Scale Drawings

Understand how scale drawings represent real objects and learn to calculate real distances from map or diagram scales.

What Is a Scale Drawing?

A scale drawing is an accurate drawing of an object or area where every measurement has been reduced (or sometimes enlarged) by the same ratio. Maps, floor plans, and model kits all use scale drawings.

The scale tells you the relationship between the drawing and the real thing.

For example, a scale of $1:100$ means every $1 \text{ cm}$ on the drawing represents $100 \text{ cm}$ (= $1 \text{ m}$ ) in real life.

Note

Architects use scale drawings to plan buildings. A scale of $1:50$ means the drawing is 50 times smaller than the actual building. Without scale drawings, building would be almost impossible!

Reading a Scale

A scale is written as a ratio: $1 : n$

$1:50$ → 1 cm on drawing = 50 cm in real life
$1:200$ → 1 cm on drawing = 200 cm = 2 m in real life
$1:1000$ → 1 cm on drawing = 1000 cm = 10 m in real life

To find the real distance: multiply the drawing measurement by the scale factor.

$\text{Real distance} = \text{Drawing distance} \times n$

To find the drawing distance: divide the real distance by the scale factor.

$\text{Drawing distance} = \frac{\text{Real distance}}{n}$

Worked Examples

Example 1: A map uses a scale of $1:500$ . A path on the map measures $6 \text{ cm}$ . What is the real length?

$6 \times 500 = 3000 \text{ cm} = \mathbf{30 \text{ m}}$

Example 2: A room is $9 \text{ m}$ long. You draw it at a scale of $1:300$ . How long is it on the drawing?

$9 \text{ m} = 900 \text{ cm}, \quad 900 \div 300 = \mathbf{3 \text{ cm}}$

Tip

Always convert both measurements to the same unit before calculating. It is easiest to work in centimetres, then convert the answer to metres at the end.

Scale Drawings on Maps

Maps often use scales like $1 : 50\,000$ , meaning $1 \text{ cm}$ on the map = $50\,000 \text{ cm} = 500 \text{ m}$ in real life.

Example: Two towns are $4.5 \text{ cm}$ apart on a $1 : 50\,000$ map. What is the real distance?

$4.5 \times 50{,}000 = 225{,}000 \text{ cm} = \mathbf{2.25 \text{ km}}$

Warning

After multiplying, remember to convert your answer into sensible units. A room length of 300 cm should be reported as 3 m, not left as 300 cm.

Real world: architect's blueprint

An architect draws a room at scale 1:50. The drawing shows the room as 7 cm × 5 cm. Real dimensions: $7 \times 50 = 350\text{ cm} = 3.5\text{ m}$ by $5 \times 50 = 250\text{ cm} = 2.5\text{ m}$ . Builders use this blueprint to lay out walls precisely on site.

Real world: model-making

A model-train builder works at 1:87 (HO scale). A real locomotive is 21 m long. Model length $= 2100\text{ cm} \div 87 \approx 24.1\text{ cm}$ . Scale drawings ensure every detail is proportionally accurate to the original.

Real world: Ordnance Survey map

A 1:25 000 Ordnance Survey map shows a lake as 3.2 cm long. Real length $= 3.2 \times 25\,000 = 80\,000\text{ cm} = 800\text{ m}$ . Hikers use this to estimate walking distances and plan realistic routes.

Tip Always convert to the same unit before multiplying or dividing. Work in centimetres throughout, then convert the final answer to metres or kilometres.

Practice Problems

A scale drawing uses the scale $1:200$. A wall on the drawing is $3.5 \text{ cm}$ long. What is the real length?

Show answer

$3.5 \times 200 = 700 \text{ cm} = 7 \text{ m}$.

A garden is $15 \text{ m}$ wide. You want to draw it using a scale of $1:300$. How wide will it be on the drawing?

Show answer

$15 \text{ m} = 1500 \text{ cm}$. $1500 \div 300 = 5 \text{ cm}$.