We looked into the original model railroad track gauges and their relationship to full-sized standard gauge track gauge. NOW let’s see how those became the original model railroad imperial scales.
The original model railroad track gauges set by the Society of Model Railroad Engineers were not chosen at random. Nor were they based on simple inches. They were picked to match the imperial miniature scales already in use. They did however cheat. They used five feet as the full-sized standard gauge in order to avoid complicated fractions. Therefore 0 gauge was set as one and a quarter inches to match the existing imperial scale of 1/48 also known as quarter-inch scale. So if the standard gauge were 60 inches instead of the accurate 56 1/2 inches, 1 1/4 inches is accurate for 0, or 1/48 scale. See, simple. #1 gauge is set to 1 3/4 inches so that it becomes 60 inches in 1/32 scale. And so on…