# Height

**Height**is measure of vertical distance, either vertical extent or vertical position.

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

When the term is used to describe vertical position from sea level, height is more often called

*altitude*.

Furthermore, if the point is attached to the Earth, then altitude is called

*elevation*.

In a two-dimensional Cartesian space, height is measured along the vertical axis 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 is zero. In three-dimensional space, height is measured along the vertical

*z*axis, describing a distance from the

*x-y*plane.

## Etymology

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 mathematics

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:

- The altitude of a triangle, which is the length from a vertex of a triangle to the line formed by the opposite side;
- A measurement in a circular segment of the distance from the midpoint of the arc of the circular segment to the midpoint of the line joining the endpoints of the arc ;
- In a rooted tree, the height of a vertex is the length of the longest downward path to a leaf from that vertex;
- In algebraic number theory, a "height function" is a measurement related to the minimal polynomial of an algebraic number; among other uses in commutative algebra and representation theory;
- In ring theory, the height of a prime ideal is the supremum of the lengths of all chains of prime ideals contained in it.
## In geosciences

### In geology

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.### In geodesy

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

Defining the height of geographic landmarks becomes a question of reference. For example, the highest mountain by elevation in reference to sea level belongs to Mount Everest, located on the border of Nepal and Tibet, China; however the highest mountain by measurement of apex to base belongs to Mauna Kea in Hawaii, United States.

## In aviation

In aviation terminology, the terms*height*,

*altitude*, and

*elevation*are not synonyms. Usually, the altitude of an aircraft is measured from sea level, while its height is measured from ground level. Elevation is also measured from sea level, but is most often regarded as a property of the ground. Thus, elevation plus height can equal altitude, but the term

*altitude*has several meanings in aviation.

## In human culture

is one of the areas of study within anthropometry. While height variations within a population are largely genetic, height variations between populations are mostly environmental.The United Nations uses height to monitor changes in the nutrition of developing nations. In human populations, average height can distill down complex data about the group's birth, upbringing, social class, diet, and health care system.

In their research, Baten, Stegl and van der Eng came to the conclusion that a change in the average height is a sign for a change in the economic development. With broad data of Indonesia, the researchers state that several incidents in the history of the country has led not only to a change in the economy but also to a change in the population’s average height.