Height

Last updated January 31, 2025

Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is). For an example of vertical extent, "This basketball player is 7 foot 1 inches in height." For an example of vertical position, "The height of an airplane in-flight is about 10,000 meters."

In a two-dimensional 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 is zero. In the case of three-dimensional space, height is measured along the vertical z axis, describing a distance from (or "above") 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 height or altitude of a triangle, which is the length from a vertex of a triangle to the line formed by the opposite side;
The height of a pyramid, which is the smallest distance from the apex to the base;
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 (see diagram in circular segment);
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

Although height is normally 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 addition to vertical position, the vertical extent of geographic landmarks can be defined in terms of topographic prominence. 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 tallest mountain, by measurement of apex to base, is Mauna Kea in Hawaii, United States.

In geodesy

Geodesists formalize mean sea level (MSL) by means of the geoid, the equipotential surface that best fits MSL. Then various types of height (normal, dynamic, orthometric, etc.) can be defined, based on the assumption of density of topographic masses necessary in the continuation of MSL under the continents.

A purely geometric quantity is the ellipsoidal height , reckoned from the surface of a reference ellipsoid, see Geodetic system, vertical datum.

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

Human height is one of the areas of study within anthropometry. While environmental factors have some effect on variations in human height, these influences are insufficient to account for all differences between populations, suggesting that genetic factors are important for explaining variations between human populations.^[3]

The United Nations uses height (among other statistics) 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.^[4]

Related Research Articles

Geodesy or geodetics is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D. It is called planetary geodesy when studying other astronomical bodies, such as planets or circumplanetary systems. Geodesy is an earth science and many consider the study of Earth's shape and gravity to be central to that science. It is also a discipline of applied mathematics.

Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system the base unit for length is the metre.

Atmospheric pressure, also known as air pressure or barometric pressure, is the pressure within the atmosphere of Earth. The standard atmosphere is a unit of pressure defined as 101,325 Pa (1,013.25 hPa), which is equivalent to 1,013.25 millibars, 760 mm Hg, 29.9212 inches Hg, or 14.696 psi. The atm unit is roughly equivalent to the mean sea-level atmospheric pressure on Earth; that is, the Earth's atmospheric pressure at sea level is approximately 1 atm.

A geographic coordinate system (GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on Earth as latitude and longitude. It is the simplest, oldest and most widely used type of the various spatial reference systems that are in use, and forms the basis for most others. Although latitude and longitude form a coordinate tuple like a cartesian coordinate system, the geographic coordinate system is not cartesian because the measurements are angles and are not on a planar surface.

<span class="mw-page-title-main">Altitude</span> Height in relation to a specified reference point

Altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context. Although the term altitude is commonly used to mean the height above sea level of a location, in geography the term elevation is often preferred for this usage.

Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. These points are usually on the surface of the Earth, and they are often used to establish maps and boundaries for ownership, locations, such as the designated positions of structural components for construction or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales.

Mean sea level is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datum – a standardised geodetic datum – that is used, for example, as a chart datum in cartography and marine navigation, or, in aviation, as the standard sea level at which atmospheric pressure is measured to calibrate altitude and, consequently, aircraft flight levels. A common and relatively straightforward mean sea-level standard is instead a long-term average of tide gauge readings at a particular reference location.

Earth radius is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly 6,378 km (3,963 mi) to a minimum of nearly 6,357 km (3,950 mi).

Physical geodesy is the study of the physical properties of Earth's gravity and its potential field, with a view to their application in geodesy.

A geodetic datum or geodetic system is a global datum reference or reference frame for unambiguously representing the position of locations on Earth by means of either geodetic coordinates or geocentric coordinates. Datums are crucial to any technology or technique based on spatial location, including geodesy, navigation, surveying, geographic information systems, remote sensing, and cartography. A horizontal datum is used to measure a horizontal position, across the Earth's surface, in latitude and longitude or another related coordinate system. A vertical datum is used to measure the elevation or depth relative to a standard origin, such as mean sea level (MSL). A three-dimensional datum enables the expression of both horizontal and vertical position components in a unified form. The concept can be generalized for other celestial bodies as in planetary datums.

<span class="mw-page-title-main">Arc measurement</span> Technique of determining the radius of Earth

Arc measurement, sometimes called degree measurement, is the astrogeodetic technique of determining the radius of Earth and, by extension, its circumference. More specifically, it seeks to determine the local Earth radius of curvature of the figure of the Earth, by relating the latitude difference and the geographic distance surveyed between two locations on Earth's surface. The most common variant involves only astronomical latitudes and the meridian arc length and is called meridian arc measurement; other variants may involve only astronomical longitude or both geographic coordinates . Arc measurement campaigns in Europe were the precursors to the International Association of Geodesy (IAG). Nowadays, the method is replaced by worldwide geodetic networks and by satellite geodesy.

