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Converting Model Railroad Scales

Feb 21, 2008
Prototyping is the word used to describe the use of scaling real-life objects down and typically for Model Railroading different names are given to differing 'scales' to represent the percentage of the original. For instance the 'HO' scale means 3.5mm represents 1 foot, with a ratio of 1:87.086 ... needless to say this can get difficult.

Fortunately you rarely need to convert between scales that are already set " but what about when you want to figure out what the scale conversion of an existing object or building should be to fit into your diorama? That's when you remember your third-grade math teacher who told you there'd be days like this.

First be aware of the measure of scale being used: is it the percentage or a millimeter (mm) scale? With the ratio the right-most number shows how many units (normally in inches or centimeters) on the original are equal to one unit on the replica so a 1:200 scale means that if the miniature is 1 tall then the original was 200 or 16.67 feet tall. If the scale simply lists a height such as 25mm or 54mm as is common with many figurines then they are referring to the # of mm to a certain height and an assumed ratio has been made based on the original's size.

In theory to convert a ratio scale into a 'height' scale you first assume that the height scale is measuring to 'eye' height on the figure and that ratio scales measure to 'head' height and divide 1610 by the scale. For example a 1/285 figure comes out to approximately a 6 mm figure (1610 / 285 = 5.6) while a 1/64 scale is about 64.4 mm " this may help if you find figures online that would work in your diorama but don't know if the scale is the same.

So you are probably wondering where we got the '1610' from right? With figurines and deciding to use 'eye' height we assume a man's eyes average a height of 5'3 for a 5'8 tall man (the average human) and convert that to millimeters. If the height was specified to 'head' height we would have had a number of 1730, equivalent to the average 5'8 tall man.

You can also use tricks like this to determine scale from photos, as follows:

First you need to have at least ONE known measurement such as the eye or head height for the man we used above, and the photo must be full on either the front or side of the source. So long as these are given, the following can determine the scale you need to use to create or build a prototype:

Cut out and paste or print the photo onto an A4 sheet of paper adjusting so it fills half the A4 sheet so you are on an approximately 1/35'th scale. Since there are 25.4 mm per inch you can now calculate the known measurement (say 100 width) by 25.4 to get a known 2540 mm or 2.54 meters. This can now be multiplied by the 28.57 that represents the 1/35 scale giving 72.57mm which means at 1/35 scale the width is 72.57mm " you can now measure the photo with a ruler.

Let's say that you get 90 millimeters on the 'actual' photo " you can now divide the 90 by 72.57 to get the factor to divide by " in this case 1.24. You can now measure and just divide by 1.2 (approximately) to know the size to match a 1/35 scale ... using different size pages to adjust for differing scales can allow you to calculate most any ratio from any image so long as you know the scale of the printed paper size and at least one accurate measurement from the image in question.

It may seem like rocket science but it really isn't, and many resources and tools to help exist out there " but isn't figuring things like this out part of the fun? On the other hand I may just buy all my prototyping in a set scale ... I DID get a C- in geometry after all ...
About the Author
Remember that the scale of your railroad is also important when choosing your model train scenery. Find out more about building and running your model railway at The Model Railroader
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