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.
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 k^{2} times the area of the object.

The volume of the image will be k^{3} times the volume of the object.