Scale Factor
(KS3, Year 7)

The Lesson

A scale factor is used to describe an enlargement. A scale factor describes how much larger (or smaller) the enlarged shape is compared to the original shape.

Dictionary Definition

The Oxford English Dictionary defines a scale factor as "a numerical factor by which each of a set of quantities is multiplied."

Understanding a Scale Factor

When a shape is enlarged, the length of each side becomes larger (or smaller). Each side becomes larger (or smaller) by same amount. The length of each side is multiplied by a scale factor.

A Real Example of a Scale Factor

A scale factor is easier to understand with an example. The image below shows a light blue shape being enlarged to a dark blue shape.

The scale factor is 2. Each side of the dark blue shape is 2 × longer than the corresponding side of the light blue shape.

Types of Scale Factors

Scale factors have different effects depending on how large the number is.
Scale Factor Description
Greater than 1 The shape gets larger
Equal to 1 The shape stays the same size
Greater than 0, less than 1 The shape gets smaller
Negative The shape is on the other side of the center of enlargement, and is the other way around

What Is an Enlargement?

An enlargement resizes a shape. An enlargement makes a shape larger or smaller. An enlargement is a type of transformation.

Scaling Lengths, Areas and Volumes

If a scale factor is k:
  • Each length on the image will be k times the length of the object.

  • The area of the image will be k2 times the area of the object.

  • The volume of the image will be k3 times the volume of the object.

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See Also

What is an enlargement? What are transformations?