⛰ Steep slope
Contours are close together. The land rises or falls a lot over a short distance.
Cartographic Skills » Contours, Gradient and Cross-Sections
What you'll learn this session
Study time: 30 minutes
Cambridge spec: Geographical skills, Cartographic skills
- How contour lines, spot heights and triangulation pillars show height and shape
- How to recognise slopes, valleys, ridges, hills and plateaus from contours
- How to calculate height differences and gradient
- How to draw and interpret a cross-section, and what a transect is
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Unlock This CourseShowing height on a flat map
A map is flat, but the land is not. Geographers call the shape and height of the land its relief. On the maps in this course, relief is shown with three tools: contour lines, spot heights and triangulation pillars.
Key terms:
- Relief: the shape and height of the land.
- Contour line: a line on a map joining places that are the same height above sea level.
- Contour interval: the difference in height between one contour line and the next. It is given in the key.
- Spot height: a point on the map marked with a dot and a number that gives its exact height.
- Triangulation pillar: a surveyor's concrete marker on a hilltop, drawn as a triangle with a dot and its height beside it.
Imagine slicing a hill into layers like a cake, each layer the same thickness. The edge of every slice, seen from above, is a contour line. If the contour interval is 20 m, the lines are at 20 m, 40 m, 60 m and so on.
Reading contour patterns
The spacing and shape of contours tell you what the land looks like. Look at the numbers first, so you know which way is uphill.
🏖 Gentle slope
Contours are far apart. The land rises or falls only a little over the same distance.
| Landform | What the contours look like |
|---|---|
| Hill | Closed rings, one inside another, with the highest number in the middle. |
| Valley | V-shaped or U-shaped bends pointing uphill, towards higher ground. A river flows down the valley the opposite way. |
| Ridge | Bends pointing downhill, away from the higher ground, along a raised strip of land. |
| Plateau | Contours close together at the sides (steep edges), then a wide area inside with few or no contours (a high, flat top). |
Calculating height differences
To find a difference in height, subtract the lower height from the higher height. Read each height from a contour label, a spot height or a triangulation pillar. If a point is between two contours, say so: it is higher than the lower line and lower than the upper line.
Worked example
On a made-up map of Kestrel Hill, a triangulation pillar on the summit is marked 218 m and a spot height beside the lake is marked 74 m.
Height difference = 218 − 74 = 144 m.
Calculating gradient
Gradient tells you how steep a slope is.
Gradient
Gradient = vertical difference (height) ÷ horizontal distance. Both must be in the same units, so change kilometres or centimetres to metres first.
Give the answer as a ratio, written 1 in x. A gradient of 1 in 20 can also be written as the ratio 1:20, and it means the land rises 1 m for every 20 m you go across. The smaller the number after "1 in", the steeper the slope. So 1 in 5 is steeper than 1 in 20.
Worked example 1
Point A is at 120 m and point B is at 170 m. On a 1:25 000 map they are 4 cm apart.
Step 1: height difference = 170 − 120 = 50 m.
Step 2: 4 cm × 250 m = 1000 m. (On 1:25 000, 1 cm is 250 m.)
Step 3: gradient = 50 ÷ 1000 = 1/20, so 1 in 20.
Worked example 2
Point C is at 200 m and point D is at 350 m. On a 1:50 000 map they are 3 cm apart.
Step 1: height difference = 350 − 200 = 150 m.
Step 2: 3 cm × 500 m = 1500 m. (On 1:50 000, 1 cm is 500 m.)
Step 3: gradient = 150 ÷ 1500 = 1/10, so 1 in 10. This is steeper than example 1.
Drawing a cross-section
A cross-section is a side view of the land along a straight line drawn on the map. It shows the ups and downs as if the land had been cut open.
Key term:
- Cross-section: a diagram of the height of the land along a line, seen from the side.
- Draw a straight line on the map between the two points (X and Y).
- Lay the straight edge of a strip of paper along the line. Mark X, then mark every place where a contour crosses the edge. Write the height by each mark. Mark Y.
- Draw a horizontal axis on graph paper the same length as the line, so the horizontal scale matches the map.
