# Scale model

A scale model is a model of an actual object that is different in size. Usually, a scale model is smaller than the object it is modeled after. However, many types of scale models exist, and a scale model can also represent a smaller object, such as a scale model of a cell. Scale models are used throughout many different fields including architecture, engineering, hobby models, and more.

The photo shown below is a scale model of the original Stourbridge Lion, the first locomotive steam engine operated in the United States. Model sizes differ, but such a model may have a scale of 1:50. This means that any measurement on the model, such as a length of 10 cm, is 50 times smaller than the real object. A 10 cm measurement on the model would therefore be 500 cm, or 5 m.

## How to find the scale

It can be useful to know how to find the scale of some object. Assuming that the scale model and object are proportional, we only need to know one measurement of the actual object to be able to determine the scale of the model.

1. Identify one dimension of the actual object (such as its width).
2. Identify (or measure) that same dimension on the scale model (convert units as necessary).
3. Divide the dimension of the actual object by that of the scale model.
4. Take the reciprocal of the result, then write the resulting fraction as a ratio.

Example

The length of a football field is 100 yards. What is the scale of a model that has a length of 180 inches?

Since we are given the measurements, we do not need to measure the model. We just need to ensure that the units are the same, then divide the actual length by the length of the model. There are 36 inches in 1 yard, so:

180 ÷ 36 = 5

Therefore, 180 inches is equal to 5 yards. Next, divide the actual length by the model's length:

100 ÷ 5 = 20

The reciprocal of 20 is 1/20. Written in the form of a ratio, this is 1:20. Therefore, the scale of the model is 1:20.