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Bearings

What you'll learn

  • What a bearing is and why it is always written with three figures.
  • How to read a bearing from a diagram.
  • How to draw a bearing using a protractor.
  • How to find a reverse bearing, such as going back from B to A.

The basics you need first

A compass direction tells you which way something is facing. The main compass directions are North, East, South and West.

A North line is a line drawn upwards from a point and usually labelled N. It is the starting line for every bearing.

Clockwise means the direction the hands of a clock move: round to the right, then down, then left.

What is a bearing?

A bearing is a special angle used to describe direction.

Definition

Bearing

A bearing is an angle measured from North, going clockwise, and written using three figures, such as 067° or 125°.

A bearing is measured clockwise from the North line at the starting point.

Key Idea

The three bearing rules

  • Start measuring from North.
  • Measure clockwise.
  • Write the answer using three figures.

Reading a bearing from a diagram

When a question says “the bearing of B from A”, you start at A. The word from tells you where the angle begins.

Example

Reading a bearing from a diagram

Imagine point A has a North line drawn upwards. The line from A to B is to the right of North, and the clockwise angle from North to AB is 67°.

The bearing of B from A is the clockwise angle measured at A from North to AB.

  1. Start at A, because the bearing is of B from A.

  2. Look at the North line drawn at A.

  3. Turn clockwise from North until you are pointing along the line AB.

  4. The angle is 67°, so write it as a three-figure bearing: 067°.

Common Mistake

Mixing up from and to

In “the bearing of B from A”, you measure at A, not at B. If you measure at the wrong point, you usually find the opposite direction.

Three-figure bearings

A three-figure bearing always has three digits.

So:

  • 7° becomes 007°
  • 42° becomes 042°
  • 115° stays 115°

You add zeros at the front if the angle has fewer than three digits.

Tip

Leading zeros matter

If your bearing is less than 100°, check whether you need a zero at the front. For example, 58° must be written as 058°.

Example

Writing a small angle as a bearing

At point P, the clockwise angle from North to point Q is 34°. Write the bearing of Q from P.

A small clockwise angle from North is written as a three-figure bearing using a leading zero.

  1. The angle has been measured from North.

  2. It has been measured clockwise.

  3. The angle is 34°, which has only two digits.

  4. Add a zero at the front, so the bearing of Q from P is 034°.

Drawing a bearing

To draw a bearing, you usually need a ruler and a protractor. A protractor is the tool used to measure and draw angles.

The key idea is: draw the North line first, then measure clockwise from it.

Example

Drawing a bearing

Draw point Q so that it is 5 cm from P on a bearing of 120°.

A bearing of 120° is measured clockwise from North and places Q down and to the right of P.

  1. Draw and label point P.

  2. Draw a vertical North line upwards from P and label it N.

  3. Place the centre of your protractor on P.

  4. Line up 0° on the protractor with the North line.

  5. Measure 120° clockwise and make a small mark.

  6. Draw a straight line from P through the mark.

  7. Measure 5 cm along this line and label the point Q.

Tip

Check the direction

A bearing of 120° should point down and to the right, because it is more than 90° but less than 180°.

When the angle is on the other side of North

Sometimes a diagram shows a small angle going anticlockwise from North. Anticlockwise means the opposite direction to the hands of a clock.

That small angle is not the bearing. Bearings must go clockwise, so you need to go all the way round from North.

Example

Finding a bearing using 360°

At point C, the line to D is 35° anticlockwise from North. Find the bearing of D from C.

The marked 35° anticlockwise angle is not the bearing; the bearing is the clockwise angle all the way round from North to CD.

  1. Start at C, because the bearing is of D from C.

  2. The 35° angle goes anticlockwise, so it is not the bearing.

  3. A full turn around a point is 360°. Subtract the small angle from a full turn:

    360∘−35∘=325∘360^\circ - 35^\circ = 325^\circ360∘−35∘=325∘

  4. The bearing of D from C is 325°.

Common Mistake

Using the small anticlockwise angle

If the diagram shows 35° to the left of North, the bearing is not 035°. You must measure clockwise, so the answer is 325°.

Reverse bearings

A reverse bearing is the bearing for travelling back the other way.

For example, if you know the bearing of B from A, the reverse bearing is the bearing of A from B.

Definition

Reverse bearing

A reverse bearing points in the opposite direction. Opposite directions differ by 180°.

Reverse bearings are opposite directions, so their directions differ by 180°.

To find a reverse bearing:

  • If the bearing is less than 180°, add 180°.
  • If the bearing is more than 180°, subtract 180°.
Example

Finding the bearing back again

A walker travels from village V to tower T on a bearing of 072°. Find the bearing of V from T.

The return journey from T to V is the reverse bearing of the original 072° journey from V to T.

  1. The new bearing starts at T, because you are finding the bearing of V from T.

  2. This is the opposite direction to the original journey.

  3. Add 180° because 072° is less than 180°:

    072∘+180∘=252∘072^\circ + 180^\circ = 252^\circ072∘+180∘=252∘

  4. The bearing of V from T is 252°.

Example

Reverse bearing when the angle is large

A ship travels from A to B on a bearing of 230°. Find the bearing of A from B.

For a bearing greater than 180°, the reverse direction is found by looking back from B to A.

  1. You are now looking back from B to A.

  2. Opposite directions differ by 180°.

  3. Subtract 180° because 230° is more than 180°:

    230∘−180∘=050∘230^\circ - 180^\circ = 050^\circ230∘−180∘=050∘

  4. Write the answer with three figures: 050°.

Exam technique

In the exam

  1. Read the wording carefully: the point after from is where you measure the angle.

  2. Check the three bearing rules before writing your answer: North, clockwise, three figures.

  3. If you have found a small anticlockwise angle, use 360° minus that angle; if you need the reverse direction, add or subtract 180°.

Self review

Check yourself

  • Why is 35° written as 035° when it is a bearing?

  • If a bearing is measured at point A, which phrase tells you that in the question?

  • What calculation helps when the marked angle is anticlockwise from North?

Recap questions

Test yourself with 5 quick questions on this guide. Answer them all correctly to complete it.

How was this guide?

Bearings Revision Guide

  1. GCSE
  2. /Maths
  3. /Bearings