A scale drawing represents a real object at a fixed ratio called the scale. The ratio 1:50 means 1 cm on paper equals 50 cm in real life. Two operations underpin all scale work: multiply to find the real length, and divide the real measurement by the scale factor to find the drawing length.
What is a scale drawing?
A scale drawing is a diagram of a real object or place that has been made smaller (or occasionally larger) by a fixed, consistent amount. The scale expresses the relationship between the drawing and reality as a ratio written in the form 1 : n.
- The 1 represents one unit of measurement on the drawing (usually centimetres).
- The n represents how many of the same unit that equals in real life.
For example, a scale of 1 : 200 means that 1 cm on the drawing equals 200 cm (2 m) in reality. Every single measurement in the drawing has been shrunk by the same factor, so the proportions of the real object are preserved exactly.
Scales can be written in three equivalent ways:
- Ratio: 1 : 50
- Unit statement: 1 cm = 50 cm (or 1 cm = 0.5 m)
- Representative fraction: 1/50
All three are equivalent. Exam questions may use any of them — make sure you can recognise all three forms.
How do I read a scale?
Reading a scale correctly is the first skill to master. The rule is simple:
The scale 1 : n means that every 1 unit on the drawing equals n units in real life.
So if a scale is 1 : 500 and you measure 3 cm on the drawing, the real-world distance is 3 × 500 = 1,500 cm = 15 m.
The important thing is that both sides of the ratio use the same unit. The ratio 1 : 50,000 means 1 cm on the map equals 50,000 cm in real life — not 50,000 m. You must convert afterwards if you want the answer in metres or kilometres.
This handy table shows some common scales and what 1 cm on a drawing equals in real life:
| Scale | 1 cm on drawing equals in real life |
|---|---|
| 1 : 10 | 10 cm |
| 1 : 100 | 100 cm = 1 m |
| 1 : 1,000 | 1,000 cm = 10 m |
| 1 : 25,000 | 25,000 cm = 250 m = 0.25 km |
| 1 : 50,000 | 50,000 cm = 500 m = 0.5 km |
How do I find the real length from a scale drawing?
To find the real length, multiply the drawing measurement by the scale factor.
Real length = drawing measurement × scale factor
Worked example 1: A floor plan is drawn at a scale of 1 : 200. A room measures 3.5 cm on the plan. What is the real length of the room?
- Real length = 3.5 × 200 = 700 cm = 7 m
Worked example 2: A map has a scale of 1 : 25,000. Two towns are 4 cm apart on the map. What is the real distance between them?
- Real distance = 4 × 25,000 = 100,000 cm
Now convert: 100,000 cm ÷ 100 = 1,000 m = 1 km
Always state the unit clearly in your final answer, and show the unit conversion as a separate step — examiners award method marks for it.
How do I create a scale drawing?
To draw a scale diagram, divide the real measurement by the scale factor.
Drawing length = real length ÷ scale factor
The key step before dividing is to convert the real measurement into the same unit as the drawing (usually centimetres).
Worked example 3: Draw a scale diagram of a corridor that is 8 m long, using a scale of 1 : 50.
Step 1: Convert the real length to centimetres. 8 m = 800 cm
Step 2: Divide by the scale factor. Drawing length = 800 ÷ 50 = 16 cm
Draw a line exactly 16 cm long to represent the corridor.
Worked example 4: A garden is 12 m long and 9 m wide. Draw a scale plan at 1 : 300.
Step 1: Convert both measurements to centimetres. 12 m = 1,200 cm and 9 m = 900 cm
Step 2: Divide each by 300. Length on drawing = 1,200 ÷ 300 = 4 cm Width on drawing = 900 ÷ 300 = 3 cm
The scale plan of the garden is a rectangle 4 cm × 3 cm.
How do map scales work?
Ordnance Survey (OS) maps are a common real-life example of scale drawings. The two most familiar OS scales in the UK are:
- 1 : 25,000 (the orange Explorer maps) — popular for walking. 4 cm on the map = 1 km in real life.
- 1 : 50,000 (the pink Landranger maps) — covers larger areas. 2 cm on the map = 1 km in real life.
Worked example 5: On a 1 : 50,000 OS map, two villages are 6 cm apart. What is the real distance between them?
Real distance = 6 × 50,000 = 300,000 cm
Convert: 300,000 cm ÷ 100 = 3,000 m = 3 km
Some maps also give a scale bar — a printed line labelled with real distances. You measure the scale bar with a ruler to find how many centimetres equal 1 km, then use that ratio. Scale bars remain accurate even if the map is photocopied at a different size, which is why they are preferred on printed maps.
What are the most common mistakes with scale drawings?
Avoid these errors and you will pick up nearly all the marks available:
1. Not converting units before multiplying or dividing. If the scale is 1 : 200 and the real room is 6 m long, you must convert 6 m to 600 cm before dividing: 600 ÷ 200 = 3 cm. A very common mistake is dividing 6 by 200 and writing 0.03 cm — a completely unrealistic answer.
2. Multiplying when you should divide (or vice versa). To go from drawing → real, multiply. To go from real → drawing, divide. If you always ask yourself "am I making the measurement bigger or smaller?", you will choose the right operation. Going to real life makes measurements bigger (multiply). Going to a drawing makes them smaller (divide).
3. Forgetting to convert back to sensible units. An answer of 150,000 cm is technically correct but almost never what the question expects. Always convert to metres or kilometres where appropriate and round sensibly.
Frequently Asked Questions
What does "drawn to scale" mean?
When a diagram is "drawn to scale", every length in the picture is proportional to the real-life length by the same fixed ratio. This means you can measure any part of the drawing with a ruler and use the scale to work out the real measurement. If a drawing is not to scale, measuring it directly would give misleading results — which is why exam diagrams carry a "not drawn to scale" warning.
How do I find the scale if I know both the real and drawing measurements?
Write the ratio as drawing measurement : real measurement and then simplify it to the form 1 : n. For example, if a 5 cm drawing represents 250 cm in real life, the scale is 5 : 250, which simplifies to 1 : 50. Always make sure both measurements are in the same unit before simplifying.
Can a scale drawing be larger than the real object?
Yes — scales like 2 : 1 or 5 : 1 mean the drawing is larger than reality. These are used for very small objects such as circuit components, insects, or grains of pollen, where you need to enlarge the drawing to see detail. In KS3, however, almost all scale drawing questions involve shrinking a real object, so the scale factor n in 1 : n is greater than 1.
Do I need to include units in the scale ratio?
A ratio scale such as 1 : 50,000 has no units — it works for any consistent unit (1 cm = 50,000 cm, or equally 1 mm = 50,000 mm). A unit statement such as "1 cm = 500 m" does include units and cannot be used unless you first convert both sides to the same unit. For KS3 exam answers, stating your working in centimetres and then converting to metres at the end is the clearest approach.
Need help with scale drawings or any other KS3 ratio topic? Visit AI Tutors — Professor Pi will guide you through every step at exactly your pace.