Scale factors

A scale factor is a number which scales or multiples a quantity. They are used to create maps and other scale diagrams.

When things are too big to draw on paper, scale factors are used to calculate smaller, proportional measurements.

Floor plans for house designs are drawn on a smaller scale. This will help a designer to see if things will fit together well in each room of the house.

The scale of the floor plan is 1:100

The scale used on this plan means that every 1 cm on the page is 1 m in real life.

Converting using a scale factor

To convert from a scale drawing to real life, measure a line in the drawing and multiply it by the scale factor to find the real length.


If a floor plan shows a scale of 1 \:\text{cm} : 100 \:\text{cm} and the kitchen measures 4 cm long on the drawing, then the real kitchen size would be 4 \times 100 = 400 \:\text{cm} (or 4 m) long.

Kitchen plan

To convert from real life to a scale drawing, divide the real life measurement by the scale factor.


If a map is drawn using a scale factor where 2 cm represents 3.5 km and the distance between Manchester and Oldham is 8.5 km then what would the length of the drawing showing the same distance be?

The length on the drawing would be 2 \div 3.5 \times 8.5 = 4.9 \:\text{cm} (to 1 dp).

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