A bearing is an angle measured clockwise from North, always written as a three-figure number (e.g. 045°, not 45°). To find a bearing, stand at the starting point, face North, then rotate clockwise until you face the target. The angle you have turned through is the bearing.
What is a bearing in maths?
A bearing describes the direction from one point to another. Navigators, pilots and map-readers use bearings because they give an unambiguous direction anywhere in the world. In KS3 maths, bearings combine angle-measuring skills with map work.
Three rules make every bearing question manageable:
- Measure from North. Always start at the North line at the point you are measuring from.
- Go clockwise. Bearings increase in the clockwise direction.
- Use three figures. Write all bearings with three digits: 005°, 045°, 180°, 270°.
How do you draw and measure a bearing?
To draw the bearing of B from A:
- Mark point A and draw a vertical North line at A (pointing upward on your page).
- Place the centre of your protractor at A, aligned with the North line.
- Measure the required angle clockwise from North.
- Draw the line from A in that direction to reach B.
To measure an existing bearing on a diagram:
- Draw a North line at the starting point if one is not already shown.
- Place your protractor at that point, zero on North.
- Read off the angle clockwise to the given direction.
- Write it with three figures.
Worked example: stating a bearing
A ship sails from Port A to Port B. B is to the north-east of A (exactly 45° clockwise from North). What is the bearing of B from A?
- Starting at A, North is straight up.
- Rotating clockwise 45° from North reaches the north-east direction.
- The bearing is written as three figures: 045°.
| Direction | Bearing |
|---|---|
| North | 000° |
| East | 090° |
| South | 180° |
| West | 270° |
| North-East | 045° |
| South-West | 225° |
How do you find the back bearing (return bearing)?
The back bearing is the bearing from B back to A. It is the reverse direction. To find it:
- If the original bearing is less than 180°, add 180°: e.g. 045° + 180° = 225°.
- If the original bearing is 180° or more, subtract 180°: e.g. 250° − 180° = 070°.
This works because A and B are directly opposite each other on a bearing, so they differ by exactly 180°.
Worked example: back bearing
A lighthouse (L) is on a bearing of 110° from a boat (B). What is the bearing of B from L?
- Original bearing 110° is less than 180°, so add 180°.
110° + 180° = 290°- The bearing of B from L is 290°.
- Check on a rough sketch: 290° is north-west, which is the opposite direction from south-east (110°). ✓
What protractor errors should you avoid?
- Using the wrong scale. Most protractors have two scales (0–180° on each half). Make sure you start at 0° and count clockwise. If the bearing should be between 090° and 180° but you read a value over 180°, check you used the clockwise scale.
- Forgetting the North line. A bearing is always measured from North, not from the horizontal. Draw the North line first every time.
- Omitting the third digit. A bearing of 45° loses the mark; write 045° for full credit.
Frequently asked questions
What is a three-figure bearing?
A three-figure bearing is a direction written using exactly three digits, always measured clockwise from North. Values run from 000° (North) to 359°. The three-figure convention prevents ambiguity — 45° could be misread as 145°, but 045° cannot.
How do you know if a bearing is correct?
Check three things: it is measured clockwise from North; it has three figures; and it looks sensible on a sketch (e.g. a point to the east should have a bearing close to 090°). If the bearing is meant to be roughly south-east and you have 035°, something has gone wrong.
Why do bearings always start from North?
North is the universal reference direction on maps and compasses. Starting every bearing from the same reference means two people measuring the same direction always get the same number, regardless of where they are or which way their map is oriented.
What is the bearing for south-west?
South-west is exactly halfway between South (180°) and West (270°). The bearing for south-west is 225°. You can calculate it as 180° + 45° = 225°, since south-west is 45° past South going clockwise.
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