📐 Scale Factors and Scale Diagrams

A scale factor shows how many times larger or smaller something is. Scale diagrams use this to represent real objects.

🎯 What You'll Learn

Understand what scale factors mean
Calculate scale factors from measurements
Use scale factors to find real-world sizes
Work with scale diagrams and maps

✏️ Explanation

A scale factor shows how many times larger or smaller something is. Scale diagrams use this to represent real objects.

🔍 Why It Matters

Essential for reading maps, architectural drawings, and model making. Used in engineering, design, and everyday navigation.

🧭 Scale Factor Applications

🗺️

Maps

Show large areas on small paper

1:50,000
1cm = 500m

🏠

Architecture

Building plans and blueprints

1:100
1cm = 1m

🚗

Models

Toy cars, trains, planes

1:64
1cm = 64cm

📏

Engineering

Technical drawings

1:10
1cm = 10cm

✏️ Worked Example

A model car is 8cm long. The real car is 4m long. What's the scale factor?

Step 1: Convert to the same units

Real car = 4m = 400cm

Step 2: Calculate the scale factor

Scale factor = Real length ÷ Model length

Scale factor = 400cm ÷ 8cm = 50

Step 3: Write as a ratio

Scale = 1:50

Answer: The scale factor is 1:50

This means 1cm on the model = 50cm in real life

📊 Common Scale Factors

Map Scale

1:25,000

1cm on map = 250m in reality
Good for hiking maps

House Plans

1:100

1cm on plan = 1m in reality
Standard architectural scale

Model Cars

1:64

1cm on model = 64cm real
Popular die-cast scale

Model Railways

1:87

1cm on model = 87cm real
HO scale trains

🧮 Scale Factor Calculator

Find Real-World Size

Model/Drawing Size

Scale (1 : ?) Enter the number after 1:

Real-World Size: 15m

Scale 1:500 means 1cm = 500cm real

3cm × 500 = 1500cm = 15m

Find Scale Factor

Model Size

Real Size

Scale Factor: 1:500

Convert to same units: 30m = 3000cm

Scale factor = 3000cm ÷ 6cm = 500, so 1:500

Find Model Size

Real Size

Scale (1 : ?) Enter the number after 1:

Model Size: 6cm

Scale 1:25 means divide real size by 25

150cm ÷ 25 = 6cm

🔢 Practice Exercises

1. A scale drawing uses 1cm : 5m. What's the real length if the drawing shows 3cm?

metres

2. Find the scale factor if 6cm represents 30m

3. A model is built to scale 1:200. If the model is 15cm tall, how tall is the real building?

metres

4. On a map, 2cm represents 1km. What distance does 7cm represent?

5. Scale factor is 1:25. If the real width is 150cm, what's the model width?

⚠️ Common Mistakes

Mixing up units (cm vs m)
Getting scale factor backwards
Not converting units consistently

✨ Quick Summary

Scale factor = Real size ÷ Model size. Keep units consistent.