Scale & Scale Drawings

What is a Scale?

A scale is a ratio used to represent real-world distances in a smaller, manageable format—often for use in maps, models, and diagrams.

It shows how measurements on a drawing compare to real-life measurements.

Example: A scale of 1 : 50 000 means 1 cm on the diagram represents 50 000 cm in real life.

This works for any consistent unit: cm, m, km, etc.

Example:

1 : 50 000 could mean:

1 cm = 50 000 cm

1 m = 50 000 m

1 km = 50 000 km

 

Using Scale on Maps

Finding Real-Life Distances

1. Measure the length on the map with a ruler.
2. Multiply by the scale factor.
3. Convert the result to suitable units (e.g. cm to km).

Example:

• Scale = 1 : 150 000
• Measured distance = 5.8 cm

$$\text{Actual distance} = 5.8 \times 150\,000 = 870\,000\text{ cm} = 8.7\text{ km}$$

 

Worked Example

(a) Finding the Scale Ratio

Given: 5 cm on a map = 0.6 km in real life

Convert both to cm:

$$\text{ km} = 600 \text{ m} = 60\,000 \text{ cm}$$

Ratio:

$$5 : 60\,000 = 1 : 12\,000$$

(b) Finding the Actual Distance

Given: 17 mm on the map. Convert to cm:

$$17 \text{ mm} = 1.7 \text{ cm}$$

Then:

$$1.7 \times 12\,000 = 20\,400 \text{ cm} = 204 \text{ m}$$

(c) Finding the Map Distance

Given: Real distance = 125 m Convert to cm:

$$125 \text{ m} = 12\,500 \text{ cm}$$

Then:

$$\text{Map distance} = \frac{12\,500}{12\,000} = 1.04 \text{ cm}$$

 

Scale Drawings

What is a Scale Drawing?

A scale drawing is an accurate diagram of an object where all measurements are in proportion to the real object, but reduced or enlarged by a scale factor.

Steps for Creating a Scale Drawing

1. Convert the scale into a practical ratio.
   • For example, 1 : 500 000 $\to$ 1 cm = 5 km
2. Use the ratio to find the scaled measurement.
   • Example:

$$\text{Real distance} = 20\text{ km} \Rightarrow \text{Drawing} = \frac{20}{5} = 4 \text{ cm}$$