Azimuth
Horizontal angle from north used in navigation and astronomy.
Azimuth is an angle measured horizontally from a fixed reference direction, most often true north, within a spherical coordinate system centered on an observer. In mathematical terms, it is the angle on a horizontal plane between a reference vector (like north) and the projection of a line from the observer to a point of interest onto that same plane. When used in astronomy, azimuth describes the horizontal direction of a celestial object, such as a star, relative to the observer's local area and true north.
The angle is typically expressed in degrees, either from 0° to 360° or from -180° to +180°. This concept is applied across fields including navigation, astronomy, engineering, mapping, geodesy, mining, and ballistics.
The word "azimuth" comes from medieval Arabic *al-sumūt*, meaning "the directions," which entered late medieval Latin through astronomical use, particularly with the astrolabe. Its first recorded use in English was in the 1390s in Geoffrey Chaucer's *A Treatise on the Astrolabe*, and the earliest known record in any Western language was in Spanish in the 1270s, in an astronomy book commissioned by King Alfonso X of Castile.
In astronomy, azimuth is one of two coordinates in the horizontal coordinate system, the other being altitude (or elevation above the horizon). It is also used for satellite dish installation. In modern astronomy, azimuth is almost always measured from the north.
In land navigation, azimuth is often denoted by the Greek letter alpha (α) and defined as a horizontal angle measured clockwise from a north baseline or meridian. More generally, it can be measured clockwise from any fixed reference plane. Today, true north is the standard reference, with east at 90°, south at 180°, and west at 270°, though some systems use south as the zero. Compass bearings may also be expressed in a quadrant system, such as "S30°E," meaning 30 degrees east of south, which corresponds to 150 degrees clockwise from north.
In geodesy, to find the azimuth from one point on Earth to another, a spherical approximation of the Earth can be used, with the formula involving the sine and cosine of latitudes and longitude. A more accurate method treats the Earth as an oblate spheroid, leading to two slightly different meanings: normal-section azimuth (measured by a theodolite perpendicular to the spheroid's surface) and geodetic azimuth (the angle between north and the shortest path on the spheroid's surface). The difference between these is negligible for distances under 100 kilometers.
- field
- Navigation, Astronomy, Geodesy, Engineering
- known_for
- Horizontal angle from north used for celestial and terrestrial positioning
Lore & Background
The azimuth is the horizontal angle measured from a reference direction, most commonly true north, to a point of interest, projected onto a plane orthogonal to the zenith. In the horizontal coordinate system used for celestial navigation, azimuth serves as one of two coordinates, paired with altitude (elevation above the horizon). Azimuth is typically expressed in degrees, either within a positive range of 0° to 360° or a signed range of -180° to +180°. For a star or other astronomical object, the reference plane is the local area around an observer on Earth’s surface, and the reference vector points to true north; the azimuth is then the angle between the north vector and the star’s vector on that horizontal plane. In land navigation, azimuth is often denoted by the Greek letter alpha (α) and defined as a horizontal angle measured clockwise from a north base line or meridian, though any fixed reference plane can be used as long as it is clearly defined. Moving clockwise on a 360-degree circle, east corresponds to 90°, south to 180°, and west to 270°. Some navigation systems use south as the reference vector instead. Compass bearings may be stated in a system where either north or south is zero, with the angle measured clockwise or anticlockwise, such as “S30°E” (30 degrees eastward from south, equivalent to 150 degrees clockwise from north). The concept is applied in navigation, astronomy, engineering, mapping, geodesy, mining, and ballistics. In geodesy, azimuth can refer to either normal-section azimuth (measured by a theodolite perpendicular to the spheroid’s surface) or geodetic azimuth (the angle between north and the shortest path on the spheroid), with the difference negligible over distances under 100 km. In cartography, grid azimuth is calculated from the coordinates of two points on a flat plane, with axes swapped relative to the mathematical polar coordinate system to maintain clockwise measurement from north.
Reader's Guide
Azimuth is a key coordinate in the horizontal coordinate system used in celestial navigation, where it is paired with altitude. In modern astronomy, azimuth is nearly always measured from the north. In land navigation, azimuth is usually denoted alpha (α) and defined as a horizontal angle measured clockwise from a north base line or meridian. However, some systems use south as the reference vector, and bearings may be stated in systems where north or south is zero, with angles measured clockwise or anticlockwise. In geodesy, azimuth can be calculated for a spherical Earth using a formula involving latitude and longitude, while for an oblate spheroid, normal-section azimuth and geodetic azimuth differ slightly, with the difference usually negligible for distances under 100 km.
Did You Know?
- The word azimuth comes from medieval Arabic السموت (al-sumūt), meaning 'the directions'.
- Its first recorded use in English is in the 1390s in Geoffrey Chaucer's A Treatise on the Astrolabe.
- In navigation, a bearing might be described as 'S30°E', meaning 30 degrees eastward from south.
Frequently Asked Questions
What is Azimuth in cartography and navigation?
Azimuth is the horizontal angle you measure away from a cardinal direction—most often true north—to pinpoint a target relative to where the observer is standing. It operates within a local, observer-centric spherical coordinate framework rather than a global grid.
Which fields rely on Azimuth as a core measurement?
Navigation, astronomy, geodesy, engineering, mining, and ballistics all treat it as a foundational quantity for locating celestial bodies or terrestrial targets. In map projection work, it helps anchor local direction before any distortion model is applied.
What reference point does Azimuth measure from?
The angle is taken from a chosen cardinal direction, with true north being the most common starting reference. This makes it inherently observer-centric: the same target will carry different azimuth values from different vantage points.
Why do cartography fans keep bringing up Azimuth in projection discussions?
Because every azimuthal equidistant or azimuthal equal-area projection is literally named for this angle—it defines the radial direction from the projection's center point. Understanding the concept clarifies why those projections preserve true bearing from the center while distorting distance elsewhere.
More in Map Projections & Cartography Foundations 1-24
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