Rectangle Scale Factor Calculator

When you scale a rectangle by a linear scale factor (let's call it k), every linear dimension—such as length and width—is multiplied directly by that factor. The fundamental equations governing this relationship are:

New Length = k × Old Length

New Width = k × Old Width

However, scaling a two-dimensional area works differently because both dimensions expand simultaneously. The area scale factor is always the square of the linear scale factor (k²), meaning the new area is calculated as:

New Area = k² × Old Area

Imagine you have a rectangular garden bed that measures 4 meters long by 2 meters wide. You want to enlarge the entire garden using a linear scale factor of 1.5. Here is how you calculate the new dimensions and the new total area:

Step 1: Find the old area.
Old Area = 4 m × 2 m = 8 square meters.

Step 2: Calculate the new length and width.
New Length = 1.5 × 4 m = 6 meters.
New Width = 1.5 × 2 m = 3 meters.

Step 3: Calculate the new area.
You can multiply the new dimensions (6 m × 3 m = 18 sq m), or use the area scale factor. The linear scale factor squared is 1.5² = 2.25. Multiplying the old area by this factor gives: 2.25 × 8 = 18 square meters.

1. Watch out for area units: Remember that if your linear dimensions are in meters, your area will be in square meters. When scaling, the area increases quadratically, not linearly—a common trap for beginners.

2. Verify with cross-multiplication: When dealing with similar rectangles, the ratio of the new side to the old side must always remain constant across both length and width.