In model train conversations it's common to hear the terms "gauge" and "scale" used interchangeably, as in "HO gauge" as a synonym for "HO scale". This is especially true for model railroading newcomers. While this causes no harm, as everyone understands what is being said, the two terms have different meanings:
Scale -- The size of the model relative to the prototype.
Gauge -- The distance between the two rails.
For example, N scale is 1:160, which means it is 160th the size of the prototype. If a prototype freight car is 80 feet long, in N scale it would be 160th of that, or 1/2 of a foot long.
In terms of gauge, prototype standard gauge is 4 ft 8.5 in between the rails, which translates to 9 mm between the rails in N scale. ("N" was chosen for the name of 1:160 scale because of the Nine mm rail gauge. )
So, if you say something is HO gauge what you are saying is that it is 1:87 (HO) scale and standard gauge. Similarly, the term "HOn3" means a model that is 1:87 scale, but representing a prototype narrow gauge of 3 feet. The "n3" of "HOn3" means: "narrow gauge, 3 feet". There is also an Nn3 -- 1:160 scale and a narrow gauge of 3 feet. Another popular example of modeling narrow gauge is On2.5 gauge -- which is O scale (1:48), narrow gauge of 2.5 feet.
The National Model Railroad Association (NMRA) has their own web page on scale and gauge which covers this topic in detail, including a list of scales common for indoor model railroads.
Although many model railroad scales have been established they clearly do not enjoy equal popularity. The most popular scale by far is HO, with N a distant (but growing) second, and the other scales further behind. TT scale (1:120) is virtually dead, killed off by the introduction of N in the 1960s. OO scale (1:76.2) is very popular -- perhaps the most popular -- in Britain but is almost unheard of elsewhere.
The NMRA web page I linked to does not, for some reason, list the "large" scales, from F (1:20.3) to H (1:32). These scales are commonly referred to as "outdoor" or "garden" railway scales because, although you can run them indoors, they are mostly used outdoors.
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