Scale and measuring distance
FoundationScale converts map distance into real distance: 1:10000 means 1 cm on the map = 100 m on the ground. Measure straight lines with a ruler and curved lines with string or paper.
- Scale comes as statement, fraction or linear bar
- 1:10000 = 1 cm to 100 m
- Ruler for straight lines; string or paper for curves
§Text Passage
1This lesson is about map scale: on a 1:10,000 map, 1 centimetre stands for 100 metres on the ground. You will learn the three ways to show scale — a line scale, a statement scale and a ratio scale — plus how to use a piece of string or a strip of paper to measure winding rivers and roads.
2The idea behind scale is simple: a map is the real world shrunk by a fixed ratio. As long as the ratio stays constant, map distance and ground distance stay proportional. Multiply the map distance by the scale denominator to get the real distance. Large-scale maps show more detail; small-scale maps cover larger areas.
3Hong Kong's most widely used HM20C maps are at 1:20,000 and are the standard for planning hikes, while national and world maps are usually small-scale. Try measuring the straight-line distance from Central to the Peak and compare it with the actual bus route — all those bends make the journey much longer.
1Summary 重點摘要
Scale converts map distance into real distance: 1:10000 means 1 cm on the map = 100 m on the ground. Measure straight lines with a ruler and curved lines with string or paper.
2Vocabulary cards Vocabulary
The ratio between map distance and real-world distance.
Written in words, e.g. '1 cm to 1 km'.
Written as a ratio, e.g. 1:10000.
A ruled bar on the map you can read directly.
A winding road or river, measured with string or a paper strip.
A map with a smaller denominator, covering less area in more detail, e.g. 1:10000.
A map with a larger denominator, covering more area in less detail, e.g. 1:1000000.
The shortest length between two points, measured with a ruler.
3Step by step Steps
- Three ways to write itScale can be written in three ways: a statement scale such as '1 cm on the map represents 1 km on the ground'; a representative fraction such as 1:100000; or a linear scale drawn as a small ruler. All three say exactly the same thing and can be converted into one another. Hong Kong's most widely used HM20C maps are drawn at 1:20000, and planning a hike or estimating a bus journey depends on reading that scale correctly.
- Learn to convertConversion is the basic skill of measuring distance: 1:10000 means 1 cm on the map equals 10000 cm on the ground — 100 m, or 0.1 km. The larger the denominator, the smaller the scale: the map covers more ground but with less detail, which is why national and world maps are usually small-scale. In answers, always lay out the conversion step by step, from centimetres to metres and then to kilometres, so the units cannot go wrong.
- Measure distanceFor a straight line, measure the distance between the two points with a ruler and convert it by the scale. Curved lines are trickier: roads and rivers bend, so lay a piece of string or a strip of paper along the curves, mark the start and end points, then straighten the string and read it against the scale. Only this method gives the distance you would actually travel — a ruler alone cannot measure a winding route.
- Curves: a tipWhen laying the string along a winding road, keep it close to the line and neither too tight nor too loose, because an over-taut string shortens the measurement. Take a real example: the straight-line distance from Central to the Peak is far shorter than the actual road journey, because the road winds — the curved distance is the distance truly travelled. Care in laying the string therefore decides how accurate the result is, so work with extra attention.
- Make the most of the linear scaleThe linear scale is a small bar printed on the map edge: copy the map distance between two points onto a strip of paper, hold the strip against the linear scale, and the ground distance can be read off directly — no multiplying or dividing needed. Better still, when a map is enlarged or reduced, statement and ratio scales both become wrong, but the linear scale shrinks and grows with the map and stays true, so rely on it especially for reprinted maps.
- Turn distance into timeOnce the ground distance is known, the walking time can be estimated: on flat ground most people manage about 4 km per hour, and climbing adds time on top of the distance. An 8 km flat section of a trail, for example, takes about 2 hours; add roughly another hour for 400 m of ascent. Working out the total time before setting out, with a margin to spare, keeps you off the trail after dark and makes the whole journey safer.
4Diagrams Diagrams
5Worked example Example
Example: two points are 5 cm apart on a map with scale 1:20000. What is the real distance?
- 1:20000 means 1 cm represents 20000 cm
- 5 cm × 20000 = 100000 cm
- Convert: 100000 cm = 1000 m = 1 km
- Recheck units step by step: cm to m to km, to avoid slips
- Answer: The real distance is 1 km. A scale of 1:20000 means 1 cm on the map stands for 20000 cm on the ground; 5 cm measured gives 5 × 20000 = 100000 cm, i.e. 1000 m — 1 km. In exams show every step of 'cm → m → km' so the units cannot go wrong.
6Common mistakes Mistakes
7Quick check Quick check
Q1On a 1:5000 map, what does 1 cm represent?
Q2Which map covers more area: 1:10000 or 1:100000?
Q3How do you measure a winding river's length?
Q4Two points are 4 cm apart on a 1:25000 map. What is the ground distance?
Q5After a map is enlarged by photocopying, which kind of scale can still be used directly?
8Recap Recap
- Scale comes as statement, fraction or linear bar
- 1:10000 = 1 cm to 100 m
- Ruler for straight lines; string or paper for curves
- Large scale = more detail; small scale = wider coverage
- Ground distance = map distance × denominator; watch the units