A scale factor is a ratio of one measure to another. It can have any useful units, including none at all. In high school geometry, the term scale factor is used to express the ratio of the linear dimensions of geometric figures.

__Examples__A square is 1 ft on a side. Another square is 18 inches on a side. The scale factor relating the first square to the second is 1 ft:18 inches. If the units are made identical, they can cancel and the scale factor becomes unit-less. 12 inches:18 inches = 12:18 = 2:3 That is, the first square has linear dimensions that are 2/3 of those of the other square. You may have seen maps with a scale factor 1 in = 18 miles, or some such. If miles are turned to inches, this can be changed to a unit-less scale factor 1:1,140,480. The USGS published topographic maps with a scale factor of 1:24000, which is 2.64 in = 1 mile In model railroading, HO scale is a popular scale. That scale is 3.5 mm = 1 ft, about 1:87.086. Computations of Body Mass Index (BMI) are defined in terms of metric units. When English units (inches, pounds) are used, a scale factor must be introduced into the formula. That scale factor (≈703) collects all the unit conversion constants into one number. It has units of (in^2)(kg)/((lb)(m^2)) and is exactly equal to (0.45359237)/(.0254^2) As in these examples, a scale factor can be determined by measurement, by the problem statement, or it can be determined by common usage or by definition. Map scales are often determined by what will conveniently fit on a printed page. To find a scale factor in a geometry problem, identify corresponding linear measures, and find their ratio. Note that area measures are related by the square of the scale factor, and volume measures are related by the cube of the scale factor.