Scale Factor Calculator
Find or apply scale factors for similar figures
Enter Corresponding Measurements
Scale Factor Formula
k = scaled / original
Scale Factor Relationships
Understanding Scale Factors
A scale factor is the ratio between corresponding measurements of similar figures. It tells you how much larger or smaller one figure is compared to another.
Scale Factor Relationships
| Dimension | Factor | Example (k=2) |
|---|---|---|
| Linear (length, perimeter) | k | 2× longer |
| Area (surface area) | k² | 4× larger |
| Volume (capacity) | k³ | 8× larger |
Types of Scaling
- Enlargement (k > 1): The scaled figure is larger than the original
- Reduction (k < 1): The scaled figure is smaller than the original
- Congruent (k = 1): The figures are the same size
Frequently Asked Questions
What is a scale factor?
A scale factor is the ratio of corresponding lengths in similar figures. It tells you how many times larger or smaller one figure is compared to another.
Why does area scale as k²?
Area is length × width. If both dimensions scale by k, the area scales by k × k = k². This is why a figure twice as large has four times the area.
Why does volume scale as k³?
Volume is length × width × height. If all three dimensions scale by k, volume scales by k × k × k = k³. A figure twice as large has eight times the volume.
How do I find the scale factor?
Divide any length in the scaled figure by the corresponding length in the original: k = scaled ÷ original.
Can the scale factor be a fraction?
Yes! A scale factor less than 1 (like 0.5 or ½) means the scaled figure is smaller. A scale factor of 0.5 means half the size.
What's the relationship between enlargement and reduction?
They're inverses. If figure B is an enlargement of A with scale factor k, then A is a reduction of B with scale factor 1/k.