Scale Factor Calculator
Calculate scale factor (k) for dilations, enlargements, and scale drawings.
Scale Factor Formulas
Find k: k = New Size / Original Size
Apply k: New Size = Original Size × k
Area Multiplier: k²
Volume Multiplier: k³
Scale Factor Types & Applications
| Scale Factor | Type | Example Application |
|---|---|---|
| k = 0.5 | Reduction (50%) | Shrink photo to half size |
| k = 1 | Congruent (same) | No change in size |
| k = 2 | Enlargement (200%) | Double size (blueprint scale) |
| k = 1/100 | Reduction (1:100) | Map scale: 1 cm = 100 km |
Frequently Asked Questions
What is a scale factor?
A scale factor (k) is a multiplier that describes how much a figure is enlarged or reduced. If k > 1, the figure enlarges. If 0 < k < 1, the figure reduces. If k = 1, the figure stays the same size (congruent).
How do I find the scale factor between two figures?
Divide the new dimension by the original dimension: k = new size / original size. Example: If original = 5 cm and new = 15 cm, then k = 15/5 = 3 (three times larger).
What is a dilation in geometry?
Dilation is a transformation that enlarges or reduces a figure from a center point. All distances from the center are multiplied by the scale factor. The shape stays the same; only the size changes.
What is the difference between enlargement and reduction?
Enlargement: k > 1 (figure gets bigger). Example: k = 2 means double the size. Reduction: 0 < k < 1 (figure gets smaller). Example: k = 0.5 means half the size.
How does scale factor affect area?
If linear scale factor = k, then area scales by k². Example: If k = 2, areas multiply by 2² = 4. A shape with area 10 cm² dilated by k = 2 becomes 40 cm².
How does scale factor affect volume?
If linear scale factor = k, then volume scales by k³. Example: If k = 2, volumes multiply by 2³ = 8. A shape with volume 10 cm³ dilated by k = 2 becomes 80 cm³.
Can scale factor be negative?
In standard dilation, scale factor is positive. Negative scale factors cause reflection and dilation (reversal + size change). Most geometry courses work with positive scale factors only.
What is scale notation for maps and blueprints?
Scale notation like "1:100" means 1 unit on the drawing = 100 units in reality. This is equivalent to scale factor k = 1/100. Blueprints use similar ratios.
How do I apply scale factor to all dimensions?
Multiply every length, width, height by the scale factor. For a rectangle with dimensions 4 × 6 scaled by k = 2, new dimensions = 8 × 12.
What are similar figures?
Figures with the same shape but different sizes. They have equal corresponding angles and sides in proportion (scaled by same factor k). Scale factor relates all corresponding sides.
How is scale factor used in real life?
Maps, blueprints, model buildings, scale drawings, photo resizing, architectural plans. Any situation where a design is enlarged or reduced maintains scale factor relationships.
What is the center of dilation?
The fixed point from which all distances are multiplied by the scale factor. Usually the origin (0,0) in coordinate geometry. Changing the center changes where the dilated figure ends up.