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A 'scale factor' is a number which scales, or multiplies, some quantity. In the equation
$y=Cx$,
$C$ 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.

Contents

Applications

Computer Science

Geometry

See also

Applications

There is also a scale factor for the expansion of the Universe

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).

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.

See also

★ Scale (ratio)

★ Scale (map)

★ Scales of scale models

★ Scale (disambiguation)

★ Scaling (geometry)

★ Scalar (mathematics)

★

★ Scale Factor