Rectangle Scale Factor Calculator
Find the linear scale factor and area scale factor between two rectangles. Free online rectangle scale factor calculator for geometry, design, and proportional scaling.
Original Rectangle
Scaled Rectangle
About This Calculator
The Rectangle Scale Factor Calculator helps you find the linear scale factor and area scale factor between two rectangles. Enter the width and length of the original rectangle and the scaled (new) rectangle to instantly compute the scale factors. This tool is essential for geometry students, architects, designers, and anyone working with scaled rectangular shapes.
The linear scale factor is calculated as the ratio of the new dimension to the original dimension: scale factor = new width / original width = new length / original length. When both ratios are equal, the rectangles are similar (proportional). The area scale factor equals the square of the linear scale factor: new area = original area x (linear scale factor)^2.
For example, if the original rectangle is 5 m x 10 m and the scaled rectangle is 15 m x 30 m, the linear scale factor is 3 (each dimension is multiplied by 3), and the area scale factor is 9 (the area grows from 50 m^2 to 450 m^2).
Applications
- Architecture & Construction: Scale building floor plans, room dimensions, and material quantities proportionally.
- Design & Graphics: Resize rectangular elements such as photos, banners, and layouts while maintaining proportions.
- Education: Understand similarity, scale factors, and proportional reasoning in geometry classes.
- Manufacturing: Scale up or down rectangular parts and components for production and prototyping.
Regional Notes
This calculator works with any unit system (metric or imperial) as long as the original and new dimensions use the same units. The scale factor itself is dimensionless and independent of the unit system, making it equally useful for users in India (cm/m), the United States (in/ft), and the United Kingdom (cm/m).
Frequently Asked Questions
What is a scale factor for a rectangle?
A scale factor is the number you multiply each dimension of a rectangle by to get a larger or smaller similar rectangle. For example, a scale factor of 2 doubles both the width and length.
How do I calculate the linear scale factor of a rectangle?
Divide the new width by the original width, or the new length by the original length. Linear scale factor = new dimension / original dimension. Both ratios should match for a properly scaled rectangle.
What is the area scale factor?
The area scale factor is the square of the linear scale factor. If the linear scale factor is 3, the area scale factor is 9, meaning the area grows 9 times. It can also be calculated as new area divided by original area.
How do I know if two rectangles are proportional?
Two rectangles are proportional (similar) when the ratio of new width to original width equals the ratio of new length to original length. This calculator checks both ratios and alerts you if they differ.
What does a scale factor of 2 mean for a rectangle?
A scale factor of 2 means every dimension is multiplied by 2. A rectangle scaled by 2 has its width and length doubled, and its area quadrupled (multiplied by 2^2 = 4).
Can the scale factor be less than 1?
Yes, a scale factor less than 1 (e.g., 0.5) means the new rectangle is smaller than the original. A scale factor of 0.5 halves each dimension and the area becomes one-quarter of the original.
What happens if the width and length scale factors are different?
If the width ratio and length ratio are not equal, the rectangles are not similar -- the shape is distorted rather than uniformly scaled. This calculator shows both ratios so you can check proportionality.
Is this calculator free to use?
Yes, all calculators on Calculy are completely free to use with unlimited calculations and no registration required.