The direction shown is east from point O. What is the bearing?
Bearings are measured clockwise from north.
East is 90° clockwise from north, so the bearing is 090°.
Bearings
Bearings describe direction using angles measured clockwise from north. They are commonly used in navigation-style GCSE Maths questions and often combine with angle rules, trigonometry and loci and constructions.
Overview
A bearing is a way of describing direction using angles.
Bearings are always measured clockwise from north.
Bearings are written as three-digit angles, for example \(045^\circ\), \(120^\circ\), \(275^\circ\)
In GCSE Maths, you need to be able to read bearings from diagrams, write them correctly, and use angle facts to solve missing bearing problems.
What you should understand after this topic
- Understand what a bearing is
- Explain why bearings are measured clockwise from north
- Write bearings using three digits
- Find reverse bearings
- Solve angle problems involving bearings
Key Definitions
Bearing
A direction given as an angle measured clockwise from north.
North Line
The vertical reference line from which a bearing is measured.
Clockwise
The same direction as the hands of a clock.
Three-digit bearing
A bearing written with three digits, such as \(007^\circ\) or \(085^\circ\).
Reverse Bearing
The bearing in the opposite direction.
Compass Direction
A direction such as north, south-east or west, often linked to bearings.
Key Rules
Start from north
Always measure the angle from the north line.
Measure clockwise
Bearings always go clockwise, never anticlockwise.
Use three digits
Write bearings like \(040^\circ\), not \(40^\circ\).
Full turn is \(360^\circ\)
This helps when calculating missing or reverse bearings.
Quick Recognition
North
\(000^\circ\)
East
\(090^\circ\)
South
\(180^\circ\)
West
\(270^\circ\)
Important:
If you are finding the reverse bearing, add \(180^\circ\) if the bearing is less than \(180^\circ\), or subtract \(180^\circ\) if it is \(180^\circ\) or more.
Important:
If you are finding the reverse bearing, add \(180^\circ\) if the bearing is less than \(180^\circ\), or subtract \(180^\circ\) if it is \(180^\circ\) or more.
How to Solve
What is a bearing?
A bearing gives the direction of one point from another. It is always measured as an angle clockwise from north.
Key idea: Always start from north.
Exam tip: Bearings are measured clockwise, never anticlockwise.
Step 1: Identify the north line
Every bearing starts from a north line. This is usually shown as a vertical line with an arrow pointing up.
Why this matters: If the north line is wrong, the bearing will be wrong.
Step 2: Measure clockwise
From the north line, rotate clockwise until you reach the direction line. The size of this turn is the bearing.
North → clockwise turn → direction line
Exam tip: If you turn anticlockwise, the answer is incorrect.
Step 3: Write as a three-digit angle
Bearings must always be written using three digits.
Exam tip: Always include leading zeros (e.g. 060°).
Correct
\(035^\circ\), \(090^\circ\), \(275^\circ\)
Incorrect
\(35^\circ\), \(90^\circ\), west of north
Reverse bearings
The reverse bearing is the direction going back the opposite way.
Reverse bearing = original bearing \( \pm 180^\circ \)
If the angle is less than 180°, add 180°.
If the angle is more than 180°, subtract 180°.
Bearings and angle facts
Bearings questions often combine direction with angle rules.
See full topic: angles.
- angles on a line = \(180^\circ\)
- angles around a point = \(360^\circ\)
- parallel line angle rules
- triangle angle rules
Bearings and scale drawings
Some questions require measuring bearings using a protractor, while others require calculating them using given angles.
Often used with loci and constructions and trigonometry.
Exam habit
Always draw the north line and clearly mark the clockwise angle.
Example Questions
Edexcel
Exam-style questions focusing on reading simple bearings from north.
Edexcel
The direction east is shown from point O.
Write the bearing for east.
Edexcel
A direction is 45° clockwise from north.
Write the bearing using three digits.
AQA
Exam-style questions focusing on reverse bearings.
AQA
The bearing of B from A is 120°.
Find the bearing of A from B.
AQA
The bearing of C from D is 260°.
Find the reverse bearing.
OCR
Exam-style questions focusing on reasoning with compass directions and missing bearing angles.
OCR
The direction west is shown from point O.
Explain why west is written as 270° as a bearing.
OCR
A point lies on a bearing of 145° from O.
Find the angle between the line and the south direction.
OCR
A ship travels from A on a bearing of 070°.
Explain why the bearing must be written as 070° and not 70°.
Exam Checklist
Step 1
Find or draw the north line first.
