A scale factor is a number which scales 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.

Scale factor is how many times the smaller figures line segments go into the bigger figures line segments.

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 scale 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:

$L\_1\; =\; L\_0\; \backslash cdot\; c$.

• 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:

$A\_1\; =\; A\_0\; \backslash cdot\; c^2$.

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

$V\_1\; =\; V\_0\; \backslash cdot\; c^3$.

• 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)

Elementary mathematics

Czynnik skali