Bearings for Beginners: How to Measure and Write Three-Figure Bearings

Bearings cause more avoidable mistakes than almost any other topic in school geometry. The idea itself is simple — describe a direction with one number — but one slip, such as reading the wrong scale or turning the wrong way, turns sound method into a wrong answer. Fix the two rules in your head and the rest becomes careful measuring.

What a bearing actually measures

A bearing is an angle measured from north and turned clockwise to the line joining your starting point to whatever you are looking at. Stand at your point, face north, then turn clockwise until you are facing the target. The angle you have turned through is the bearing. Because north is always the starting line and clockwise is the only direction allowed, every bearing sits between 000° and 360°.

Notice what a bearing does not tell you: distance. "Walk three kilometres on a bearing of 070°" carries both pieces of information — the direction and the length of the walk. A bearing on its own only says which way to look.

On a map or diagram, every north line points the same way, so they are all parallel. If you need a north line at a second point, draw it parallel to the first. A slanted north line quietly destroys an otherwise correct answer.

Why bearings are written with three figures

Bearings are normally written as three-figure angles, with the degree symbol included. A direction of 90° becomes 090°. Five degrees becomes 005°. An angle of 214° needs no padding.

The convention exists for clarity. A bare "90" on a page of working could be anything: an interior angle, a rotation, a gradient. "090°" announces itself as a bearing and nothing else. Three figures also make bearings easy to compare at a glance, because each one has the same shape and the same number of digits.

Due north is the one to think about. It is written 000°, not 360°, even though both describe the same direction. That keeps the family of answers tidy and makes it obvious you have not overshot a full turn.

Measuring a bearing with a protractor

Work through the same routine every time, even when the answer looks obvious.

1. Mark the point you are measuring from and draw a light north line through it, parallel to any other north lines on the diagram.
2. Place the centre of the protractor exactly on the point, with the 0° mark sitting on your north line.
3. Choose the scale that starts at zero on the north line. Almost every protractor has two scales running in opposite directions.
4. Read clockwise from north round to the line that joins your point to the target.
5. Write the result as three figures with a degree symbol.

When the angle is larger than 180°

Most school protractors only measure up to 180°, so a bearing of 250° will not fit on the scale directly. Measure the other way instead: read anticlockwise from north to the target line, which gives an angle under 180°, then subtract that from 360°. For a target at 250°, the anticlockwise reading is 110°, and 360° − 110° = 250°. The arithmetic is quick and it keeps you on the part of the scale you can actually read.

Five mistakes that cost marks

• Turning anticlockwise. Unless the target is due north or due south, an anticlockwise reading is not the bearing. Picture the direction of travel before you read the number.
• Reading the wrong protractor scale. The two scales give answers that add to 180°, so a bearing of 047° comes out as 133°. The wrong one often looks plausible, which is what makes it dangerous.
• Measuring from the wrong point. "The bearing of B from A" is measured at A. Reverse the two points and you need the back bearing, not the same number.
• Skipping the north line. Without it you have no starting line, and any angle you measure is guesswork.
• Dropping the leading zeros. 047° and 47° mean the same thing, but only one of them looks like a bearing.

Working backwards: back bearings

Plenty of bearing questions ask for the reverse journey. If you know the bearing of B from A, the bearing of A from B follows one rule: add 180° if the bearing is less than 180°, and subtract 180° if it is 180° or more. If B lies on a bearing of 070° from A, then A lies on a bearing of 250° from B. If the original bearing was 200°, the back bearing is 020°.

This works because the north lines at A and B are parallel, so the two bearings are allied angles and must differ by exactly 180°. It is a property of the geometry rather than a trick to memorise blindly, and knowing why it works makes it far harder to forget.

Checking your answer before you move on

Picture the compass points. East is 090°, south is 180° and west is 270°. A target to the east of your north line must have a bearing between 000° and 180°; a target to the west must fall between 180° and 360°. If your answer lands in the wrong half, you have almost certainly read the wrong scale.

Then ask whether the number is in range. Nothing above 360° or below 000° counts as a bearing. Finally, return to the wording of the question: which point came first? That is where you should have been standing.

Practising bearings so they stick

The best practice uses a real map. Take a local street map or an Ordnance Survey sheet, pick two landmarks, and work out the bearing from one to the other with a protractor and a sharp pencil. Then swap them round and check that the second answer is exactly 180° away from the first. If it is, your measuring was sound.

Sketching helps too. Draw a point, add a north line, and plot rays at 030°, 120°, 225° and 310°. A few rounds of this and the shape of the compass becomes second nature, so you can tell at a glance when an answer is pointing the wrong way.

One note if you take a compass outdoors. Magnetic north and the grid north printed on a map are not in quite the same place, and the difference depends on where you are and shifts slowly over time. For map work and exam questions, use the north lines on the page and leave the compass in your pocket.

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