Scale factor
High School
Definition
The ratio of 2 similar geometric shapes or quantities with similar unit of measurements. To find the scale factor of two similar geometric shapes. Write the lenghts of the corresponding sides of each shape to one another to get the ratio. For example, a scale of 1:2 represents the length of the second object being double of the first. Scale factors are commonly found in maps to translate the measurement of two points on a map to actual distance.
Worked examples
\(\frac{\)new length\(}{\)original length\(} = \frac{10}{5} = 2\)
A rectangle with side 5 cm is enlarged to 10 cm; the scale factor is 2.
\(\)Scale \( 1:50000 \)→\( 3\) cm on map\( = 3 \times 50000 = 150000\) cm\( = 1.5\) km\(\)
On a map with scale factor 1:50000, 3 cm represents 1.5 km in real distance.
\(\frac{4}{12} = \frac{1}{3}\)
If a triangle's side shrinks from 12 to 4, the scale factor is \(\frac{1}{3}\) (reduction).
Common mistakes
- \(\frac{\)original\(}{\)new\(}\) → \(\frac{\)new\(}{\)original\(}\) Scale factor is new divided by original, not the reverse.
- Scale factor \(2\) means add 2 to each side → Scale factor \(2\) means multiply each side by 2 Scale factor is a multiplier, not an additive change.
- Area scale factor equals length scale factor → Area scale factor equals (length scale factor)\(^2\) When lengths scale by \(k\), area scales by \(k^2\).
Where you'll use it next
Scale factor appears in similarity and congruence, dilations in coordinate geometry, and scaling area and volume. You'll use it in trigonometry, real-world modeling, architecture, and map reading.
Found in 1 StudyPug lesson
Mastering Enlargement and Reduction Scale Factors
9th Grade9thGrade 9 Math
Discover the power of scale factors in geometry. Learn to enlarge and reduce shapes, solve complex problems, and apply your knowledge to real-world scenarios. Boost your math skills with our comprehensive guide.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026