Introduction to Bearings and Maps
Bearings and maps are essential tools for navigation, helping us understand direction and location. Whether you're hiking, planning a journey, or working in fields like surveying or construction, knowing how to use bearings and interpret map scales is a crucial skill.
This page will guide you through the basics of bearings, how to read map scales, and how to use them together effectively.
What are Bearings?
A bearing is an angle, measured in degrees, that describes the direction of one point from another. Key things to remember about bearings:
- They are always measured clockwise from the North line.
- They are always written as three figures. For example, an angle of 45° is written as 045°, 90° as 090°, and 270° as 270°.
- You need a North line at the point you are measuring from.
- A protractor is used to measure bearings on a map.
How to measure a bearing (e.g., of B from A):
- Draw a North line at point A (the point you are measuring from).
- Place the centre of your protractor on point A.
- Align the 0° mark of your protractor with the North line.
- Draw a line from A to B (the point you are measuring to).
- Read the angle clockwise from the North line to the line AB. In the diagram, this is 048°.
Understanding Map Scales
A map scale tells you the relationship between a distance on a map and the corresponding distance in the real world. It's crucial for working out actual distances.
Scales can be shown in different ways:
- As a ratio: e.g., 1:50,000 (1 unit on the map represents 50,000 of the same units in reality).
- As a statement: e.g., 1 cm = 1 km (1 centimetre on the map represents 1 kilometre in reality).
- As a scale bar: A printed line on the map marked with distances.
Diagram showing a map distance and a scale bar.
Example: Using a scale of 1 cm = 100 m
If a distance on the map measures 12 cm, what is the real distance?
- Map distance = 12 cm
- Scale: 1 cm on map = 100 m in real life
- Real distance = Map distance × Scale value
- Real distance =
12 cm × 100 m/cm = 1200 m - This can also be converted to kilometres:
1200 m ÷ 1000 = 1.2 km
Using Bearings and Scales Together
Combining bearings and scales allows you to pinpoint locations and plan routes.
Back Bearings
If you know the bearing from point A to point B, the back bearing is the direction from point B back to point A. It's useful for checking your position or returning along the same path.
Rule for Back Bearings:
- If the original bearing is less than 180°, add 180° to find the back bearing.
- If the original bearing is 180° or more, subtract 180° to find the back bearing.
Example from diagram: If the bearing from A to B is 070°, the back bearing from B to A is 070° + 180° = 250°.
Worked Examples
Example 1: Calculating Real Distance
A map has a scale of 1 cm = 2 km. The distance between two towns on the map is 7.5 cm. What is the actual distance between the towns?
- Identify the map distance: 7.5 cm.
- Identify the scale: 1 cm = 2 km.
- Multiply the map distance by the scale factor for distance:
7.5 cm × 2 km/cm = 15 km.
Answer: The actual distance is 15 km.
Example 2: Finding a Bearing and Distance
Point X is directly North of point Y. Point Z is on a bearing of 120° from point Y and is 500m away. If the map scale is 1cm = 100m, describe how to find point Z from Y, and what distance you would measure on the map.
- Finding Z from Y:
- At point Y, draw a North line.
- Measure an angle of 120° clockwise from the North line.
- Point Z lies along this 120° line.
- Map Distance:
- Real distance to Z = 500m.
- Scale: 1cm = 100m.
- Map distance = Real distance ÷ Scale value (per cm) =
500m ÷ 100m/cm = 5 cm.
- Draw a line 5cm long from Y along the 120° bearing to mark point Z.
Answer: Measure 5cm from Y on a bearing of 120°.
Example 3: Calculating a Back Bearing
The bearing of a lighthouse from a ship is 310°. What is the bearing of the ship from the lighthouse?
- The original bearing is 310°.
- Since 310° is greater than 180°, subtract 180° to find the back bearing.
- Back bearing =
310° - 180° = 130°.
Answer: The bearing of the ship from the lighthouse is 130°.
Interactive Tools
Scale Distance Calculator
Convert map distance to real distance.
Back Bearing Calculator
Calculate the back bearing from a given bearing.
Test Your Skills!
1. A bearing is measured clockwise from which direction?
Answer: North
2. How many figures are used to write a bearing (e.g., 60 degrees)?
Answer: Three (e.g., 060°)
3. A map scale is 1:50,000. If a road is 4cm long on the map, what is its actual length in cm and km?
Answer: 200,000 cm, which is 2 km.
Explanation: Actual length = 4 cm × 50,000 = 200,000 cm.
To convert cm to km: 200,000 cm ÷ 100,000 (cm per km) = 2 km.
4. The bearing of town B from town A is 135°. What is the back bearing of town A from town B?
Answer: 315°
Explanation: 135° + 180° = 315°.
5. On a map with a scale 1cm = 50m, a path is drawn 6.5cm long. How long is the actual path?
Answer: 325m
Explanation: 6.5 cm × 50 m/cm = 325 m.
Exam-Style Problems
1. A hiker walks on a bearing of 045° for 3 km, then changes direction and walks on a bearing of 120° for 4 km. If the map scale is 1 cm = 0.5 km, what distances would these be on the map?
Answer: First leg: 6 cm, Second leg: 8 cm.
Explanation:
- First leg (3 km): Map distance = Real distance / Scale value (km per cm) = 3 km / 0.5 km/cm = 6 cm.
- Second leg (4 km): Map distance = 4 km / 0.5 km/cm = 8 cm.
2. A boat sails from port P on a bearing of 290° to a lighthouse L. What is the bearing of port P from the lighthouse L?
Answer: 110°
Explanation:
- Original bearing = 290°.
- Since 290° is greater than 180°, subtract 180°: 290° - 180° = 110°.
3. A map has a scale of 1:25,000. A straight path measures 8cm on the map.
a) What is the actual length of the path in cm?
b) What is the actual length of the path in metres?
c) What is the actual length of the path in kilometres?
Answers:
a) 200,000 cm
b) 2,000 m
c) 2 km
Explanation:
- a) Actual length (cm) = Map length × Scale factor = 8 cm × 25,000 = 200,000 cm.
- b) Actual length (m) = 200,000 cm ÷ 100 cm/m = 2,000 m.
- c) Actual length (km) = 2,000 m ÷ 1000 m/km = 2 km.
Key Takeaways for Bearings and Maps
- Bearings are always measured clockwise from North.
- Bearings are always written with three figures (e.g., 005°, 070°, 135°).
- A map scale shows the ratio between map distance and real-world distance.
- To find real distance: Multiply map distance by the scale factor. Ensure units are consistent or convert as needed.
- To find map distance: Divide real distance by the scale factor. Ensure units are consistent.
- Back bearings: If bearing A to B is X°, then bearing B to A is X° + 180° (if X < 180°) or X° - 180° (if X ≥ 180°).
- Always draw a North line at the point you are measuring a bearing from.