Functional Skills Maths · England

Scale drawings, maps and coordinates

Read and use map scales, work from floor plans and scale drawings, understand plans and elevations, and — at Level 2 — use coordinates in all four quadrants.

Audience
Adults & apprentices
Levels
Level 1 · Level 2 (coordinates, harder scales)
Worked examples
4
Format
Print (A4/Letter) + answers

Learn

How scales work

A scale links a length on paper to a real length. It can be written in two ways. A unit scale such as 1 cm : 2 m means every centimetre on the drawing is 2 metres in real life. A ratio scale such as 1:50 means the real object is 50 times bigger than the drawing, in the same units — 1 cm on the drawing is 50 cm in real life.

To go from drawing to real life, multiply by the scale. To go from real life to drawing, divide. The answer from a ratio scale is in the same unit you started with, so convert at the end: 6 cm at 1:25,000 is 150,000 cm, which is 1,500 m or 1.5 km.

Maps

Walking maps in the UK commonly use 1:25,000 (4 cm on the map is 1 km) or 1:50,000 (2 cm is 1 km). Measure the route carefully with a ruler — for a winding path, measure it in short straight sections and add them. Map distances combine well with speed questions: once you know the real distance, time = distance ÷ speed.

Plans and elevations

A plan is the view from directly above — the classic floor plan. An elevation is the view from the front or side, showing heights. Builders, kitchen fitters and planners use both together. In a question you may need to read dimensions from a plan, draw an object to scale, or work out which elevation matches a 3D shape. Areas from a plan must use real lengths: convert each side first, then multiply. Do not scale an area by the scale factor.

Coordinates (Level 2)

A coordinate pair (x, y) gives a position on a grid: x is how far across, y is how far up. Go along the corridor and then up the stairs. In four quadrants, negative x is to the left of the origin and negative y is below it, so (−3, 2) is three left and two up.

You can find lengths of horizontal or vertical lines by subtracting coordinates: from (−3, 2) to (5, 2) is 5 − (−3) = 8 units. The midpoint of two points is the average of the x values and the average of the y values. Coordinates often appear with shapes — for example finding the missing corner of a rectangle, then its area.

Level 1 typically covers map scales, simple scale drawings and plans. Level 2 adds coordinates in four quadrants, working out a scale, and multi-step questions such as combining a map distance with speed.

Worked example 1

Level 1: On a 1:25,000 map, a path measures 6 cm. How long is it in real life?

  1. Real length = 6 × 25,000 = 150,000 cm.
  2. ÷ 100 = 1,500 m; ÷ 1,000 = 1.5 km.

Answer: 1.5 km

Worked example 2

Level 1: A floor plan uses 1 cm : 0.5 m. A room measures 9 cm by 7 cm. What are its real dimensions?

  1. 9 × 0.5 = 4.5 m.
  2. 7 × 0.5 = 3.5 m.

Answer: 4.5 m by 3.5 m

Worked example 3

Level 2: A 7.2 m wall is drawn at a scale of 1:50. How long is it on the drawing?

  1. Convert to cm: 7.2 m = 720 cm.
  2. Real to drawing: divide. 720 ÷ 50 = 14.4 cm.

Answer: 14.4 cm

Worked example 4

Level 2: A rectangle has corners A(2, 3), B(8, 3) and C(8, 7). Find the fourth corner D and the area.

  1. D lines up with A across and C up: D = (2, 7).
  2. Width: 8 − 2 = 6 units; height: 7 − 3 = 4 units.
  3. Area: 6 × 4 = 24 square units.

Answer: D(2, 7); area 24 square units

Watch out

Common mistakes

  • Forgetting to convert units at the end of a ratio scale: 150,000 cm is 1.5 km.
  • Multiplying when converting a real length to a drawing; you should divide.
  • Scaling an area by the scale factor instead of converting each length first.
  • Reading coordinates the wrong way round: x (across) always comes first.

Real life

Where you'll use this at work or home

  • Planning a walk or cycle route from an Ordnance Survey map.
  • Checking whether furniture fits from a floor plan or estate agent's drawing.
  • Reading kitchen, extension or garden plans from a builder.
  • Using grid references and coordinates in warehouses, games and graph work.

Try it

Practice sheet

Functional Skills Maths · Level 1

Scale drawings, maps and coordinates

NameDate

Show your working. Give money to the nearest penny and include units in every answer.

  1. 1.A map scale is 1 cm : 2 km. Two villages are 4.5 cm apart. How far apart are they?
  2. 2.On a 1:100 plan, a wall is 6.5 cm long. How long is the real wall in metres?
  3. 3.A scale is 1 cm : 5 m. A garden is 8 cm long on the drawing. How long is it really?
  4. 4.On a 1:50,000 map, a road measures 3 cm. How long is it in kilometres?
  5. 5.A 12 m wall is drawn at 1 cm : 2 m. How long is it on the drawing?
  6. 6.A model car is built at 1:20. The model is 21 cm long. How long is the real car in metres?
  7. 7.On a 1:25,000 map, a walk measures 8 cm. How far is the walk?
  8. 8.On a 1:50 kitchen plan, a worktop is 5 cm long. What is its real length?
  9. 9.A drawing uses 2 cm : 1 m. How long should a 0.8 m wide door be drawn?
  10. 10.A map uses 1 cm : 4 km. How long on the map is a 34 km road?
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Questions

Frequently asked questions

1 cm on the map is 50,000 cm in real life, which is 500 m. So 2 cm is 1 km.

A plan is the view from above. An elevation is the view from the front or side, showing heights.

Put both lengths in the same unit and divide the real length by the drawn length. A 6 m wall drawn as 12 cm gives 600 ÷ 12 = 50, so the scale is 1:50.

Coordinates in four quadrants are typically a Level 2 skill. Check your awarding body's specification.

Next steps

Area, perimeter and volumeRectangles, composite shapes, circles, cuboids and cylinders.Units, time and conversionsMetric units, time, imperial conversions, speed and density.Ratio and proportionSharing in a ratio, recipes, best buys and inverse proportion.All Functional Skills Maths topicsThe full learning path, Level 1 and Level 2.

Last reviewed: 9 October 2026

Editor: Paul Smeaton CMgr FCMI