# Kappa

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{{short description|Tenth letter in the Greek Alphabet}}
{{Other uses}}{{Distinguish}}{{About|the Greek letter|the archaic Greek letter with a similar name|Koppa (letter)}}{{Distinguish|text=the similar looking Cyrillic letter [Ka](/source/Ka_(Cyrillic))}}
{{Greek Alphabet|letter=kappa}}
thumb|right|75px|Variant kappa|class=skin-invert-image
thumb|right|Greek word καί written with a handwritten variant of kappa, from the Byzantine period|class=skin-invert-image
'''Kappa''' ({{IPAc-en|'|k|æ|p|ə|audio=LL-Q1860 (eng)-Flame, not lame-Kappa.wav}};<ref>{{OED|kappa}}</ref> uppercase '''Κ''', lowercase '''κ''' or [cursive](/source/Cursive_Greek) {{not a typo|'''ϰ'''}}; {{langx|el|κάππα}}, ''káppa'') is the tenth letter of the [Greek alphabet](/source/Greek_alphabet), representing the [voiceless velar plosive](/source/voiceless_velar_plosive) {{IPA|el|k|IPA}} sound in [Ancient](/source/Ancient_Greek) and [Modern Greek](/source/Modern_Greek). In the system of [Greek numerals](/source/Greek_numerals), {{lang|el|Kʹ}} has a value of 20. It was derived from the Phoenician letter [kaph](/source/kaph) (𐤊). Letters that arose from kappa include the Roman [K](/source/K) and Cyrillic [К](/source/Ka_(Cyrillic)). 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](/source/Ancient_Rome)s' [transliteration](/source/Romanization_of_Greek)s into the [Latin alphabet](/source/Latin_alphabet): [Constantinople](/source/Constantinople), [Corinth](/source/Ancient_Corinth), [Crete](/source/Crete). [All formal modern romanizations](/source/Romanization_of_Greek) of Greek now use the letter "k", however. 

{{anchor|Cursive kappa|{{not a typo|ϰ}}}}<!--linked from [cursive kappa](/source/cursive_kappa), {{not a typo|[ϰ](/source/%CF%B0)}}, [Romanization of Greek](/source/Romanization_of_Greek), etc.-->
The [cursive](/source/Greek_cursive) form {{lang|grc|{{not a typo|ϰ}}}} is generally a simple font variant of lower-case kappa, but it is encoded separately in [Unicode](/source/Unicode) for occasions where it is used as a separate symbol in math and science. In [mathematics](/source/mathematics), the [kappa curve](/source/kappa_curve) is named after this letter; the [tangent](/source/tangent)s of this [curve](/source/curve) were first calculated by [Isaac Barrow](/source/Isaac_Barrow) in the 17th century.

==Symbol==
===Lowercase (κ)===
;Mathematics and statistics
* In [graph theory](/source/graph_theory), the [connectivity](/source/connectivity_(graph_theory)) of a [graph](/source/Graph_(discrete_mathematics)) is given by ''κ''.<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Vertex Connectivity |url=https://mathworld.wolfram.com/VertexConnectivity.html |access-date=2025-02-05 |website=mathworld.wolfram.com |language=en}}</ref>
* In [differential geometry](/source/differential_geometry), the [curvature](/source/curvature) of a curve is given by ''κ''.<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Curvature |url=https://mathworld.wolfram.com/Curvature.html |access-date=2025-02-05 |website=mathworld.wolfram.com |language=en |quote=Then the curvature κ, sometimes also called the "first curvature" (Kreyszig 1991, p. 47), is defined by...}}</ref>
* In [linear algebra](/source/linear_algebra), the [condition number](/source/condition_number) of a matrix is given by ''κ''.<ref>{{Cite web |title=DLMF: §3.2 Linear Algebra ‣ Areas ‣ Chapter 3 Numerical Methods |url=https://dlmf.nist.gov/3.2#v.p1 |access-date=2025-01-31 |website=dlmf.nist.gov}}</ref>
* The [kappa curve](/source/kappa_curve), also known as Gutschoven's curve, is a curve whose shape resembles the letter ''κ.''<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Kappa Curve |url=https://mathworld.wolfram.com/KappaCurve.html |access-date=2025-02-05 |website=mathworld.wolfram.com |language=en}}</ref>
* Kappa statistics such as [Cohen's kappa](/source/Cohen's_kappa)<ref name="Mary2012">{{cite journal|last1=McHugh|first1=Mary L.|year=2012|title=Interrater reliability: The kappa statistic|journal=Biochemia Medica|volume=22|issue=3|pages=276–282|doi=10.11613/bm.2012.031|pmc=3900052|pmid=23092060}}</ref><ref>{{Cite book |last=Gwet |first=Kilem Li |title=Handbook of inter-rater reliability: the definitive guide to measuring the extent of agreement among raters |date=2014 |publisher=Advances Analytics, LLC |isbn=978-0-9708062-8-4 |edition=Fourth |location=Gaithersburg, Md |pages=32 |quote=Cohen's Kappa Definition}}</ref> and [Fleiss' kappa](/source/Fleiss'_kappa) are methods for calculating [inter-rater reliability](/source/inter-rater_reliability).

