A last-minute revision squeeze of this chapter: the definition of scale, the two systems of measurement, the three methods of scale (with advantages and limitations), the conversion formulas in both directions, and the graphical-scale construction method, all in one place. The full detailed notes are available separately for a complete read.
1 Two definitions to learn by heart
Map Scale is the ratio between the distance measured between any two points on a map and the actual distance between those same two points on the ground; a network of lines and polygons drawn without a scale is called merely a sketch.
Representative Fraction (R.F.) is the method of expressing scale as a fraction without stating any unit, such as 1:24,000, meaning that 1 unit of distance on the map represents 24,000 units of distance on the ground.
The definitions of numerator (map distance, always 1) and denominator (ground distance), and the importance of the year 1957 in India (the Metric System was adopted after that year), are direct, fact-based questions.
2 The two systems of measurement (Box 2.1)
| Metric System | English System |
|---|---|
| 1 km = 1,000 metres | 1 mile = 8 furlongs |
| 1 metre = 100 centimetres | 1 furlong = 220 yards |
| 1 centimetre = 10 millimetres | 1 yard = 3 feet |
| (no fourth unit) | 1 foot = 12 inches |
Derived values, used in every conversion: 1 mile = 63,360 inches; 1 furlong = 7,920 inches. India used the English System before 1957, and the Metric System after.
3 Three methods of expressing scale
| Method | Advantage | Limitation |
|---|---|---|
| Statement of Scale (e.g. “1 cm = 10 km”) |
Simplest, a direct written sentence | Understood only by someone familiar with that same system; invalid once the map is enlarged/reduced |
| Graphical/Bar Scale (horizontal line, primary-secondary divisions) |
Remains valid even when the map is enlarged/reduced | Still useful only to someone familiar with the marked unit |
| Representative Fraction (R.F.) (e.g. 1:24,000) |
Unit-free, universally valid, considered the most suitable | The book names no separate limitation; it is read by converting it into one’s own system |
Do not assume the Graphical Scale shares every limitation of the Statement of Scale. The Graphical Scale remains valid even when the map’s size changes (it does not carry the Statement of Scale’s limitation); its only real limitation is that the reader must be familiar with the unit it uses.
4 The universality of the Representative Fraction: one example
| Reading | Result |
|---|---|
| R.F. 1:36,000, Metric (centimetre) reading | 1 cm represents 360 metres |
| R.F. 1:36,000, English (inch) reading | 1 inch represents 1,000 yards |
Both readings of the same R.F. are equally correct: this is what makes the Representative Fraction universally valid.
5 Converting scale: both directions
| Direction | Method (as a formula) |
|---|---|
| Statement → R.F. | Convert the given distance on both sides into the same small unit (inch/centimetre), then replace the unit name with ‘unit’ to write the R.F. E.g.: 1 inch = 4 miles → 4×63,360 = 253,440 inches → R.F. 1:253,440 |
| R.F. → Statement | Divide the denominator by the number that converts it into a convenient larger unit (100,000 cm in 1 km, or 63,360 inches in 1 mile). E.g.: R.F. 1:253,440 → 253,440 ÷ 100,000 = 2.53 → 1 cm represents 2.53 km |
6 Constructing a Graphical Scale: step by step (R.F. 1:50,000 example)
- Take a conventional length (Metric ≈15 cm, English ≈6 inches) → calculate the ground distance it represents (15×50,000÷100,000 = 7.5 km) → choose the nearest round number (5 km) → work out the new line length accordingly (15×5÷7.5 = 10 cm) → draw the line and divide it into main parts (5×1 km) and the left part into sub-divisions (10×100 m)
When the resulting line length is awkward (such as 6.34 inches), measuring it out directly into equal parts is inaccurate. Method (book): draw lines at 40° or 45° from the start node and the end node of the line (one above, one below), divide each into the same number of equal parts (e.g. 5 parts of 1 or 1.5 inches), join the divisions with dotted lines (1 to 4, 2 to 3, 3 to 2, 4 to 1), and mark where the joins cut the line: these are the equal parts.
- Scale = ratio of map distance : ground distance; without scale = sketch
- Two systems: Metric (km-m-cm, used in India after 1957) and English (mile-furlong-yard-foot, used in India before 1957)
- Three methods: Statement (simple, invalid on resizing), Graphical (valid even after resizing), Representative Fraction (unit-free, universal, most suitable)
- Remember the derived values: 1 mile = 63,360 inches, 1 furlong = 7,920 inches, 1 km = 100,000 cm
- Statement→R.F.: convert the distance into one unit and write it as a fraction; R.F.→Statement: divide the denominator by the appropriate conversion number
- 5 construction steps: conventional length → ground-distance calculation → nearest round number → new length → draw and divide the line; use the 40°/45° geometric method if the length is awkward
Can I state, in order, all five steps of constructing a graphical scale from R.F. 1:50,000? Can I explain why the Representative Fraction is called a universal method? Do I remember that 1 mile = 63,360 inches and 1 furlong = 220 yards?