In aviation, atmospheric sciences and broadcasting, a height above ground level is a height measured with respect to the underlying ground surface. This is as opposed to height above mean sea level, height above ellipsoid, or height above average terrain. In other words, these expressions indicate where the "zero level" or "reference altitude" – the vertical datum – is located.

The orthometric height is the vertical distance along the plumb line from a point of interest to a reference surface known as the geoid, the vertical datum that approximates mean sea level. Orthometric height is one of the scientific formalizations of a layman's "height above sea level", along with other types of heights in Geodesy.

In the oil and gas industry, depth in a well is the distance along a well between a point of interest and a reference point or surface. It is the most common method of reference for locations in the well, and therefore, in oil industry speech, "depth" also refers to the location itself.

The National Geodetic Vertical Datum of 1929 is the official name since 1973 of the vertical datum established for vertical control surveying in the United States of America by the General Adjustment of 1929. Originally known as Sea Level Datum of 1929, NGVD 29 was determined and published by the United States Coast and Geodetic Survey and used to measure the elevation of a point above and depression below mean sea level (MSL).

The North American Vertical Datum of 1988 is the vertical datum for orthometric heights established for vertical control surveying in the United States based upon the General Adjustment of the North American Datum of 1988.

Aerial photographic and satellite image interpretation, or just image interpretation when in context, is the act of examining photographic images, particularly airborne and spaceborne, to identify objects and judging their significance. This is commonly used in military aerial reconnaissance, using photographs taken from reconnaissance aircraft and reconnaissance satellites.

In geodesy, surveying, hydrography and navigation, vertical datum or altimetric datum is a reference coordinate surface used for vertical positions, such as the elevations of Earth-bound features and altitudes of satellite orbits and in aviation. In planetary science, vertical datums are also known as zero-elevation surface or zero-level reference.

Vertical position or vertical location is a position along a vertical direction above or below a given vertical datum . Vertical distance or vertical separation is the distance between two vertical positions. Many vertical coordinates exist for expressing vertical position: depth, height, altitude, elevation, etc. Points lying on an equigeopotential surface are said to be on the same vertical level, as in a water level.

Height above mean sea level is a measure of a location's vertical distance in reference to a vertical datum based on a historic mean sea level. In geodesy, it is formalized as orthometric height. The zero level varies in different countries due to different reference points and historic measurement periods. Climate change and other forces can cause sea levels and elevations to vary over time.

References

↑ Strahler, Alan (2013). Introducing Physical Geography (6th ed.). Hoboken, N.J.: Wiley. p. 42. ISBN 9781118396209. OCLC 940600903.
↑ Petersen, James F.; Sack, Dorothy; Gabler, Robert E. (4 February 2016). Physical Geography. Cengage Learning. p. 113. ISBN 978-1-305-65264-4. Note that altitude usually refers to a height in the air (above sea level) and elevation refers to height on the surface [of the Earth] above (or below) sea level.
↑ Stulp, G; Barrett, L (February 2016). "Evolutionary perspectives on human height variation" (PDF). Biological Reviews. 91 (1): 206–34. doi:10.1111/brv.12165. PMID 25530478. S2CID 5257723.
↑ van der Eng, Pierre; Baten, Joerg; Stegl, Mojgan (2010). "Long-Term Economic Growth and the Standard of Living in Indonesia" (PDF). SSRN Electronic Journal. doi:10.2139/ssrn.1699972. S2CID 127728911.

External links

Media related to Height at Wikimedia Commons
The dictionary definition of height at Wiktionary
The dictionary definition of high at Wiktionary

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[1] Strahler, Alan (2013). Introducing Physical Geography (6th ed.). Hoboken, N.J.: Wiley. p. 42. ISBN 9781118396209. OCLC 940600903.

[2] Petersen, James F.; Sack, Dorothy; Gabler, Robert E. (4 February 2016). Physical Geography. Cengage Learning. p. 113. ISBN 978-1-305-65264-4. Note that altitude usually refers to a height in the air (above sea level) and elevation refers to height on the surface [of the Earth] above (or below) sea level.

[3] Stulp, G; Barrett, L (February 2016). "Evolutionary perspectives on human height variation" (PDF). Biological Reviews. 91 (1): 206–34. doi:10.1111/brv.12165. PMID 25530478. S2CID 5257723.

[4] van der Eng, Pierre; Baten, Joerg; Stegl, Mojgan (2010). "Long-Term Economic Growth and the Standard of Living in Indonesia" (PDF). SSRN Electronic Journal. doi:10.2139/ssrn.1699972. S2CID 127728911.

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