What is a three-figure bearing?
A bearing is a direction given as an angle measured clockwise from north, always written with three digits from 000° to 360°. Due east is 090°, due south is 180°, and due west is 270°.
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Compass bearings
Turn an east and north displacement into a three-figure compass bearing measured clockwise from north, plus the straight-line distance, shown on a compass rose with the bearing line and angle drawn from the start point.
bearing = (90° − atan2(N, E)) mod 360°
Frequently asked questions
Why always three digits?
Writing bearings as three figures (for example 045° rather than 45°) avoids confusion and keeps a consistent format on maps, charts, and in aviation and marine communication.
Can you give a worked example?
Moving 10 units east and 10 units north gives a bearing of 045° (north-east) and a straight-line distance of √(10² + 10²) ≈ 14.14 units.
How is the distance found?
The straight-line distance between the start and end points comes from Pythagoras applied to the east and north components: distance = √(east² + north²).
Where is this used in real life?
Sailors and pilots plot courses, hikers and orienteers navigate with map and compass, search-and-rescue teams coordinate directions, and surveyors record the bearings of boundaries.