Map Scale

What is map scale?

The Earth is huge and paper is small, so every map shrinks the land by a fixed amount. The scale is the ratio of a distance on the map to the same distance on the ground.

Scale = map distance : ground distance

If a 5 km road is drawn 5 cm long, then 1 cm on the map stands for 1 km on the ground.

Methods of showing scale

1. Statement of scale

Written in words, like "1 cm represents 10 km". Easy to read, but only people who know those units (cm, km) understand it. If the map is enlarged, the statement becomes wrong.

2. Representative fraction (RF)

Written as a ratio or fraction, like 1 : 100,000 or 1/100,000. The numerator is always 1 and both sides are in the same unit. So 1 : 100,000 means 1 cm = 100,000 cm, or 1 inch = 100,000 inches. Because it has no unit, anyone anywhere can use it. That is why it is called the universal method.

RF = distance on map ÷ distance on ground (same units).

3. Graphical (bar or linear) scale

A straight line divided into equal parts, each marked with the ground distance it stands for. You measure with a divider or ruler and read the distance directly. It stays correct when a map is enlarged or reduced by photocopy, because the bar changes size with the map.

Construction of a graphical scale

Example: Construct a bar scale for RF 1 : 50,000 and read distances in km and metres.

1. Find what 1 cm stands for: 1 cm = 50,000 cm = 0.5 km.
2. Choose a line length that gives a round number. Lines of about 12–15 cm are easy to draw. Here 10 cm = 10 × 0.5 = 5 km (a round number).
3. Draw a 10 cm line. Divide it into 5 equal primary parts of 2 cm; each = 1 km.
4. Divide the first (left) primary part into 4 equal secondary parts; each = 250 m.
5. Write 0 at the end of the first primary part. Mark 1, 2, 3, 4 km to the right of zero and 250, 500, 750 m (1 km) to the left.
6. Write the RF and "Kilometres" under the bar.

Formula for line length: length of line (cm) = (chosen ground distance × 100,000) ÷ RF denominator.

Conversion of scale

Statement → RF

Change both sides into the same unit, then write 1 : n.

• 1 cm represents 5 km → 5 km = 5 × 100,000 cm = 500,000 cm → RF = 1 : 500,000.
• 1 inch represents 4 miles → 4 × 63,360 in = 253,440 in → RF = 1 : 253,440.

RF → statement

• Metric: divide the denominator by 100,000 to get km per cm. 1 : 250,000 → 1 cm = 2.5 km.
• English: divide by 63,360 to get miles per inch. 1 : 126,720 → 1 inch = 2 miles.

English statement → metric statement

1 inch represents 1 mile → RF 1 : 63,360 → 63,360 cm ÷ 100,000 = 0.63 km → 1 cm represents 0.63 km.

Useful units: 1 km = 1,000 m = 100,000 cm; 1 mile = 1,760 yards = 63,360 inches.

Measuring distance on a map

For a straight road, measure with a ruler or divider and read it on the bar scale. For a curved road or river, lay a thread along it, straighten the thread, measure, then use the scale. You can also use a wheel-shaped tool called an opisometer (map measurer).

Try it at home

Measure your classroom (say 8 m long) and draw it 8 cm long. Your scale is 1 cm = 1 m, or RF 1 : 100. Now draw a bar scale for it. Then use the slider in the last 3D step to predict before you check: how long is a 10 km road at 1 : 250,000?

Key formulas and definitions

• Scale = map distance : ground distance
• RF = map distance ÷ ground distance (same unit), written 1 : n
• 1 km = 100,000 cm; km per cm = n ÷ 100,000
• 1 mile = 63,360 inches; miles per inch = n ÷ 63,360
• Line length (cm) = ground distance (km) × 100,000 ÷ n

Worked examples

Common mistakes

• Writing different units in an RF, like 1 cm : 5 km. An RF has no units; convert first.
• Using 1 km = 10,000 cm. It is 100,000 cm (1,000 m × 100 cm).
• Putting zero at the left end of a bar scale. Zero comes after the first primary part, so secondary parts are to its left.
• Thinking a bigger denominator means a bigger scale. 1 : 1,000,000 is a smaller scale than 1 : 50,000.