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model railway scale and gauges
It is important to understand the difference between gauge and scale.
A model trains "Scale" is the relationship between its size and the size of an actual train, usually measured as a ratio or as a millimetre to inch conversion. OO scale is said to be 4mm:ft or  1:76.

A model trains "Gauge" is the distance between the inner edges of the two rails.

Historically there are broadly two main groups:
"standard gauge" which is based on a 4ft 8 1/2in prototype, and there is also
"narrow gauge" which includes any railway with a track gauge less than "standard gauge".

The more popular scales and gauges are discussed below. This is not a definative list and there are some missing as they are not that popular in the UK.

2mm Scales.
N Gauge
2mm to 1ft, 1:148 scale in UK
9mm gauge (inside track width)
This gauge is half the size of 00 and therefore you should in theory be able to lay four times as much track. This is becoming a very popular gauge with a full range of locomotives, rolling stock and accessories available from many companies.

2mm Scale
2mm to 1ft, 1:152.3 scale
9.42mm gauge (inside track width)
The purists of N gauge developed this scale. It is slightly more accurate than the mainstream scale of 1:148.

3mm Scales.
TT Gauge
3mm to 1ft, 1:101.6 scale
12mm gauge (inside track width)
This gauge originated in the USA, and was also produced at 2.5mm to 1ft, 1:120 scale. Enthusiasts using this scale need specialist support through the Three Millimetre Society.

4mm scales.
HO Gauge
3.5mm to 1ft, 1:87 scale
16.5mm gauge (inside track width)
This is the major gauge used outside the UK. At 3.5mm to 1ft, the track gauge at 16.5mm is virtually exact to scale for the standard gauge. When using this gauge it must not be confused with 00 gauge, HO gauge is almost 15% smaller. One can run HO gauge rolling stock on 00 gauge layouts, the track gauges both being 16.5mm, but the difference in scale will immediately become very obvious.

00 Gauge
4mm to 1ft, 1:76 scale
16.5mm gauge (inside track width)
This is the most popular scale for British modellers and is probably the best supported in the industry with a wide range of ready-to-run models, kits and accessories.. However the track gauge is considered too narrow to be accurate by many. This makes this scale a bit of a compromise. Smaller track profiles make this incorrect scaling less noticeable, and increasing the sleeper spacings makes it even less noticeable.

EM Gauge
4mm to 1ft, 1:76 scale
18.2mm gauge (inside track width)
This scale is an attempt to make the 00 layout track gauge more realistic. At 18.2mm it still falls short of the ideal 18.83mm, but was felt by those involved to be near enough.

P4/S4 Gauge
4mm to 1ft, 1:76 scale
18.83mm gauge (inside track width)
As EM is still slightly under scale, P4 was established. Locomotive and rolling stock kits are available to fit this gauge.

009 Gauge
4mm to 1ft, 1:76 scale
9.00mm gauge (inside track width)
The most popular narrow gauge scale as this allows for the use of N gauge chassis and most 4mm accessories. Track and turnouts are available from a wide range of manufacturers.

00n3 Gauge
4mm to 1ft, 1:76 scale
12mm gauge (inside track width)
Used for models of the Isle of Man railways and the Irish 3ft gauge systems.

7mm Scales
0 Gauge
7mm to 1ft, 1:43.5 scale
32mm gauge (inside track width)
This scale has become more popular due to the availability of a large range of quality locomotive and rolling stock kits. Technically the inside track width of 32mm is 3% under scale.

7mm to 1ft, 1:45 scale
32mm gauge (inside track width)
Scale used mainly in Germany, Japan, Russia, Czech

7mm to 1ft, 1:48 scale
32mm gauge (inside track width)
This scale is commonly found in the USA.

Scale Seven
7mm to 1ft, 1:43.5 scale
33mm gauge (inside track width)
This is the scale track option for 7mm scale with a 33mm width between tracks.

0-16.5 Gauge
7mm to 1ft, 1:43.5 scale
Uses OO gauge spaced track allowing commercial OO gauge locomotive chassis to be used under narrow gauge 7mm kit.

Larger scales
Gauge 1
10mm to 1ft 1:32 scale
45mm gauge (inside track width)
This scale is mainly used outside for electric and live steam operation.

Re-size chart

Several of our customers have asked us how to resize our scale models using either a copier or printer. Use this table to give the appropriate enlarge or reduce to re scale the drawing.

  G Scale O Scale S Scale OO Scale HO Scale TT Scale N Scale Z Scale
G Scale --- 213% 284% 339% 386% 533% 711% 977%
O Scale 47% --- 133% 158% 181% 250% 333% 458%
S Scale 35% 75% --- 119% 136% 188% 250% 344%
OO Scale 30% 63% 84% --- 115% 158% 211% 289%
HO Scale 26% 55% 73% 87% --- 138% 184% 253%
TT Scale 19% 40% 53% 63% 73% --- 133% 183%
N Scale 14% 30% 40% 48% 54% 75% --- 138%
Z Scale 10% 22% 29% 35% 40% 55% 73% ---
Find your scale in the table along the top, then scroll down to the desired scale and find out the factor you need to enlarge or reduce. So, if, say, I have HO scale plans I want to enlarge to O scale, I run across the top to HO, then down to O scale, and see that I need to enlarge the plans to 181%. If I have O scale plans I want to reduce to S scale, I run across the top to O and down to S, and see I need to reduce the plans to 75%.

Thickness chart
We found this handy table that gives the actual dimensions of thicknesses of different sheets sizes. Plastic sheets and extrusions are generally measured in THOU so this conversion chart gives metric and imperial real thicknesses of those sheets.

It would be nice to include 3mm and 3.5mm into this chart but my maths head is broken. If anyone can fill in the missing scales that would be great.
Material Thickness Prototype Dimensions
Thou Actual Inches Actual mm Inches 2mm Inches 4mm Inches 7mm
5 0.005 0.127 1 1/2 1/4
10 0.010 0.254 1 1/2 3/4 1/2
15 0.015 0.381 2 1 5/8
20 0.020 0.508 3 1 1/2 3/4
25 0.025 0.635 4 2 1
30 0.030 0.762 5 2 1/4 1 1/2
40 0.040 1.1016 6 3 1 3/4
50 0.050 1.27 8 4 2
60 0.060 1.524 9 4 1/2 2 1/2
70 0.070 1.778 11 5 1/2 3
80 0.080 2.03 12 6 3 1/2
90 0.090 2.286 14 7 4
100 0.100 2.54 15 8 4 1/2