North, east, south and west
A compass needle points north. Stand facing north, and east is on your right, south is behind you and west is on your left. These four are the main directions, called the cardinal points.
Going round clockwise, the way the hands of a clock turn, they come in the order north, east, south, west, and then north again. Each one is a quarter turn from the next. A full turn is 360°, so a quarter turn is 360 ÷ 4 = 90°.
The four cardinal points, with north at the top. Each is a quarter turn, 90°, from the next.
The four directions between them
Halfway between north and east is northeast, written NE. Its name is made of its two neighbors, north and east. The other three are named the same way: southeast (SE) is halfway between south and east, southwest (SW) between south and west, and northwest (NW) between north and west.
In each of these names, north or south comes first and east or west second. Northeast and northwest both start from north, but they lie on opposite sides of it: northeast leans toward east, northwest toward west.
Northeast lies halfway between north and east.
Eight points, 45° apart
The four new directions split each quarter turn exactly in half, so the compass now has eight points, spaced evenly around a full turn. The step from one point to the next is 360 ÷ 8 = 45°, half of a quarter turn.
Counting clockwise from north, one step reaches northeast, 45° from north. Two steps reach east, 2 × 45 = 90°. Then come southeast at 135°, south at 180°, southwest at 225°, west at 270° and northwest at 315°. One more step, 8 × 45 = 360°, is a full turn and brings you back to north.
The eight-point compass. Each point is one step of 45° from the next.
Turning clockwise and counterclockwise
A clockwise turn goes the way the hands of a clock go: from north toward east. A counterclockwise turn goes the other way: from north toward west.
From north, a quarter turn clockwise, 90°, reaches east. An eighth of a turn clockwise, 45°, stops halfway, at northeast. An eighth of a turn counterclockwise from north stops at northwest instead.
To turn by a number of points, count the steps one at a time. Face east and turn 3 points clockwise: southeast, south, southwest. You face southwest, after a turn of 3 × 45 = 135°. Face east and turn 2 points counterclockwise: northeast, north. You face north, after a turn of 2 × 45 = 90°.
Four points in either direction is 4 × 45 = 180°, a half turn, and it always reaches the opposite direction: east and west are opposite, and so are northeast and southwest.
A quarter turn clockwise from north, 90°, ends at east. It passes northeast halfway, at 45°.
The angle between two directions
To find the angle between two directions, count the steps from one to the other and multiply by 45°. There are two ways round, and they give different angles.
From north to southwest, going clockwise, the steps are northeast, east, southeast, south and southwest: 5 steps, so 5 × 45 = 225°. Going counterclockwise, they are northwest, west and southwest: 3 steps, so 3 × 45 = 135°.
The two ways round always make one full turn together: 225 + 135 = 360. So once you have one of them, the other is 360° minus it.
Clockwise from north to southwest is 5 steps, 225°. Counterclockwise it is 3 steps, 135°, and 225 + 135 = 360.
The usual mistakes
Taking the neighbor on the wrong side. Halfway between north and east is northeast. Northwest also starts with north, but it lies on the other side of north, away from east.
Turning the wrong way. A quarter turn clockwise from north reaches east; west is a quarter turn counterclockwise.
Counting a step as a quarter turn. There are eight points, so one step is 360 ÷ 8 = 45°, an eighth of a turn. A quarter turn is two steps.
A direction as an angle from north
The application below also names each direction by its angle measured clockwise from north, written with three figures by putting zeros in front: northeast is 045°, east is 090° and south is 180°. A direction given this way is called a bearing.
Turning clockwise adds to that angle, and turning counterclockwise takes away from it. Two steps clockwise from northeast is 045° + 90° = 135°, which is southeast.
Worked example: A Harbor Radar Aerial Stepping Round in Eighth-Turns
Question A harbor radar aerial parks facing north-east. To watch the eastern approach the operator steps it 3 eighth-turns clockwise. To watch the river mouth he then steps it 2 eighth-turns counterclockwise. (a) Which compass point does the aerial face after the first move, and what is that as a three-figure bearing? (b) Which compass point, and which bearing, after the second move?
1.A full turn is 360° and there are eight points on the compass, so one eighth-turn is 360 ÷ 8 = 45°. North-east is one eighth-turn clockwise from north, a bearing of 045°.
One eighth-turn is 360 ÷ 8 = 45°, and north-east is one eighth-turn from north: 045°. 2.Three eighth-turns clockwise add 3 × 45 = 135° to the bearing: 045 + 135 = 180°.
Three eighth-turns clockwise add 3 × 45 = 135°: 045 + 135 = 180°. 3.(a) A bearing of 180° is due south, so after the first move the aerial faces south.
(a) A bearing of 180° is due south, so the aerial faces south. 4.Two eighth-turns counterclockwise take 2 × 45 = 90° off the bearing: 180 − 90 = 90, written with three figures as 090°.
Two eighth-turns counterclockwise take off 2 × 45 = 90°: 180 − 90 = 090°. 5.(b) A bearing of 090° is due east, so the aerial finishes facing east. Check: three steps clockwise and two back leaves one step clockwise from north-east, and one step clockwise from 045° is 045 + 45 = 090°, due east.
(b) A bearing of 090° is due east, so the aerial finishes facing east.
Answer: (a) south, 180°; (b) east, 090°
Common mistakes
- Treating an eighth-turn as 90° because a quarter-turn is 90°. There are eight compass points in a full turn, so one step is 360 ÷ 8 = 45°, half of a quarter-turn.
- Adding the counterclockwise steps as well, giving 180 + 90 = 270° and calling the aerial west. A clockwise turn increases a bearing and a counterclockwise turn decreases it, so the second move is subtracted.
More compass directions and bearings problems, worked step by step →