What you'll learn
Maps, scale drawings and scale factors let us represent large real distances on paper. In this guide you will learn what a scale and scale factor mean, how to use map scales and ratios to convert between drawing and real distances, how to make and read scale drawings, and how to combine scales with bearings. These practical skills appear in GCSE geometry and functional questions.
Key terms and definitions
Scale — the ratio between a length on a drawing and the real length.
Scale factor — the number you multiply by to go from drawing to real (or vice versa).
Scale drawing — an accurate drawing where all lengths are in proportion to real life.
Ratio scale — a scale written as a ratio, e.g. 1 : 50 000.
Unit conversion — changing between units such as cm, m and km.
Core concepts
Understanding scale
A scale tells you how a drawing length relates to a real length. It can be written as a ratio (1 : 50 000), meaning 1 unit on the map represents 50 000 of the same units in real life, or as a statement (1 cm represents 2 km). The scale must use the same units on both sides when written as a ratio.
Converting drawing to real distance
To find a real distance, multiply the map distance by the scale factor (and convert units). For a 1 : 50 000 map, 1 cm represents 50 000 cm = 0.5 km, so 4 cm represents 4 × 0.5 = 2 km.
Converting real to drawing distance
To find a drawing distance, divide the real distance by the scale factor (with consistent units). For the same scale, a real distance of 3 km = 300 000 cm ÷ 50 000 = 6 cm on the map.
Making scale drawings
To make a scale drawing, choose a sensible scale, convert each real length to a drawing length, and draw accurately with a ruler and protractor. For example, a 6 m wall at a scale of 1 cm : 1 m is drawn 6 cm long. Keep all lengths to the same scale and label the scale used.
Scale with bearings
Scale drawings often combine with bearings to solve navigation problems. Draw each leg at the correct bearing (measured clockwise from north) and the correct scaled length, then measure the required distance or bearing from the completed drawing, converting back to real units.
Worked examples
Example 1: Map to real
On a 1 : 25 000 map, two towns are 8 cm apart. How far apart are they really?
1 cm represents 25 000 cm = 0.25 km, so 8 × 0.25 = 2 km.
Example 2: Real to map
A field is 500 m long. At a scale of 1 : 10 000, how long is it on the map?
500 m = 50 000 cm; 50 000 ÷ 10 000 = 5 cm.
Example 3: Scale statement
A scale is 1 cm : 2 m. What real length does 7 cm represent?
7 × 2 = 14 m.
Common mistakes and how to avoid them
Mixing up units. Convert so both sides of a ratio use the same units (cm with cm).
Multiplying when you should divide. Drawing → real: multiply; real → drawing: divide.
Forgetting to convert the final answer. Change cm to m or km as required.
Inaccurate drawing. Use a sharp pencil, ruler and protractor for scale drawings.
Misreading the scale. Note whether it's a ratio or a "1 cm represents…" statement.
Exam technique for Maps and Scale Drawings
Read the scale carefully and note the units.
Multiply for real distances, divide for drawing distances.
Convert units at the end (cm → m or km).
Draw accurately with ruler and protractor for scale drawings.
Combine with bearings by drawing each leg at the right angle and length.
Quick revision summary
A scale relates a drawing length to a real length, written as a ratio (1 : 50 000, same units both sides) or a statement (1 cm represents 2 km). To find a real distance, multiply the map distance by the scale factor and convert units (on a 1 : 50 000 map, 4 cm → 2 km). To find a drawing distance, divide the real distance by the scale factor with consistent units (3 km on a 1 : 50 000 map → 6 cm). To make a scale drawing, pick a sensible scale, convert each real length, and draw accurately with a ruler and protractor, labelling the scale. Scale drawings combine with bearings: draw each leg at the correct bearing and scaled length, then measure off the answer and convert back. The common errors are mixing units, multiplying instead of dividing (or vice versa), forgetting the final unit conversion, and inaccurate drawing. Read the scale and units, multiply or divide appropriately, convert units, and draw precisely.