Scale drawings and map scales

A scale drawing shows a real object bigger or smaller, with every length changed by the same scale. Use the scale to find real and drawing lengths.

The idea: every length changes the same way

A map, a floor plan and a model car are scale drawings. Every length on the drawing matches a real length by the same ratio, called the scale.

A scale like 1 cm : 5 km means each centimetre on the map stands for 5 kilometres in real life. A scale is just a ratio, so ratio tables and proportions work here too.

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

map cmreal km0015210315420525630735
A map scale as a double number line: 1 cm is 5 km, so 7 cm is 35 km.
4 cm38 cm6× 2
A scale factor of 2 doubles every length: 4 by 3 becomes 8 by 6.
drawing (in)real (ft)145202.510× 5
On a plan where 1 inch is 4 feet, a 20-foot wall is 5 inches.

From the drawing to real life

Measure the drawing, then multiply by the scale. On a map with 1 cm : 5 km, two towns 7 cm apart are 7 × 5 = 35 km apart.

A ratio table makes it clear: 1 cm is 5 km, 2 cm is 10 km and 7 cm is 35 km.

From real life to the drawing

Divide the real length by the scale. On a plan where 1 inch stands for 4 feet, a 20-foot wall is 20 ÷ 4 = 5 inches long.

Always check the units. If the scale is 1 cm : 2 m and the room is 750 cm long, change it to 7.5 m first.

Solve a scale problem

Write the scale on the left and the length you know on the right. Leave the missing length empty.

Scale factors

A scale factor tells you what to multiply every length by. A scale factor of 3 makes a copy three times as long and three times as wide. A scale factor of 1/2 halves every length.

Area changes by the square of the scale factor. Doubling the sides of a rectangle makes its area 2 × 2 = 4 times as big, not twice as big.

Scales written without units

Maps often show a scale like 1 : 50,000. That means 1 unit on the map is 50,000 of the same units in real life. So 1 cm is 50,000 cm, which is 500 m.

Change big numbers to sensible units at the end. 4 cm on this map is 200,000 cm, which is 2 km.

Quiz: scale drawings

Use the scale or the scale factor to find the length.

Where this fits: ratios step by step

  1. What is a ratio
  2. Part-to-part and part-to-whole ratios
  3. Equivalent ratios
  4. Simplifying ratios
  5. Ratio tables
  6. Double number lines
  7. Tape diagrams
  8. Comparing ratios
  9. Unit rates
  10. Unit price and best buy
  11. Speed, distance and time
  12. Solving proportions
  13. Proportional relationships
  14. Constant of proportionality
  15. Scale drawings and maps (this page)
  16. Ratio word problems

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

  1. “On this map, 1 cm is 5 km. Two towns are 7 cm apart. How far really?” (35 km.)
  2. “How did you work it out?” (7 times 5.)
  3. “A real road is 20 km. How long on the map?” (4 cm.)
  4. “If we double a drawing, what happens to each side?” (It doubles.)
  5. “And the area?” (It gets 4 times bigger.)

More worked examples

Example 1: map to real

1 cm : 20 km. A river is 6.5 cm long on the map. 6.5 × 20 = 130 km.

Example 2: real to plan

1 in : 8 ft. A garden is 40 ft long. 40 ÷ 8 = 5 in on the plan.

Example 3: scale factor

A 6 cm by 4 cm photo is enlarged by a scale factor of 2.5. The new size is 15 cm by 10 cm.

Example 4: ratio scale

Scale 1 : 25,000. 8 cm on the map is 200,000 cm = 2,000 m = 2 km.

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

  1. 1 cm : 10 km. 4 cm is?
  2. 1 cm : 5 km. 9 cm is?
  3. 1 in : 4 ft. A 24 ft wall on the plan?
  4. 1 cm : 2 m. A 13 m room on the plan?
  5. Scale factor 3. A 5 cm side becomes?
  6. Scale factor 1/2. A 12 cm side becomes?
  7. Scale factor 2. Area 10 cm² becomes?
  8. 1 : 100. 3 cm is how many metres?
  9. A 2 cm model of a 6 m car. Scale?
  10. Stretch: 1 : 50,000. How many cm on the map for 4 km?
Show the answers
  1. 40 km
  2. 45 km
  3. 6 in
  4. 6.5 cm
  5. 15 cm
  6. 6 cm
  7. 40 cm²
  8. 3 m
  9. 1 : 300
  10. 8 cm

Common mistakes

Dividing when you should multiplyDivides 7 cm by 5 to get 1.4 km.Fix: drawing to real means multiply by the scale.
Mixing unitsUses 750 cm with a scale in metres.Fix: change to the same unit before using the scale.
Doubling the area with the sidesSays doubling the sides doubles the area.Fix: area grows by the scale factor squared: 2 × 2 = 4 times.

How to teach it at home

Room plan

Measure a room and draw it with 1 cm for 50 cm.

Map hunt

Use a map scale to find the distance to a friend’s house or a park.

Toy scale

Find the scale of a model car, like 1 : 43, and work out the real length.

By grade

More for each grade: Grade 7 math and the CBSE class 7 maths guide.

Worksheets and practice

Scale drawings worksheet, page 1

Scale drawings worksheet: printable PDF with an answer key. · Make a fresh test

Ratio practice · ratio calculator · unit rate calculator · ratio games · ratios for kids · percentages

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Questions parents ask

What is a scale drawing?

A drawing of a real object where every length is changed by the same ratio, like a map or a floor plan.

How do you use a map scale?

Measure the map distance and multiply by the scale. At 1 cm : 5 km, 7 cm is 35 km.

How do you find a length on a scale drawing?

Divide the real length by the scale. At 1 in : 4 ft, a 20 ft wall is 5 inches.

What is a scale factor?

The number every length is multiplied by. A scale factor of 2 doubles every length.

What grade learns scale drawings?

Grade 7 under Common Core 7.G.A.1. In India, class 7.