Scale Drawings and Map Scales

What you will learn

• How to read scales such as 1 : 50 000.
• How to convert drawing lengths into real lengths.
• How to convert real lengths into drawing lengths.
• How to use a map scale bar.
• How to choose sensible units such as cm, m or km.
• How to check whether a scaled answer is realistic.

Key facts before you start

Scale drawings and map scales infographic

Why this matters

Maps, floor plans, construction drawings, model designs and route diagrams all use scales. A small measurement on a page can represent a much larger real distance.

Scale questions are often straightforward once the units are tidy. Most mistakes come from mixing cm, m and km.

Prior knowledge

You should already be comfortable with:

• ratio notation, such as 1 : 200,
• multiplying and dividing by powers of 10,
• metric conversions: 100 cm = 1 m and 1000 m = 1 km,
• measuring lines accurately with a ruler,
• checking whether an answer makes sense in context.

Clear explanation

What a scale means

A scale compares a length on a drawing with the matching real length. The scale 1 : 50 000 means:

So, on a 1 : 50 000 map, each 1 cm represents 0.5 km.

A scale in the form 1 : n compares matching lengths in the same unit. It does not mean 1 cm must be used, but cm is often the easiest unit for maps and plans because ruler measurements are in cm.

Map length to real distance

Multiply the map length by the scale factor, then convert units if needed.

Real distance to drawing length

Work in matching units first, then divide by the scale factor.

Using a scale bar

A scale bar gives a direct comparison. If a 2 cm bar represents 1 km, then 1 cm represents 0.5 km.

If 2 cm represents 1 km, then a 6 cm route represents 3 km.

Length scale is not area scale

If a question asks for an area on a plan, scale the lengths first and then multiply the scaled lengths. Do not multiply an area by the length scale once.

Worked examples

Quick checks

Choose an answer, then check your thinking.

Practice questions

Answers and marking guidance

The exact practice answers are hidden under each question so you can try first. For scale drawings and maps, marks usually come from converting both measurements into compatible units, applying the scale factor in the correct direction, labelling drawing and real distances clearly, and checking whether the final answer should be in cm, m or km. When a question asks for the scale itself, compare matching lengths in the same unit before simplifying to 1 : n. For plan-area questions, scale the lengths first and then calculate the area.

Common mistakes

• Mixing units: convert real lengths into the same unit as the drawing before dividing.
• Multiplying when you should divide: map to real usually multiplies; real to map usually divides.
• Forgetting that 100 000 cm = 1 km: this is useful for map scales.
• Measuring carelessly: small ruler errors can create large real-distance errors.
• Leaving impossible units: a real town-to-town distance should usually be in km, not cm.
• Scaling area like a length: if the task asks for area, convert the side lengths on the drawing first, then multiply them.

Extension challenge

A rectangular garden is 14 m by 9 m. It is drawn on a plan at scale 1 : 200. Find the area of the rectangle on the plan in cm².

Exam-board guidance

Scale drawings and map scales are common across GCSE Maths. Expect questions involving ratio, proportional reasoning, metric conversions, plans, maps and real-life measurements.

Next lesson

Next, build on rates and units with Compound Measures: Speed, Density and Pressure.