Height
Overview

Height is the measurement of vertical distance
Distance
Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...

, but has two meanings in common use. It can either indicate how "tall" something is, or how "high up" it is. For example "The height of the building is 50 m" or "The height of the airplane is 10,000 m". When used to describe how high something like an airplane or mountain peak
Mountain peak
A mountain peak is the highest part of a mountain; a mountaintop; the summit.Mountain Peak may also refer to:* Blue Mountain Peak, Jamaica* Hole in the Mountain Peak, Nevada, USA...

is from sea level
Sea level
Mean sea level is a measure of the average height of the ocean's surface ; used as a standard in reckoning land elevation...

, height is more often called altitude
Altitude
Altitude or height is defined based on the context in which it is used . As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context...

. Height is measured along the vertical (y) axis between a specified point and another point.
English high is derived from Old English hēah, ultimately from Proto-Germanic *xauxa-z, from a PIE
Pie
A pie is a baked dish which is usually made of a pastry dough casing that covers or completely contains a filling of various sweet or savoury ingredients....

base *keuk-.
Encyclopedia
Height is the measurement of vertical distance
Distance
Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...

, but has two meanings in common use. It can either indicate how "tall" something is, or how "high up" it is. For example "The height of the building is 50 m" or "The height of the airplane is 10,000 m". When used to describe how high something like an airplane or mountain peak
Mountain peak
A mountain peak is the highest part of a mountain; a mountaintop; the summit.Mountain Peak may also refer to:* Blue Mountain Peak, Jamaica* Hole in the Mountain Peak, Nevada, USA...

is from sea level
Sea level
Mean sea level is a measure of the average height of the ocean's surface ; used as a standard in reckoning land elevation...

, height is more often called altitude
Altitude
Altitude or height is defined based on the context in which it is used . As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context...

. Height is measured along the vertical (y) axis between a specified point and another point.

## Etymology

English high is derived from Old English hēah, ultimately from Proto-Germanic *xauxa-z, from a PIE
Pie
A pie is a baked dish which is usually made of a pastry dough casing that covers or completely contains a filling of various sweet or savoury ingredients....

base *keuk-. The derived noun hight, also highth, is from Old English híehþo, later héahþu, as it were from Proto-Germanic *xaux-iþa.

## In mathematics

Dimensional models define height as the third dimension
Dimension
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

, the other two being length
Length
In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...

and width. If we construct a plane formed by the length and width, and construct a line which intersects that plane at a 90 degree angle, then the height is measured along that line.

Height can also refer to:
1. The altitude
Altitude (triangle)
In geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to a line containing the base . This line containing the opposite side is called the extended base of the altitude. The intersection between the extended base and the altitude is called the foot of the...

of a triangle, which is the length from a vertex of a triangle to the line formed by the opposite side;
2. A measurement in a circular segment
Circular segment
In geometry, a circular segment is an area of a circle informally defined as an area which is "cut off" from the rest of the circle by a secant or a chord. The circle segment constitutes the part between the secant and an arc, excluding the circle's center...

of the distance from the midpoint of the arc of the circular segment to the midpoint of the line line joining the endpoints of the arc (see diagram in circular segment
Circular segment
In geometry, a circular segment is an area of a circle informally defined as an area which is "cut off" from the rest of the circle by a secant or a chord. The circle segment constitutes the part between the secant and an arc, excluding the circle's center...

).
3. In algebraic number theory, a "height function" is a measurement related to the minimal polynomial
Minimal polynomial (field theory)
In field theory, given a field extension E / F and an element α of E that is an algebraic element over F, the minimal polynomial of α is the monic polynomial p, with coefficients in F, of least degree such that p = 0...

of an algebraic number
Algebraic number
In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with rational coefficients. Numbers such as π that are not algebraic are said to be transcendental; almost all real numbers are transcendental...

.

## 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
Sea level
Mean sea level is a measure of the average height of the ocean's surface ; used as a standard in reckoning land elevation...

. Both altitude and elevation
Elevation
The elevation of a geographic location is its height above a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface ....

, 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
Mount Everest
Mount Everest is the world's highest mountain, with a peak at above sea level. It is located in the Mahalangur section of the Himalayas. The international boundary runs across the precise summit point...

, located on the border of Nepal
Nepal
Nepal , officially the Federal Democratic Republic of Nepal, is a landlocked sovereign state located in South Asia. It is located in the Himalayas and bordered to the north by the People's Republic of China, and to the south, east, and west by the Republic of India...

and Tibet
Tibet
Tibet is a plateau region in Asia, north-east of the Himalayas. It is the traditional homeland of the Tibetan people as well as some other ethnic groups such as Monpas, Qiang, and Lhobas, and is now also inhabited by considerable numbers of Han and Hui people...

, China
China
Chinese civilization may refer to:* China for more general discussion of the country.* Chinese culture* Greater China, the transnational community of ethnic Chinese.* History of China* Sinosphere, the area historically affected by Chinese culture...

; however the highest mountain by measurement of apex to base belongs to Mauna Kea
Mauna Kea
Mauna Kea is a volcano on the island of Hawaii. Standing above sea level, its peak is the highest point in the state of Hawaii. However, much of the mountain is under water; when measured from its oceanic base, Mauna Kea is over tall—significantly taller than Mount Everest...

in Hawaii
Hawaii
Hawaii is the newest of the 50 U.S. states , and is the only U.S. state made up entirely of islands. It is the northernmost island group in Polynesia, occupying most of an archipelago in the central Pacific Ocean, southwest of the continental United States, southeast of Japan, and northeast of...

, United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...

.

## 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; see Altitude in aviation.

## In human culture

Human height
Human height
Human height is the distance from the bottom of the feet to the top of the head in a human body standing erect.When populations share genetic background and environmental factors, average height is frequently characteristic within the group...

is one of the areas of study within anthropometry
Anthropometry
Anthropometry refers to the measurement of the human individual...

. While height variations within a population are largely genetic
Genetics
Genetics , a discipline of biology, is the science of genes, heredity, and variation in living organisms....

, height variations between populations are mostly environmental.

The United Nations
United Nations
The United Nations is an international organization whose stated aims are facilitating cooperation in international law, international security, economic development, social progress, human rights, and achievement of world peace...

uses height (among other statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

) to monitor changes in the nutrition
Nutrition
Nutrition is the provision, to cells and organisms, of the materials necessary to support life. Many common health problems can be prevented or alleviated with a healthy diet....

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
Health care system
A health care system is the organization of people, institutions, and resources to deliver health care services to meet the health needs of target populations....

. However, the height of a human is not always directly connected or related to such things as nutrition, social class, etc.

• CGS unit
• Chinese unit
• Imperial unit
Imperial unit
The system of imperial units or the imperial system is the system of units first defined in the British Weights and Measures Act of 1824, which was later refined and reduced. The system came into official use across the British Empire...

• International System of Units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

• U.S. customary units
• Human height
Human height
Human height is the distance from the bottom of the feet to the top of the head in a human body standing erect.When populations share genetic background and environmental factors, average height is frequently characteristic within the group...

• Acrophobia
Acrophobia
Acrophobia is an extreme or irrational fear of heights. It belongs to a category of specific phobias, called space and motion discomfort that share both similar etiology and options for treatment.Most people experience a degree of natural fear when exposed to heights, especially if there is little...

(Fear of heights)