A model train's "scale" is the relationship between its size and the size of an actual train. "Gauge" is the distance between a track's rails. In model railroading, beginners sometimes use the terms “gauge” and “scale” interchangeably. Serious modelers are careful to use the terms correctly.
Popular Scales
Author's photo. (Click image to enlarge).
The most popular scales in model railroading are O, HO, N, and Z scale. The photo shows O, HO, and N scale locomotives next to a familiar object so you can get a feel for their actual sizes. The O scale locomotive (the largest), bearing number 8628 (enlarge the image to see this) is an Atlantic class steam locomotive made by Lionel. The HO scale diesel in the middle is a Union Pacific EMD GP40 from Bachmann. The smallest of the three, the N scale locomotive, is a Kato Santa Fe EMD F7 diesel, part of their Super Chief set.
Railroad Track Gauge
In North America, the space between the rails of a real-life "standard gauge" railroad track is 4 feet 8 inches (1,422.4 mm). The scale of HO trains is 1/87.1; so you would calculate standard gauge in HO scale by dividing 1,422.4mm by 87.1. Your result, 16.33mm, is very close to the 16.5mm adopted by model train manufacturers as HO gauge. This page lists the scales and gauges standardized by the National Model Railroad Association for modeling standard gauge railroads. In real-life railroading there were also narrow gauges; 3 feet being common in the United States. Modeling narrow gauges is done by a small, but growing segment of the model railroad community.O Scale - 1:48
Gauge: 1.25” (31.8mm)Marklin, the German toy manufacturer who originated O scale around 1900 chose the 1/48th proportion because it was the scale they used for making doll houses. In O scale 1/4 inch equals 1 foot. Interestingly, O scale was originally called Zero Scale, because it was a step down in size from 1 scale. From the 1920s until after World War II, O scale dominated the model train market. But as model trains became more affordable for the average person, the space required to set up the tracks became a major consideration in purchasing model railroad trains.
HO Scale 1:87.1
Gauge: 0.649” (16.5mm)The most popular scale worldwide*, HO (pronounced "aitch-oh") boasts the broadest range of products from the greatest number of manufacturers. In HO scale 3.5mm equals 1 foot. The designation HO stands for "Half O". Of course if it was actually one-half of O scale it would be 1/96th, but because HO is actually a metric based scale and O is based on English units of measure the fractions become awkward. The model railroading industry says HO is "approximately half O".
*Although HO is the most popular scale worldwide, the most popular scale in the UK is OO scale, which is covered later in this article.
S Scale - 1:64
Gauge: 0.884” (22.4mm)S scale trains were introduced to the model railroad market by A.C. Gilbert as American Flyer products in 1939. In S scale 3/16ths of an inch equals 1 foot. Though very few companies manufacture S scale trains today, the American Flyer brand still exists as Lionel product line.
TT Scale - 1:120
Gauge: 0.47”(12mm)Although invented in America after World War II, this scale is popular in Russia, eastern Germany, and other countries of the former Soviet Union. The use of 1/120th scale is common in engineering diagrams because it allows 1 inch to equal 10 feet. Though TT scale nicely fills the niche between HO and N scale, it hasn't received great acceptance outside of eastern Europe.
N Scale - 1:160
Gauge: 0.353” (8.97mm)The "N" is short for nine millimeter (although the actual gauge is 8.97mm). In N scale 2mm is approximately 1 foot. N scale is the second most popular scale worldwide. Many modelers select N scale as an alternative to HO scale because it allows more complex layouts to be built in the space available to them. Traditional thinking is that N scale trades detail for space. However, modern manufacturing and painting processes are producing N scale models with surprising levels of detail today.
Z Scale - 1:220
Gauge: 0.257” (6.52mm)Peior to 2008, Z scale was the smallest commercially available scale in model railroading. Z scale is popular with apartment dwellers and others with very limited layout space. Z scale is awkward mathematically, approximately 0.0545 inches to the foot, but that doesn't hurt its popularity. Z scale is the fastest growing scale in model railroading today. Some Z scale manufacturers offer briefcase layouts; entire track layouts with landscape, buildings, and a power supply all in a briefcase. These are high-end executive toys that sell for around $1,000.
OO Scale - 1:76.2
Gauge: 0.649” (16.5mm)In OO scale 4mm equals 1 foot. This metric based scale is the most popular scale in the United Kingdom. The British firm Hornby is the largest manufacturer of OO scale trains.
G Scale - 1:22.5
Gauge: 1.75” (45mm)G, or "garden”, is the largest common consumer scale. In G scale 1 foot is approximately 1/2 inch. G scale was introduced by LGB in 1968. Today LGB G Scale trains are manufactured by Marklin. The original G Scale trains were narrow gauge prototypes, and shared the same gauge track with 1 Scale. However, today there is a tendency on the part of some "G Scalers" to refer to any train that runs on 1 Gauge track as G scale. This adds further confusion to the market most accurately referred to as "Large Scale". Because of their large size, G scale trains are frequently used outdoors and often referred to as "Garden Scale". However, Lionel makes a very nice animated G scale Christmas set to circle the base of Christmas trees.