Greek word καί written with a handwritten variant of kappa, from the Byzantine period

Kappa (uppercase Κ, lowercase κ or cursive ; el, κάππα, ''káppa'') is the 10th letter of the

Greek alphabet The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as w ...

, representing the

voiceless velar plosive The voiceless velar plosive or stop is a type of consonantal sound used in almost all spoken languages. The symbol in the International Phonetic Alphabet that represents this sound is , and the equivalent X-SAMPA symbol is k. The sound is a ver ...

sound in

Ancient Ancient history is a time period from the beginning of writing and recorded human history to as far as late antiquity. The span of recorded history is roughly 5,000 years, beginning with the Sumerian cuneiform script. Ancient history cov ...

and

Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the dialects of the Greek language spoken in the modern era, including the official standardized form of the ...

. In the system of

Greek numerals Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to tho ...

, has a value of 20. It was derived from the Phoenician letter kaph . Letters that arose from kappa include the Roman K and Cyrillic К. The uppercase form is identical to the Latin K. Greek proper names and placenames containing kappa are often written in English with "c" due to the

Roman Roman or Romans most often refers to: *Rome, the capital city of Italy *Ancient Rome, Roman civilization from 8th century BC to 5th century AD *Roman people, the people of ancient Rome *'' Epistle to the Romans'', shortened to ''Romans'', a lette ...

transliteration Transliteration is a type of conversion of a text from one script to another that involves swapping letters (thus ''trans-'' + '' liter-'') in predictable ways, such as Greek → , Cyrillic → , Greek → the digraph , Armenian → or L ...

s into the

Latin alphabet The Latin alphabet or Roman alphabet is the collection of letters originally used by the ancient Romans to write the Latin language. Largely unaltered with the exception of extensions (such as diacritics), it used to write English and th ...

Constantinople la, Constantinopolis ota, قسطنطينيه , alternate_name = Byzantion (earlier Greek name), Nova Roma ("New Rome"), Miklagard/Miklagarth (Old Norse), Tsargrad ( Slavic), Qustantiniya ( Arabic), Basileuousa ("Queen of Cities"), Megalopolis ( ...

Corinth Corinth ( ; el, Κόρινθος, Kórinthos, ) is the successor to an ancient city, and is a former municipality in Corinthia, Peloponnese (region), Peloponnese, which is located in south-central Greece. Since the 2011 local government refor ...

Crete Crete ( el, Κρήτη, translit=, Modern: , Ancient: ) is the largest and most populous of the Greek islands, the 88th largest island in the world and the fifth largest island in the Mediterranean Sea, after Sicily, Sardinia, Cyprus, ...

. All formal modern romanizations of Greek now use the letter "k", however. The cursive form is generally a simple font variant of lower-case kappa, but it is encoded separately in

Unicode Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, wh ...

for occasions where it is used as a separate symbol in math and science. In mathematics, the

kappa curve In geometry, the kappa curve or Gutschoven's curve is a two-dimensional algebraic curve resembling the Greek letter . The kappa curve was first studied by Gérard van Gutschoven around 1662. In the history of mathematics, it is remembered as one o ...

is named after this letter; the

tangent In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. Mo ...

s of this

curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that ...

were first calculated by Isaac Barrow in the 17th century.

Symbol

Lowercase (κ)

;Mathematics and statistics * In

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...

, the

connectivity Connectivity may refer to: Computing and technology * Connectivity (media), the ability of the social media to accumulate economic capital from the users connections and activities * Internet connectivity, the means by which individual terminal ...

of a

graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...

is given by ''κ''. * In differential geometry, the curvature of a curve is given by ''κ''. * In

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrices ...

, the condition number of a matrix is given by ''κ''. * Kappa statistics such as

Cohen's kappa Cohen's kappa coefficient (''κ'', lowercase Greek kappa) is a statistic that is used to measure inter-rater reliability (and also intra-rater reliability) for qualitative (categorical) items. It is generally thought to be a more robust measure th ...

and

Fleiss' kappa Fleiss' kappa (named after Joseph L. Fleiss) is a statistical measure for assessing the reliability of agreement between a fixed number of raters when assigning categorical ratings to a number of items or classifying items. This contrasts with ...

are methods for calculating

inter-rater reliability In statistics, inter-rater reliability (also called by various similar names, such as inter-rater agreement, inter-rater concordance, inter-observer reliability, inter-coder reliability, and so on) is the degree of agreement among independent obse ...

. ;Physics * In

cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...

