In North America and most of Europe, “N-scale” means 1:160 scale (one real inch equates to 160 scale inches, or 13’ 4”). In Britain, it means 1:148 scale (Britain also has “2mm finescale”, which is 1:152). But in Japan, it can mean either 1:150 or 1:160 scale.
All of these (except 2mm finescale) use N-gauge track, with rails 9 mm apart. In fact, the “N” comes from the word for “nine” in several of the languages in which small-scale trains were first created (Brittish “nine” from 1:160 OOO-gauge, originally 8mm and later 9mm; German “neun” from Arnold, the original N-scale, and probably French “neuf” as MOROP standards are bilingual in French and German). (note: gauge refers to rail spacing of track, scale refers to relative dimensions of models to the prototype).
At that spacing, a scale of 1:160 represents standard gauge (1,435 mm) track, so American/European N and Japanese Shinkansen N are the only scales that are really “correct”. To represent the typical Japanese gauge (a.k.a., Cape gauge) of 3’ 6” (1,067 mm) on 9mm track, 1:119 scale would be needed. The latter was a bit too extreme apparently, as Japanese manufacturers seem to have settled on using 1:160 for Shinkansen (which use standard gauge track), and 1:150 scale for most other trains, both ordinary narrow gauge and some of the lines that use other gauges. In this scale, nine millimeters works out to 4’ 5” (1,350 mm), so it’s not a very accurate representation of narrow gauge track, and why they even bothered if it wasn’t going to be close is a mystery to me.
The Keiyo railway, and some others, use a gauge of 4’ 6” (1,372 mm), reportedly because this was (and still is) a gauge used by tram railways (streetcars) in Tōkyō (and also used in Hakodate), with which at one time they interoperated. This may explain the selection of 1/150 scale in Japan as originating in models of trams. This gauge (full size) was first used in Scotland, and is thus sometimes known as Scotch gauge. It doesn’t appear to have come to Japan from Scotland, but rather from British and European consultants hired by the Japanese to build their first railroad. However a Scottish merchant, Thomas Blake Glover (who incidentally was a supporter of the rebellion that toppled the Shogunate and brought in the Meiji government), brought the first steam locomotive to Japan, at the trade port of Nagasaki, where his offices were, and demonstrated it. It’s not clear what gauge this was, but much of what was exported to British colonies was Cape Gauge, so it’s possible it was too.
But there you have it, right out of the gate, measurements in Japanese modeling are going to be approximate. The models comes in two scales, and except for Shinkansen none of them match the spacing of the tracks they use. If you’re a “rivet counter” who has to have every detail correct, Japanese N-Scale will quickly drive you to drink.
Since I’m modeling primarily commuter trains, which use narrow gauge and are built to 1:150 scale, I’m going to use that ratio in any size calculations, and when I say “N-scale” elsewhere on this site, that’s the ratio I mean unless I’m specifically talking about a Shinkansen model. But that won’t stop me from running Shinkansen trains or using 1:160-sized buildings, people, cars or other objects. Many of those are only approximately 1:160 anyway.
Note: while I don’t model Japanese HO, it should be noted that they use “HO”, which normally means 1:87 (3.5mm to the foot), to mean 1:80 scale or 3.8mm/foot (most of the time, anyway; I’ve seen 1:87 scale Japanese models too). Standard 16.5mm HO-gauge track is still used. In this case, the British also have a difference scale, but they used a different name: “OO” scale is 1:76.2 scale (4mm to the foot) but uses HO-gauge track (which isn’t exactly “standard gauge” in that scale).
Apparently some older steam locomotives by both Micro Ace and Kato were done in 1:140 scale, or even 1:130. See (thread no longer available) on the JNS Forum for further info.