Step 2
Measure or calculate the angle clockwise from north.
Step 3
Write the bearing with three digits.
Step 4
For reverse bearings, add or subtract \(180^\circ\).
Most common exam mistakes
Wrong direction
Measuring anticlockwise instead of clockwise.
Wrong starting point
Starting from the travel line instead of the north line.
Formatting mistake
Writing \(45^\circ\) instead of \(045^\circ\).
Reverse bearing mistake
Forgetting to change the direction by \(180^\circ\).
Common Mistakes
These are common mistakes students make when working with bearings in GCSE Maths.
Measuring anticlockwise instead of clockwise
Incorrect
A student measures the angle in an anticlockwise direction.
Correct
Bearings are always measured clockwise from north. Measuring anticlockwise will give the wrong answer.
Not measuring from north
Incorrect
A student starts measuring the angle from the direction of travel instead of north.
Correct
Bearings must always be measured from the north line. The angle is taken clockwise from north to the direction of travel.
Forgetting three-figure bearings
Incorrect
A student writes a bearing as \(45^\circ\) instead of \(045^\circ\).
Correct
Bearings must be written using three digits, for example \(045^\circ\), \(120^\circ\), or \(300^\circ\).
Using the wrong reverse bearing
Incorrect
A student uses the original bearing instead of finding the reverse.
Correct
The reverse bearing differs by \(180^\circ\). Add or subtract \(180^\circ\) and ensure the result is between \(000^\circ\) and \(360^\circ\).
Ignoring angles around a point
Incorrect
A student calculates angles without considering the full turn.
Correct
Angles around a point add up to \(360^\circ\). This is often needed when finding missing bearings.
Try It Yourself
Practise measuring and calculating bearings using angles and diagrams.
Foundation
Foundation Practice
Read simple bearings from north and write bearings using three digits.
A direction is 45° clockwise from north. Write the bearing using three digits.
Bearings below 100° need a leading zero.
45° is written as 045°.
What is the bearing of south from point O?
South is a half turn from north.
South is 180° clockwise from north.
Write the bearing shown.
West is three quarters of a full turn clockwise from north.
The bearing of west is 270°.
Which rule is correct for bearings?
Bearings always start from north.
Bearings are measured clockwise from north and written with three digits.
A ship travels on a bearing of 070°. What angle is this clockwise from north?
Ignore the leading zero when finding the angle size.
070° means 70° clockwise from north.
Which is the correct three-digit bearing for 8° clockwise from north?
Use leading zeros.
8° as a bearing is written as 008°.
What is the three-digit bearing for 95° clockwise from north?
It is less than 100°, so add one leading zero.
95° is written as 095°.
A bearing of 000° points in which direction?
The angle from north is zero.
A bearing of 000° points north.
A bearing is 135°. How many degrees is it past east?
East is 090°.
135° − 90° = 45°, so it is 45° past east.
Higher
Higher Practice
Calculate reverse bearings and missing angles using diagrams.
The bearing of B from A is 120°. Find the bearing of A from B.
Reverse bearings differ by 180°.
120° + 180° = 300°, so the reverse bearing is 300°.
The bearing of Q from P is 045°. What is the bearing of P from Q?
Add 180° because 045° is less than 180°.
045° + 180° = 225°.
The bearing of C from D is 260°. Find the reverse bearing.
If the bearing is more than 180°, subtract 180°.
260° − 180° = 80°, so the reverse bearing is 080°.
The bearing of Y from X is 310°. What is the bearing of X from Y?
Subtract 180° when the bearing is greater than 180°.
310° − 180° = 130°.
A point lies on a bearing of 145° from O. Find the angle between the line and the south direction.
South is 180° from north.
180° − 145° = 35°.
A bearing is 235°. How many degrees west of south is this?
South is 180°.
235° − 180° = 55°, so it is 55° west of south.
A bearing is 070°. Find the smaller angle between the line and east.
East is 090°.
90° − 70° = 20°.
A student writes a bearing as 70°. What should they write instead?
Bearings use three digits.
70° should be written as 070°.
The bearing of B from A is 018°. Find the bearing of A from B.
Add 180°.
018° + 180° = 198°.
The bearing of B from A is 205°. Find the bearing of A from B.
Subtract 180°.
205° − 180° = 25°, so the reverse bearing is 025°.
Games
Practise this topic with interactive games.
Games coming soon.
Frequently Asked Questions
What is a bearing?
A direction measured clockwise from north.
How are bearings written?
As three-digit numbers.
What tool is used?
A protractor.