Suppose you have two similar figures, one larger than the other. The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure.
Example:
Here,
. So, the scale factor is 4.
Note that when a two-dimensional figure is enlarged (dilated) by a scale factor of k, the area of the figure is changed by a factor of k2, and the volume is changed by a factor of k3.