Rectangle Scale Factor Calculator

Calculate the scale factor between two rectangles, area ratio, and check if they are proportional.

Enter Both Rectangles

Original Rectangle
Scaled Rectangle

Result

Scale Factor (k)
--
Original dimensions--
Scaled dimensions--
Scale factor (length)--
Scale factor (width)--
Proportional?--
Original area--
Scaled area--
Area ratio (k^2)--

Step-by-Step Solution

k = scaled / original, Area ratio = k^2

Understanding Scale Factors

A scale factor is the ratio of corresponding lengths of two similar figures. When a rectangle is scaled by a factor of k, each linear dimension is multiplied by k. The area, however, is multiplied by k squared (k^2), because area is a two-dimensional measurement.

Linear Scale Factor

The ratio of corresponding sides.

k = scaled length / original length

Area Scale Factor

The square of the linear scale factor.

Area ratio = k^2

Proportionality Check

Both dimension ratios must be equal for true scaling.

L2/L1 = W2/W1 (proportional)

Checking Proportionality

Two rectangles are proportional (similar) if and only if the ratio of their lengths equals the ratio of their widths. If these ratios differ, the rectangles have different aspect ratios and one is not simply a scaled version of the other.

Scale Factor Types

  • k > 1: Enlargement - the scaled rectangle is larger than the original.
  • k = 1: Congruent - both rectangles are the same size.
  • 0 < k < 1: Reduction - the scaled rectangle is smaller than the original.

Applications

Scale factors are used in architecture (blueprints), mapmaking, model building, photography (print enlargements), manufacturing, and computer graphics. Understanding how scaling affects both linear dimensions and area is crucial for accurate planning and design work.