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A direction measured in angular units from some reference line. Also known as an azimuth or a heading.

The reference line could be a grid line, a meridian (longitude line), or magnetic north.

The angular units are usually in degrees-minutes-seconds, decimal degrees, or gons (grads).

While bearing and azimuth are synonyms, there are context-based distinctions:

North American surveyors sometimes distinguish between azimuths as ranging clockwise [0 - 360), and bearings as ranging clockwise or anticlockwise [0 - 90) in four quadrants, N-E, N-W, S-E, S-W.

Geodesists sometimes distinguish between azimuths as measured from a meridian on an ellipsoid, and bearings as measured from a grid line on a plane (map).

Related concepts:

A declination is an angular difference between two different north directions. Typically, a declination diagram illustrates and quantifies the relationships between grid north, true north (the local meridian), and magnetic north.

An orientation, ranging [0 - 180), can be considered to be a non-specific bearing in the sense that a line segment has one orientation but two bearings (depending which end has the "arrow-head").

A deflection angle (sometimes used by surveyors) is a direction measured (left or right) from the forward direction of travel.

A turned angle (often used by surveyors) is a direction measured (left or right) from the reverse direction of travel.

Note for programmers:

In mathematics and computing, directions are usually measured counter-clockwise from the easterly grid line (ie, the +ve X-axis) in radians, so conversions are often required.