- Draw a vertical axis for height. Choose a sensible scale, such as 1 cm = 20 m, and label it.
- Move the paper onto the graph. At each mark, plot a cross at the right height.
- Join the crosses with a smooth line. Label X and Y, and add the scale and a title.
Worked example
A line X to Y on a made-up 1:25 000 map is 9 cm long. The contour interval is 20 m. Reading along the line gives:
| Distance from X (cm) | 0 | 1.0 | 1.8 | 2.2 | 3.8 | 5.0 | 7.0 | 9.0 |
|---|---|---|---|---|---|---|---|---|
| Height (m) | 40 | 60 | 80 | 100 | 100 | 80 | 60 | 40 |
A spot height of 108 m is on the summit between 2.2 cm and 3.8 cm. With a vertical scale of 1 cm = 20 m, the crosses go at 2, 3, 4 and 5 cm up the axis, and the summit at 5.4 cm.
West side, from 1.8 cm to 2.2 cm: 0.4 cm × 250 m = 100 m across, 20 m up, so the gradient is 20 ÷ 100 = 1 in 5 (steep).
East side, from 3.8 cm to 7.0 cm: 3.2 cm × 250 m = 800 m across, 40 m down, so the average gradient is 40 ÷ 800 = 1 in 20 (gentle).
To interpret a cross-section, describe the shape using figures: where it is highest, where it is steepest, where it is gentle or flat. The steep side is where the line climbs quickly. A cross-section with a larger vertical scale than horizontal scale makes slopes look steeper than they really are.
Transects
Key term:
- Transect: a straight line across an area along which measurements or observations are made at set points.
A cross-section shows height along a line. A transect also records data along a line, but it can record things other than height, such as plant cover, pebble size or the number of people. To interpret one, look for the overall trend, then the biggest change, and quote figures.
Made-up transect from the sea inland across sand dunes:
| Distance from the sea (m) | 0 | 20 | 40 | 60 | 80 |
|---|---|---|---|---|---|
| Plant cover (%) | 0 | 5 | 20 | 50 | 70 |
Plant cover increases steadily with distance from the sea, from 0% to 70%. The biggest increase is between 40 m and 60 m, where it rises by 30 percentage points.
Common mistakes
Common mistakes
- Saying contours show how far apart places are. They show height.
- Mixing units in a gradient: 50 m divided by 4 (cm) is wrong. Convert the distance to metres first.
- Writing the gradient as 20 in 1 instead of 1 in 20.
- Calling close contours a gentle slope. Close together means steep.
- Joining the plotted crosses of a cross-section with straight ruler lines instead of a smooth line, or not labelling the axes.
- Reading a contour height wrongly because the contour interval was not checked in the key.
Exam-style question
Fig. 1.1 is a made-up 1:50 000 map of part of a valley. Point A is at 45 m and point B is at 120 m. They are 3 cm apart on the map.
(a) Define the term contour line. [1]
(b) Calculate the difference in height between A and B. [1]
(c) Calculate the gradient from A to B. Give your answer as 1 in x. [3]
(d) Describe how contour lines show a steep slope. [2]
(e) Explain how contours, spot heights and a cross-section can be used together to describe the relief of an area. [6]
Model answer
(a) A line on a map that joins places of the same height above sea level (1).
(b) 120 − 45 = 75 m (1).
(c) 3 cm × 500 m = 1500 m (1). 75 ÷ 1500 (1) = 1/20, so 1 in 20 (1).
(d) The contour lines are close together (1), because the height changes a lot over a short distance (1).
(e) Level 3 (5-6 marks): Contour lines show the shape of the land: where they are close together the slope is steep, and where they are far apart it is gentle, and closed rings show a hill. Spot heights give the exact height of particular points such as a summit, which the contour lines alone cannot do. A cross-section is then drawn along a line by marking each contour crossing and plotting its height, which turns the flat map into a side view. This shows clearly where the land is highest, where it is steepest and where it is flat. The gradient of each part can be calculated from the heights and the scale. Together, the three methods give a complete description of the relief.
Exam tip
In a gradient question, write the height difference and the distance in metres on separate lines before you divide. Marks are often given for each step, even if the final answer is wrong.