Rectangle Scale Factor Calculator

Created by Steven Wooding
Reviewed by Vishnuvardhan Shakthibala
Last updated: Sep 29, 2022

Use this rectangle scale factor calculator to find the linear and area scale factors between two rectangles. In this short article, we will present:

  • What does scale factor mean?
  • How to calculate the scale factor of a rectangle; and
  • Scale factor formula.

What does scale factor mean?

A scale factor means that you multiple each dimension of an object by the same value. This operation means that you only change the size of the thing and not its shape. For example, changing only the height of a building is not applying a scale factor; you would also need to change the width and length.

How to calculator the scale factor of a rectangle – Scale factor formula

In the case of a rectangular, there are two dimensions that need to be multiplied by the same number to apply a scale factor; its length and width. We can write down the following two formulas for each dimension:

new width = scale factor × current width

new length = scale factor × current length

So we can find the scale factor by either looking at the change in the width or the length of the current and new rectangles:

scale factor = new width/current width

scale factor = new length/current length

These are two examples of scale factor formulas.

If we are given the dimensions of the current rectangle and one of the dimensions of the new rectangle (e.g., the new width), we can use substitution to derive an equation for the new length:

new length = (new width/current width) × current length

Another option is to scale with the area of a rectangle. The formula for that is:

new area = area scale factor × current area

The area scale factor is the square of the linear scale factor. The rectangle scale factor calculator also supports calculating the area scale factor.

How to use the rectangle scale factor

The calculator is very flexible and offers several ways you can use it. Let's say we have a rectangle of width 5 m and length of 10 m, and we know the scaled rectangle has a width of 15 m. Our calculator can help in the finding of the scale factor:

  1. Enter 5 and 10 in the width and length input fields in the current rectangle section of the calculator, respectively. The area is then also calculated.
  2. Input 15 into the width field of the new rectangle.
  3. The calculator then gives you the new length (30) and the linear scale factor between the two rectangles (3).
  4. It also gives you the area of the new rectangle and the area scale factor.

Alternatively, if you know the value of the linear scale factor, start by typing that in and the dimensions of the current rectangle. Then you will be rewarded with the dimensions of the linearly scaled rectangle.

FAQ

How to write a scale factor?

When specifying the scale factor of building blueprints or model vehicles, you write 1 followed by a semicolon and then the scale factor. For example, if a model car says it is a 1:10 scale model, then the linear scale factor for all three dimensions is 10.

What is a scale factor of 2?

A scale factor of 2 means that every measurement is multiplied by 2 in each dimension. For example, a rectangle scaled by a factor of 2 has its width and length multiplied by 2.

Steven Wooding
Current rectangle size
Width
ft
Length
ft
Area
ft²
New rectangle size
Width
ft
Length
ft
Area
ft²
Scale factors
Linear scale factor
Area scale factor
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