Rectangle Scale Factor Calculator
Calculate linear and area scale factors between rectangles with step-by-step solutions
Calculate Rectangle Scale Factor
Choose whether to calculate scale factor from dimensions or apply a known scale factor
Current Rectangle
Width of the original rectangle
Length of the original rectangle
New Rectangle
Calculated from new length
Length of the scaled rectangle
Current: 0 × 0
Results
Enter rectangle dimensions to calculate scale factors
Please enter positive values for current rectangle dimensions.
Example Calculations
Example 1: Double Size
Original: 5 × 10
Scale Factor: 2
New Size: 10 × 20
Area Factor: 4 (2²)
Example 2: Half Size
Original: 8 × 12
Scale Factor: 0.5
New Size: 4 × 6
Area Factor: 0.25 (0.5²)
Example 3: From New Width
Original: 3 × 7
New Width: 9
Scale Factor: 3 (9/3)
New Length: 21 (7×3)
Example 4: Model Scale
Original: 100 × 50 m
Scale Factor: 1/10 (0.1)
Model Size: 10 × 5 m
Ratio: 1:10
Scale Factor Guide
Linear Scale Factor
Multiplies each dimension by same value
Area Scale Factor
Square of linear scale factor
Scale > 1
Enlargement (bigger rectangle)
Scale < 1
Reduction (smaller rectangle)
Key Formulas
Scale Factor = New Dimension ÷ Original Dimension
New Dimension = Original × Scale Factor
Area Scale Factor = (Linear Scale Factor)²
New Area = Original Area × Area Scale Factor
Scale Factor maintains shape proportions
Understanding Rectangle Scale Factors
What is a Scale Factor?
A scale factor is a number that multiplies each dimension of a shape by the same value. When scaling a rectangle, both the width and length are multiplied by the same scale factor, which preserves the shape while changing the size.
Types of Scaling
- Enlargement: Scale factor > 1 (makes rectangle larger)
- Reduction: Scale factor < 1 (makes rectangle smaller)
- No change: Scale factor = 1 (same size)
- Area scaling: Area multiplied by (scale factor)²
Practical Applications
Architecture
Blueprints, floor plans, building models
Engineering
Technical drawings, prototypes, scaled models
Design
Graphics, layouts, proportional sizing
Manufacturing
Product scaling, material calculations
Scale Factor Properties
Linear Scaling
Each dimension multiplied by same factor
Area Scaling
Area multiplied by square of linear scale factor
Shape Preservation
Rectangle remains a rectangle after scaling
Proportional
Ratios between dimensions remain constant