Absolute height

Height is the measure of vertical distance, either how "tall" something or someone is, or how "high" the position is.

For example "The height of that building is 50 m" or "The height of an airplane is about 10,000 m".

When the term is used to describe how high something like an airplane or a mountain peak is from sea level, height is more often called altitude.

In a cartesian space, height is measured along the vertical axis (y) between a specific point and another that does not have the same y-value. If both points happen to have the same y-value, then their relative height equals to zero.

The English-language word high is derived from Old English hēah, ultimately from Proto-Germanic *xauxa-z, from a PIE base *keuk-. The derived noun height, also the obsolete forms heighth and highth, is from Old English híehþo, later héahþu, as it were from Proto-Germanic *xaux-iþa.

In elementary models of space, height may indicate the third dimension, the other two being length and width. Height is normal to the plane formed by the length and width.

Height is also used as a name for some more abstract definitions. These include:

among other uses in commutative algebra and representation theory.

Although height is relative to a plane of reference, most measurements of height in the physical world are based upon a zero surface, known as sea level. Both altitude and elevation, two synonyms for height, are usually defined as the position of a point above the mean sea level. One can extend the sea-level surface under the continents: naively, one can imagine a lot of narrow canals through the continents. In practice, the sea level under a continent has to be computed from gravity measurements, and slightly different computational methods exist; see Geodesy, heights.

Instead of using the sea level, geodesists often prefer to define height from the surface of a reference ellipsoid, see Geodetic system, vertical datum.

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