Rectangle Scale Factor Calculator

Enter a rectangle's original length and width plus a scale factor k to find the new dimensions, perimeter, and area (New Side = k × Original Side, New Area = k² × Original Area).

Quick Facts

Linear scale factor
New side = k × original side
Every length and width is multiplied by the same factor k for a similar rectangle.
Area scale factor
New area = k² × original area
Area scales by the square of k, since both length and width are multiplied by k.
Perimeter scale factor
New perimeter = k × original perimeter
Perimeter is a linear measurement, so it scales the same way length does.

Your Results

Calculated
New Length
-
k × original length
New Width
-
k × original width
New Area
-
k² × original area
New Perimeter
-
k × original perimeter

Ready

Enter the original dimensions and a scale factor, then press Calculate.

Formula and Method for Rectangle Scale Factor

A scale factor k describes how much larger or smaller a rectangle becomes when every linear dimension is multiplied by the same number. If a rectangle has an original length L and width W, a similar (proportional) rectangle scaled by factor k has a new length of k × L and a new width of k × W. Because both dimensions are multiplied by k, the new area is multiplied by k², while the new perimeter — a sum of linear measurements — is multiplied by k, just like the sides.

How the calculation works

Enter the original length and width, choose a unit, and enter the scale factor k. The calculator multiplies each side by k to get the new length and new width, adds them and doubles the sum to get the new perimeter (P = 2(L+W)), and multiplies the new length by the new width to get the new area. A factor greater than 1 enlarges the rectangle; a factor between 0 and 1 shrinks it; a factor of exactly 1 leaves it unchanged. If you instead know the dimensions of two similar rectangles and need the scale factor itself, divide corresponding sides: k = new length ÷ original length = new width ÷ original width.

Common mistakes

  • Applying k to area directly: multiplying the original area by k (instead of k²) understates how much a rectangle grows — area always scales by the square of the linear scale factor.
  • Scaling only one side: for the result to be a true similar rectangle, both length and width must be multiplied by the same factor k; scaling them differently changes the shape, not just the size.
  • Mixing units: keep length, width, and any comparison dimensions in the same unit before computing a scale factor — feet mixed with inches will give a meaningless ratio.

Real-world applications

  • Scaling architectural or engineering drawings and floor plans up or down while keeping proportions accurate
  • Enlarging or shrinking a photo, map, or diagram print size while preserving its aspect ratio
  • Resizing a garden bed, rug, or table footprint to a new proportional size
  • Model-making and prototyping, where a scale factor like 1:24 or 1:48 converts full-size dimensions to model dimensions

Frequently Asked Questions

What is a scale factor for a rectangle?
A scale factor k is the number you multiply every linear dimension of a rectangle by to produce a similar (proportional) rectangle: New Length = k × Original Length and New Width = k × Original Width. A factor greater than 1 enlarges the rectangle; a factor between 0 and 1 shrinks it.
How does area change when you scale a rectangle?
Area scales by the square of the scale factor: New Area = k² × Original Area. This happens because both length and width are each multiplied by k, so the product (area) is multiplied by k × k = k². Doubling the scale factor (k = 2) quadruples the area.
How do I find the scale factor between two rectangles?
Divide corresponding sides of the new rectangle by the original rectangle: k = New Length ÷ Original Length = New Width ÷ Original Width. For the rectangles to be truly similar (proportional), both divisions must give the same value.
Does perimeter scale the same way as area?
No. Perimeter scales linearly by k, the same as length and width, because it is a sum of linear measurements: New Perimeter = k × Original Perimeter. Only area (and other two-dimensional measurements) scale by k².

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