## Math, Science, Randomness: The Origins of Model Scales

One of the key attributes of collectible vehicles is the scale in which they are reproduced. Most collectors know about 1/64 scale cars, such as Hot Wheels, as well as other popular sizes such as 1/18 and 1/43. But have you ever thought about HOW and WHY these particular model scales became the standards in their hobbies?

There are many reasons why model companies gravitate towards certain scales. As it turns out, a lot of scales are the result of simple math involving division by 2 or by 10. But several scales are the result of scaling down model trains, or more specifically the track they run on, which we’ll discuss in a moment.

So put on your thinking cap, get out your calculators, and let’s hop into the hobbyDB Shrink-O-Matic to discover the origins of the scales! *(All images are approximately to scale.)*

**1/1 through 1/6** – The scales in this range are simple ratios, easy to calculate. These are of course, large scales, so they’re usually reserved for real items that are not particularly big. Of course, there are some larger objects modeled at full size.

**1/8** – Hey, we skipped 1/7! It turns out you don’t get into a lot of prime numbers outside of single digits. Seven is hard to divide by. But 1/8 equals half of a half of a half, so the math is pretty easy. This scale has become popular in recent years for super detailed model car kits. 1/8 scale is often used for replicas of race car driver helmets as well as standalone models of engines.

**1/10** – Not that commonly used, but, the math is pretty easy when you multiply and divide by ten. Think metric!

**1/12** – Here, one inch equals one foot. This is very common in the world of action figures, as an “average” person of six feet tall scales down to six inches.

**1/16** – Not really used all that often, but it equals half of a half of a half of a half, so the math is pretty easy to convert.

**1/18** – This is a widely used scale for model vehicles, but has only been in use since about the mid 1970s. It translates to two thirds of an inch equalling one foot, which is a weird ratio. In this case, its origin likely lies in model cars measuring in at a pleasing size technically known as “big enough for lots of nice detail but not too big to fit on your shelf.”

**1/22.5** – Wait, what? Perhaps you recognize this as “G scale,” popular for large scale outdoor model railroad equipment. It’s based on a measurement of 1.75 inches between the rails, yielding a strange ratio. G scale is often mistakenly referred to as “LGB” or “Lawn-Garden-Basement” scale, which are common locations for such layouts. However, LGB is just a brand name that has nothing to do with those words.

**1/24** – This is a popular scale for model car kits, particularly in the U.S. But why? It’s pretty simple if you don’t live in the metric world… one half inch equals one foot at this size. Meanwhile, in other countries…

**1/25** – On the other hand, this is a popular scale for model kits everywhere else in the world, as it divides nicely into 100, which is great for the metric system.

**1/32** – This size shows up in cars meant as toys as well as some brands of model kits. Its use in toys probably comes from being small enough for little hands but not so small as to be a choking hazard. As with several scales we’ve visited before, the math is easy to calculate, equalling half of a half of a half of a half of a half.

**1/36**– This size shows up in cars meant as toys as well as some smaller model kits. Corgi popularized it as an alternative to smaller scales because it resulted in larger models without too much extra material, so it felt like a good value to the consumer. It’s also half of 1/18 scale, which may shed light on how that scale came to be.

**1/40** – A scale divisible by four and by ten would be ideal for metric and English, perhaps: It never really took off, so who knows? Diapet is one company that used this size.

**1/42** – Not familiar with this scale? It’s not really used that often. Tri-Ang, a British toy company settled on this size for their model trains and were consistent when adding model cars and trucks to their line. The standard railroad track measurement of 4-feet, 8.5 inches (don’t get me started on where that oddball measurement came from!) reduced to 33 millimeters, then rounded down slightly equals 1/42. For some reason, other companies settled on a different scale…

**1/43** – Honestly, this one’s a head scratcher. It’s one of the most-used scales for models of all kinds, but the ratio makes very little sense. It does come out to 7 millimeters per foot, but that’s a weird juxtaposition of measuring methods. The standard track measurement reduced to 33 millimeters, rounded UP slightly equals 1/43. Or close to it, anyway. Confusing? You bet. And having to multiply or divide by 43 all day will make your head hurt. Many theories suggest that 1/43 originated as a rounding error that went too far to fix. While popular for cars and trucks, this scale never really caught on for trains, and was eventually replaced by yet another scale, which is not too much smaller…

**1/48** – This is technically the exact definition of “O Scale,” the size popularized by **Lionel** trains among other brands. It rounds out to 1.25 inches between the rails, which makes some sense. And 1/48 works out to .25 inches per foot, which makes for some easy math. When we get to smaller ratios like this, the difference of a few points is hard to notice, which is why 1/43 cars go along with 1/48 trains and no one seems to complain. This is sometimes called “O27” scale (that’s a letter O, not a zero), meaning an O scale train capable of handing a 27 inch radius curve.

