Scale factor

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A scale factor is a number which scales, or multiplies, some quantity. In the equation $y = C x$ , $C$ is the scale factor for $x$ . $C$ is also the coefficient of $x$ , and may be called the constant of proportionality of $y$ to $x$ . For example, doubling distances corresponds to a scale factor of 2 for distance.

[edit] Computer Science

Scale factors are used in computer science when certain real world numbers need to be represented on a different scale in order to fit a required number format. See Scale Factor (Computer Science).

[edit] Geometry

A factor can be used to scale shapes in 1, 2, or 3 dimensions (and conceptually even more.) There are a few interesting properties of scaling which are relevant:

The length of a line that is scaled is the previous length times the scale factor. In other words:

$L_1 = L_0 \cdot c$ .

The area of a shape in two-space (a circle, for example) is equal to the previous area times the square of the scale factor. In other words:

$A_1 = A_0 \cdot c^2$ .

The volume of a shape in three-space is equal to the cube of the scale factor times the initial volume. In other words:

$V_1 = V_0 \cdot c^3$ .

The scale factor also scales the coordinates of the centroid of a shape.
The inverse of scaling a shape is scaling it again, with the reciprocal of the first factor.