, the

Einstein gravitational constant In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Einstein in 1915 in the form ...

is denoted by ''κ''. * In

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

, the torsional constant of an oscillator is given by ''κ''. * In physics, the coupling coefficient in magnetostatics is represented by ''κ''. * In physics, the dielectric coefficient is represented by ''κ''. * In fluid dynamics, the

von Kármán constant In fluid dynamics, the von Kármán constant (or Kármán's constant), named for Theodore von Kármán, is a dimensionless constant involved in the logarithmic law describing the distribution of the longitudinal velocity in the wall-normal directio ...

is represented by ''κ''. * In

thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of th ...

, the

compressibility In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a f ...

of a compound is given by ''κ''. ;Engineering * In

structural engineering Structural engineering is a sub-discipline of civil engineering in which structural engineers are trained to design the 'bones and muscles' that create the form and shape of man-made structures. Structural engineers also must understand and cal ...

, ''κ'' is the ratio of the smaller factored moment to the larger factored moment and is used to calculate the critical elastic moment of an unbraced steel member. * In electrical engineering, ''κ'' is the multiplication factor, a function of the ''R''/''X'' ratio of the equivalent power system network, which is used in calculating the peak short-circuit current of a system fault. ''κ'' is also used to denote conductivity, the reciprocal of resistivity,

rho Rho (uppercase Ρ, lowercase ρ or ; el, ρο or el, ρω, label=none) is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Phoenician letter res . Its uppercase form uses the sa ...

. ;Biology and biomedical science * In

biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...

, kappa and kappa prime are important

nucleotide Nucleotides are organic molecules consisting of a nucleoside and a phosphate. They serve as monomeric units of the nucleic acid polymers – deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), both of which are essential biomolecule ...

motifs for a tertiary interaction of

group II intron Group II introns are a large class of self-catalytic ribozymes and mobile genetic elements found within the genes of all three domains of life. Ribozyme activity (e.g., self- splicing) can occur under high-salt conditions ''in vitro''. However, ...

s. * In

, kappa designates a subtype of an

antibody An antibody (Ab), also known as an immunoglobulin (Ig), is a large, Y-shaped protein used by the immune system to identify and neutralize foreign objects such as pathogenic bacteria and viruses. The antibody recognizes a unique molecule of the ...

component. * In pharmacology, kappa represents a type of

opioid receptor Opioid receptors are a group of inhibitory G protein-coupled receptors with opioids as ligands. The endogenous opioids are dynorphins, enkephalins, endorphins, endomorphins and nociceptin. The opioid receptors are ~40% identical to somatostatin ...

. ;Psychology and psychiatry * In

psychology Psychology is the scientific study of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, including feelings and thoughts. It is an academic discipline of immense scope, crossing the boundaries between ...

and

psychiatry Psychiatry is the specialty (medicine), medical specialty devoted to the diagnosis, prevention, and treatment of mental disorders. These include various maladaptations related to mood, behaviour, cognition, and perceptions. See glossary of psych ...

, kappa represents a measure of diagnostic reliability. ;Economics * In macroeconomics, kappa represents the capital-utilization rate.

Uppercase (Κ)

;History * In

textual criticism Textual criticism is a branch of textual scholarship, philology, and of literary criticism that is concerned with the identification of textual variants, or different versions, of either manuscripts or of printed books. Such texts may range in da ...

, the

Byzantine text-type In the textual criticism of the New Testament, the Byzantine text-type (also called Majority Text, Traditional Text, Ecclesiastical Text, Constantinopolitan Text, Antiocheian Text, or Syrian Text) is one of the main text types. It is the form fo ...

(from Κοινη, ''Koine'', the common text). ;Mathematics and statistics * In

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...

, kappa is often used to denote an ordinal that is also a cardinal. ;Chemistry * In chemistry, kappa is used to denote the

denticity In coordination chemistry, denticity () refers to the number of donor groups in a given ligand that bind to the central metal atom in a coordination complex. In many cases, only one atom in the ligand binds to the metal, so the denticity equals ...

of the compound. * In

pulping Pulp is a Lignocellulosic biomass, lignocellulosic fibrous material prepared by chemically or mechanically separating cellulose fibers from wood, fiber crops, Paper recycling, waste paper, or cotton paper, rags. Mixed with water and other chemica ...

, the

kappa number The Kappa number is an indication of the residual lignin content or bleachability of wood pulp by a standardized analysis method. Measuring method The Kappa number is determined by ISO 302:2004. ISO 302 is applicable to all kinds of chemical an ...

represents the amount of an oxidizing agent required for bleaching a pulp.

Character encodings

* Mathematical Kappa These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

References

{{reflist Greek letters