Talk: Railroad modelling scales
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Reference to a posting on trains.com
O scale/gauge has an interesting history. If you divide 1-1/4" gauge and 4' 8-1/2" standard gauge, you get 1:45 scale, or 17/64" = 1 foot. A few people did model in that in the early days of the hobby, most notably Minton Cronkhite. It was sometimes called "Q scale".
Otherwise, everyone else chose something simpler. In Britain and Europe, where metric measuring was better known, the went to 7mm = 1 ft., or 1:43.55 scale. That's why there's so many European made automobile models in 1:43 scale. In the US, we went with 1/4" = 1 ft., or 1:48 scale. So our US "O scale" trains are slightly undersized compared to the track, and in Europe they have the opposite problem.
BTW since HO ("Half O") started in Europe, HO scale became half of European O scale's 1:43.55 ratio, so is 1:87.1, or 3.5mm = 1 ft. In the UK as mentioned, the smallest motors available wouldn't fit in UK-style engines, so they used 4mm = 1 ft or "OO" scale, still running on HO gauge track.
I believe 2mm = 1 ft, sometimes called "OOO scale", is half of British OO and runs on N gauge track, resulting again in slightly oversized trains for the track (I think OOO is 1:148, correct N scale is 1:160).