Fun fact: a **Lego Minifigure** is equal to about a 1/48 six foot tall person, so this scale plays nicely in Legoland, too.

**1/55 through 1/63** – You know what? we’ll come back to these seemingly random ratios in a minute. But first…

**1/64** – This scale serves so many purposes in the hobby world. In its earliest uses it became known as “S Scale,” or “Standard Scale,” the size of **American Flyer** brand trains. The distance between the rail is .875 inches, but more importantly, 1/64 is basically half of a half of a half of a half of a half of a half. Whew!

Of course, this is probably the most popular scale in the diecast world, representing most offerings from Hot Wheels, Matchbox, Johnny Lightning and countless other brands. But hold on a second… Many of these cars aren’t *really* 1/64. They’re all about 3 inches or 10 centimeters long. Even though the vast majority of them fall well above or below this exact scale, “1/64” it has become a convenient shorthand for vehicles around that size. So what gives? Well…

**1/55 through 1/63 and 1/65 through 1/80** – Back to those larger scales we skipped a moment ago, plus some smaller ones. Many cars called “1/64” size are really smaller or larger than that. The key is that the model companies often use the wheels as the basis for what size the model will actually be. A toy Mini Cooper model might use the same wheels as a Hummer H2 and therefore be about the same length, but their scales will be radically different. **Majorette** is one brand who puts the proper scale on the bottom of their cars, usually falling in the ranges listed here. **Tomica** is known for this practice as well. Which brings us to…

**3-Inch Scale** – The wide range of 1/64-ish vehicles we just discussed ultimately fall under this umbrella, all about three inches long. This could include anything from a 1/30 **scooter** to a 1/2,000 model of the **U.S.S. Enterprise**.

**1/72** – Popular for many military kits such as planes, tanks and helicopters where the more standard kit scales produce very large models. They don’t look too out of scale when placed on an HO scale model railroad. The ratio itself is kind of a mystery, but **Tri-Ang** used it for many trains and accessories, similar to the way they used the “almost but not quite” 1:42 scale.

**1/76** – Also known as OO, EM or P4 scales, this is a popular size in Europe. The exact origin of this number doesn’t relate to any particular ratio that makes sense mathematically. OO rails are 16.5 mm apart, which isn’t accurate to that ratio. Truth is, it’s a mishmash of a one scale of rail (the equivalent of HO, which you’ll see in a moment) and a slightly larger body. According to many sources, the larger body was to accommodate wind up clock mechanisms that were just a tad to big for smaller bodies back when this scale started. Got all that?

**1/87** – You probably recognize this as the most common scale for model trains in the world. 1/87 is better known as “HO scale,” an abbreviation for “Half of O scale.” But it’s not precisely half, it’s just sort of close. HO represents .625 inches between the rails. Technically, the ratio is 1/87.0857142, rounded to 1/87.1 if you want to be a tiny bit less precise. The names “HO” and “OO” are often used interchangeably or as “HO/OO” since their appearance is close and they use the same track.

**1/120** – Also known as TT Scale, this is popular in Russia. The ratio would be easy to divide by 12 or by 10, so it’s handy for English or Metric scales. TT stands for “Table Top,” by the way.

**1/148 – 1/160** – 1/160 is known as “N Scale,” or more accurately “N Gauge,” which sets the distance between the rails for a standard train at .375 inches. Confused? In model railroading, “gauge” refers only to the rails, while “scale” refers to the size of everything else. There’s some wiggle room in that some models might be built to slightly larger sizes (all the way up to 1/148), but regardless of the discrepancy, the rails and the wheels that run on them must be exactly 1/160.

While we’re on the subject of “N Gauge,” this track is sometimes used on HO scale railroads. See, in many steep, mountainous locations around the world, railroads were built with rails much closer together than the standard width. If you were to create a narrow gauge railroad in HO scale, it would conveniently use N-Gauge track but with the height of the rails (and everything else) in HO scale.

**1/220** – Also known as “Z Scale.” In this case, the track is .25 inches between the rails, which is tiny, about as tiny as a working electric train can be without needing a nanotechnolgy. As with the other train sizes, only the rail gauge is perfectly accurate, while many objects and details are slightly larger, especially the couplers that connect the rolling stock.

**1/400** and beyond- We’re getting into some really tiny scales now, best used to make manageable models of enormous objects like airplanes, ships and buildings. These scales simply take nice round numbers in multiples of 100.

**1/1,200 and 1/1,250** – Somewhere in the vast range of tiny scales we should mention these two. Both are used for models of large warships, the first being a traditionally British model scale, and the latter being German.

*There are many more scales of course, some of which are rarely used. If you know how any other scales came to be, let us know in the comments.*