Scale Drawings
Learn how to read and create scale drawings using ratios and proportions.
Definition
- 1 cm on the drawing = 100 cm in real life
- Every measurement is divided by 100
- To find actual size: Drawing size Scale factor
- To find drawing size: Actual size Scale factor
Try it now
Worked Examples
A map has a scale of . Two cities are 4 cm apart on the map. What is the actual distance?
Understand the scale
means 1 cm on map = 50,000 cm in reality → Scale factor = 50,000
Multiply drawing measurement by scale factor
→ 200,000 cm
Convert to appropriate units
→ 2 km
Answer: The actual distance between the cities is 2 km.
Common Mistakes
Multiplying when you should divide (or vice versa)
Why it's wrong: Going from drawing to actual: multiply by scale factor. Going from actual to drawing: divide by scale factor.
Correct: Remember: Drawings are SMALLER, so drawing measurements multiplied by scale = actual size.
Forgetting to use the same units
Why it's wrong: Mixing cm and m in calculations leads to answers that are off by factors of 100.
Correct: Always convert to the SAME units before calculating, then convert the answer to appropriate units.
Confusing with
Why it's wrong: means the drawing is smaller (1/50 size). would mean the drawing is 50 times bigger (enlargement).
Correct: means reduce by factor of . means enlarge by factor of .
Interactive Visual
Ratio Tape Diagram
Adjust the ratio parts using + and - buttons.
Linear Function Explorer
Interactive Sandbox
Expression Calculator
Try these:
History
No calculations yet
Practice Problems
15 problemsA map has a scale of . What does this mean?
Why It Matters
- Architecture: Blueprints show buildings at or scale
- Maps: A hiking map at means 1 cm = 250 m
- Model Making: Model cars are often at or scale
- Engineering: Technical drawings use precise scales for manufacturing
Real World Applications
Navigation and Maps
Hikers, pilots, and sailors use scale maps to plan routes and calculate distances.
Example:
A hiking map at scale means 4 cm on the map = 1 km of actual hiking distance.
You are planning a bike route. On a map with scale , your route measures 6 cm.
How many kilometers will you actually cycle?
Step 1: Write the mathematical expression
Calculate: cm, then convert to km
Interior Design
Interior designers create floor plans to help clients visualize furniture placement.
Example:
A floor plan at scale shows a sofa that measures 10 cm long. The actual sofa is 200 cm (2 m) long.
You want to draw your bedroom (3 m by 4 m) using a scale.
What dimensions will you draw?
Step 1: Write the mathematical expression
Convert m to cm, then divide by 25
Model Building
Model enthusiasts build miniature versions of cars, planes, trains, and buildings.
Example:
A scale model airplane of a Boeing 747 (70 m wingspan) has a model wingspan of about 97 cm.
You are building a scale model of the Eiffel Tower, which is 330 m tall.
How tall will your model be?
Step 1: Write the mathematical expression
Calculate:
Key Takeaways
- 1A scale drawing uses a consistent ratio to represent real objects at a different size
- 2Scale is written as Drawing : Actual (e.g., means 1 unit on drawing = 100 units in real life)
- 3To find actual size: multiply the drawing measurement by the scale factor
- 4To find drawing size: divide the actual measurement by the scale factor
- 5Always use the same units when calculating, then convert your answer appropriately
Frequently Asked Questions
Glossary
- Scale
- The ratio between measurements in a drawing and the corresponding actual measurements
- Scale factor
- The number by which you multiply or divide to convert between drawing and actual sizes
- Scale drawing
- A proportional representation of an object where all dimensions use the same scale
- Blueprint
- A technical drawing, typically of a building or machine, made to scale
- Proportion
- An equation stating that two ratios are equal