;Physics
* In [cosmology](/source/cosmology), the [Einstein gravitational constant](/source/Einstein_gravitational_constant) is denoted by ''κ''.<ref>{{Cite book |last=Carmeli |first=Moshe |title=Classical fields: general relativity and gauge theory |date=1982 |publisher=J. Wiley |isbn=978-0-471-86437-0 |location=New York |pages=85 |quote=Here ''κ''  is some constant called ''Einstein's gravitational constant''.}}</ref>
* In [physics](/source/physics), the [torsional constant](/source/torsion_spring) of an [oscillator](/source/oscillation) is given by ''κ''.<ref>{{Cite book |last1=Halliday |first1=David |title=Principles of physics |last2=Resnick |first2=Robert |last3=Walker |first3=Jearl |date=2023 |publisher=Wiley |isbn=978-1-119-82061-1 |edition=Twelfth |series=International adaptation |location=Singapore |pages=447 |quote=Here ''κ'' (Greek ''kappa'') is a constant, called the '''torsion constant''',}}</ref>
* In physics, the coupling coefficient in magnetostatics is represented by ''κ''.<ref>{{Cite book |last=Stancil |first=Daniel D. |title=Theory of magnetostatic waves |date=1993 |publisher=Springer-Verlag |isbn=978-0-387-97969-4 |location=New York |pages=200 |quote=The coupling coefficient (7.136) can now be written ''κ''{{sub|ab}} =...}}</ref>
* In physics, the dielectric coefficient is represented by ''κ''.
* In [fluid dynamics](/source/fluid_dynamics), the [von Kármán constant](/source/von_K%C3%A1rm%C3%A1n_constant) is represented by ''κ''.<ref>{{Cite journal |last1=Monkewitz |first1=Peter A. |last2=Nagib |first2=Hassan M. |date=2023 |title=The hunt for the Kármán 'constant' revisited |url=https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/hunt-for-the-karman-constant-revisited/F9DA84F93A1E268BFC5F9E1CB5622E5E |journal=Journal of Fluid Mechanics |language=en |volume=967 |article-number=A15 |doi=10.1017/jfm.2023.448 |issn=0022-1120|arxiv=2303.08071 |bibcode=2023JFM...967A..15M }}</ref>
* [thermal conductivity](/source/thermal_conductivity)<ref>{{Cite web |title=Thermal Conductivity - Definition and Detailed Explanation |url=https://byjus.com/chemistry/thermal-conductivity/ |access-date=2025-02-05 |website=BYJUS |language=en |quote=It is generally denoted by the symbol 'k' but can also be denoted by 'λ' and 'κ'.}}</ref>
* In [thermodynamics](/source/thermodynamics), the [compressibility](/source/compressibility) of a compound is given by ''κ''.<ref>{{Cite book |title=Transition metal and rare earth compounds. 3 |date=2004 |publisher=Springer |isbn=978-3-540-20948-5 |series=Topics in current chemistry |location=Berlin Heidelberg |pages=5 |quote=The isothermal compressibility, ''κ'' ...}}</ref>

;Engineering
* In [structural engineering](/source/structural_engineering), ''κ'' is the ratio of the smaller factored moment to the larger factored moment and is used to calculate the critical [elastic moment](/source/elastic_moment) of an unbraced steel member.
* In [electrical engineering](/source/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](/source/rho).

