To convert a measurement from a scale drawing to its actual size, you need to multiply the measurement from the drawing by the scale factor.

A scale drawing is a proportional representation of an object or area, either smaller or larger than its actual dimensions. The scale factor is the ratio that relates the dimensions of the drawing to the corresponding dimensions in reality. For example, a scale of $1:50$ indicates that $1$ unit on the drawing corresponds to $50$ units in real life.

To perform the conversion, the first step is to identify the scale factor. If the scale is presented as a ratio (like $1:50$), the scale factor is simply $50$. If the scale is expressed in a different format, such as $1 \text{ cm} = 2 \text{ m}$, you must convert the units to a consistent type before determining the scale factor. In this case, $1 \text{ cm}$ on the drawing translates to $200 \text{ cm}$ (or $2 \text{ m}$) in reality, giving a scale factor of $200$.

Once you have established the scale factor, you can convert the drawing measurement to the actual size by multiplying it by the scale factor. For example, if a length on the drawing measures $3 \text{ cm}$ and the scale factor is $50$, the actual length can be calculated as follows:

This is equivalent to $1.5$ meters.

It’s crucial to keep track of your units and convert them as needed to ensure accuracy. This method enables you to accurately determine the real-world dimensions from a scaled representation.