2.1) What are the equivalent figure, wargaming, railroad, dollhouse, and miniature scales?

These are the approximate equivalent figure/wargaming, railroad, and dollhouse miniature scales:

2.1.1) How do you calculate figure and wargaming scales?

Figure and wargaming scales basically indicate the height of a man in that scale. A figure of a man in 10mm scale would be 10 mm high. Here's how you convert to fractions or ratio scale measurements:

1 inch = 25.4 mm

Considering that the average height of a man was (this has been increasing over time) 5 feet 8 inches (68 inches), that would make an average man 1727.2 mm tall.

mm_scale/height_of_man = 1/scale
or
height_of_man/mm_scale = scale

For example, 54mm scale:
1727.2mm/54mm = scale
31.99 = scale
So 54mm scale is approximately 1/32 (fraction) or 1:32 (ratio).

Another example, 12mm scale:
1727.2mm/12mm = scale
143.93 = scale
So 12mm scale is approximately 1/144 (fraction) or 1:144 (ratio).

To make things more complicated, sometimes the average height of a man used is 6 feet (1828.8 mm) instead of 5 feet 8 inches, and sometimes the measurement is made from the ground to eye level instead of the top of the head (this is due to difficulties in measuring the height of a figure wearing tall head gear, as was common historically). Needless to say, figure/wargaming scales are approximate.

2.1.2) How do you calculate dollhouse and miniature scales?

Dollhouse and miniature scales are an indication of how big a foot (12 inches) would be in that scale. Here's how you convert to fractions or ratio scale measurements:

inch_scale/foot = 1/scale
or
foot/inch_scale = scale

For example, the most common dollhouse scale is 1" scale:
12"/1" = scale
12 = scale
So 1" scale is 1/12 (fraction) or 1:12 (ratio).

Another example, 1/4" scale:
12"/(1/4") = scale
48 = scale
So 1/4" scale is 1/48 (fraction) or 1:48 (ratio).

"Dollhouse dollhouse" scale is the scale a dollhouse inside a dollhouse would be (1/12 of 1/12 scale), this is 1/12" scale:
12"/(1/12") = scale
144 = scale
So 1/12" scale is 1/144 (fraction) or 1:144 (ratio).

2.1.3) How do you calculate railroad scales?

Your guess is as good as mine. All I could figure out were these three things:

1. British 2mm scale: The British 2mm scale indicates how big a foot (12 inches, or 304.8 mm since 1 inch = 25.4 mm) would be in that scale. Here's how you convert to fraction or ratio scale measurement:

   mm_scale/foot = 1/scale
   or
   foot/mm_scale = scale

   304.8mm/2mm = scale
   152.4 = scale
   So British 2mm scale is 1/152 (fraction) or 1:152 (ratio).

2. H prefix: The prefix H stands for half - as in HO is half the size of O scale, and HHO is half the size of HO scale. There was some talk of an HZ scale, but I have heard of no trains yet being built in that scale (1/440).
3. N scale: N gauge (or N scale) stands for "nine millimeter gauge". The railway gauge is the standard distance between the track rails, which is 4 feet 8 inches or 1422.4 mm (1 inch = 25.4 mm). In N scale, this distance is 9 mm, so the scale is:

   scale_gauge/actual_gauge = 1/scale
   or
   actual_gauge/scale_gauge = scale

   1422.4mm/9mm = scale
   158.04 = scale
   So N scale is approximately 1/158 (fraction) or 1:158 (ratio).

   Because the standard distance between rails may have been different in different countries and because the working motors of the railway engines, especially early on, were hard to make to fit the small engine bodies, the exact scale of N scale was never agreed upon. Typically N scale is 1/160 scale in North America, 1/148 scale in the United Kingdom, and 1/150 scale in Japan.

2.2) What would be considered an accurate range of scales?

What would be considered an accurate range of scales depends on how accurate you want your collection to be, and how big the items are. A 1% difference is considered very accurate, but some consider a difference of 10% to also be acceptable. A 15% difference is insignificant in a small item, but very inaccurate in a large one. Here is a table of ranges for differences of 1%, 5%, 10%, and 15%:

2.3) What are the typical size differences between the scales?

These are the scale lengths of four typical lengths: a man's height (6 feet), the length of a vehicle (15 feet), a fighter's wingspan (35 feet), a bomber or transport's wingspan (100 feet), and the length of an aircraft carrier (1000 feet):

[Decimal/Fraction conversions]