;Biology and biomedical science
* In [biology](/source/biology), kappa and kappa prime are important [nucleotide](/source/nucleotide) motifs for a tertiary interaction of [group II intron](/source/group_II_intron)s.
* In [biology](/source/biology), kappa designates a subtype of an [antibody](/source/antibody) component.
* In [pharmacology](/source/pharmacology), kappa represents a type of [opioid receptor](/source/opioid_receptor).<ref>{{Cite book |title=Opioids and Their Receptors: Present and Emerging Concepts in Opioid Drug Discovery II |date=2022 |publisher=MDPI - Multidisciplinary Digital Publishing Institute |isbn=978-3-0365-4352-9 |editor-last=Spetea |editor-first=Mariana |location=Basel |quote=From a chemical standpoint, opioids comprise a diverse group of drugs, but they all share a common affinity towards μ,δ, and κ  receptors |editor-last2=van Rijn |editor-first2=Richard M.}}</ref>

;Psychology and psychiatry
* In [psychology](/source/psychology) and [psychiatry](/source/psychiatry), kappa represents a measure of diagnostic reliability.<ref>{{Cite book |last=Sadler |first=John Z. |title=Values and psychiatric diagnosis |date=2005 |publisher=Oxford University Press |isbn=978-0-19-852637-7 |series=International perspectives in philosophy and psychiatry |location=Oxford New York, NY |pages=118 |quote=...the other (4b) involve the new (to psychiatry) use of the kappa statistic as a means of measuring diagnostic reliability.}}</ref>

;Economics
* In [macroeconomics](/source/macroeconomics), kappa represents the capital-utilization rate.<ref>{{Cite web|title=University of Hong Kong School of Business|url=http://www.sef.hku.hk/tpg/econ6022b/lecture_note_6_revised.pdf|website=HKU}}</ref>

;Chemistry

* In [chemistry](/source/chemistry), kappa is used to denote the [denticity](/source/denticity) of the compound.<ref>{{Cite book |last=Strohfeldt |first=Katja A. |title=Essentials of Inorganic Chemistry: For Students of Pharmacy, Pharmaceutical Sciences and Medicinal Chemistry |date=2015 |publisher=John Wiley & Sons, Incorporated |isbn=978-0-470-66558-9 |location=Newark |pages=251 |quote=In terms of the nomenclature, the denticity of the ligand is denoted by the Greek letter κ (kappa)}}</ref>

===Uppercase (Κ)===
;History
* In [textual criticism](/source/textual_criticism), the [Byzantine text-type](/source/Byzantine_text-type) (from Κοινη, ''Koine'', the common text).

;Mathematics and statistics
* In [set theory](/source/set_theory), kappa is often used to denote an [ordinal](/source/ordinal_number) that is also a [cardinal](/source/cardinal_number).

;Chemistry
* In [pulping](/source/Pulp_(paper)), the [kappa number](/source/kappa_number) represents the amount of an oxidizing agent required for bleaching a pulp.

==Unicode==

* {{unichar|039A|html=}}
* {{unichar|03BA|html=}}
* {{unichar|03F0|html=}}
* {{unichar|2C94|html=}}
* {{unichar|2C95|html=}}
* {{unichar|2CB8|html=}}
* {{unichar|2CB9|html=}}
* {{unichar|1D6B1|html=}}{{efn|The {{sc|mathematical}} symbols are only used for math. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.}}
* {{unichar|1D6CB|html=}}
* {{unichar|1D6DE|html=}}
* {{unichar|1D6EB|html=}}
* {{unichar|1D705|html=}}
* {{unichar|1D718|html=}}
* {{unichar|1D725|html=}}
* {{unichar|1D73F|html=}}
* {{unichar|1D752|html=}}
* {{unichar|1D75F|html=}}
* {{unichar|1D779|html=}}
* {{unichar|1D78C|html=}}
* {{unichar|1D799|html=}}
* {{unichar|1D7B3|html=}}
* {{unichar|1D7C6|html=}}
{{notelist}}

{{commons category|Kappa (letter)}}{{wiktionary|Κ|κ}}

==References==
{{reflist}}

Category:Greek letters

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Adapted from the Wikipedia article [Kappa](https://en.wikipedia.org/wiki/Kappa) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Kappa?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.