What you'll learn
This topic covers bearings — a way of describing direction used in navigation and map work. In this guide you will learn how to measure and write bearings, how to find a back bearing, how to combine bearings with scale drawings, and how to use them with trigonometry. Careful measuring and the three-figure rule are the keys to success.
Key terms and definitions
Bearing — an angle measured clockwise from north, written with three figures.
North line — the reference direction (straight up) from which bearings are measured.
Back bearing — the bearing for the return journey (the reverse direction).
Three-figure bearing — a bearing always written with three digits (e.g. 050°).
Scale drawing — an accurate diagram used to find real distances and directions.
Core concepts
Measuring a bearing
A bearing is measured clockwise from north and always written with three figures — so 50° is written 050° and a full turn is 360°. Always draw the north line at the point you are measuring from, then measure the clockwise angle to the direction of travel.
Writing bearings correctly
Because they have three figures, bearings range from 000° to 360°. East is 090°, south is 180° and west is 270°. The three-figure rule avoids confusion, so never write a bearing as just "50".
Back bearings
The back bearing is the direction for the return journey. If the outward bearing is less than 180°, add 180°; if it is 180° or more, subtract 180°. For example, a bearing of 070° has a back bearing of 250°.
Bearings with scale drawings
To solve a journey problem by scale drawing, draw a north line, measure the bearing with a protractor, and draw the distance to scale. Repeat for each leg. You can then measure the final bearing and distance back to the start.
Bearings with trigonometry
Right-angled journeys can be solved with Pythagoras and trigonometry instead of drawing. Form a right-angled triangle from the north–south and east–west components, find the missing side or angle, then convert the angle into a three-figure bearing.
Worked examples
Example 1: Back bearing
The bearing of B from A is 065°. Find the bearing of A from B.
Less than 180°, so add 180°: 065 + 180 = 245°.
Example 2: Back bearing (over 180°)
The bearing of Q from P is 210°. Find the bearing of P from Q.
210 − 180 = 030°.
Example 3: Cardinal direction
Write the three-figure bearing for due west.
270°.
Common mistakes and how to avoid them
Dropping a figure. Always write three figures (050°, not 50°).
Measuring anticlockwise. Bearings go clockwise from north.
No north line. Draw it at the point you measure from.
Adding/subtracting 180° the wrong way. Add if under 180°, subtract if 180° or more.
Mismeasuring with the protractor. Line up 0° with north carefully.
Exam technique for Bearings
Measure clockwise from north and write three figures.
Draw a north line at each measuring point.
Use +180° or −180° for back bearings.
Draw legs to scale for journey problems.
Use trigonometry for right-angled bearing problems.
Quick revision summary
A bearing is measured clockwise from north and written with three figures (050°, not 50°), ranging from 000° to 360° — east is 090°, south 180°, west 270°. Always draw a north line at the point you are measuring from and measure the clockwise angle. The back bearing (return direction) is found by adding 180° if the bearing is under 180°, or subtracting 180° if it is 180° or more. For journey problems, use a scale drawing — north line, protractor angle, distance to scale for each leg — or, for right-angled cases, use Pythagoras and trigonometry on the north–south and east–west components. The common errors are dropping a figure, measuring anticlockwise, omitting the north line, and adjusting back bearings the wrong way. Measure clockwise from north, write three figures, draw north lines, and use scale drawings or trigonometry to solve.