Kappa

Kappa (/ˈkæpə/;^[1] uppercase Κ, lowercase κ or cursive ϰ; Greek: κάππα, káppa) is the tenth letter of the Greek alphabet, representing the voiceless velar plosive IPA: [k] sound in Ancient and Modern Greek. In the system of Greek numerals, Kʹ 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 Romans' transliterations into the Latin alphabet: Constantinople, Corinth, Crete. All formal modern romanizations of Greek now use the letter "k", however.^{[citation needed]}

The cursive form ϰ is generally a simple font variant of lower-case kappa, but it is encoded separately in Unicode for occasions where it is used as a separate symbol in math and science. In mathematics, the kappa curve is named after this letter; the tangents of this curve were first calculated by Isaac Barrow in the 17th century.

Symbol

Lowercase (κ)

Mathematics and statistics

In graph theory, the connectivity of a graph is given by κ.^[2]
In differential geometry, the curvature of a curve is given by κ.^[3]
In linear algebra, the condition number of a matrix is given by κ.^[4]
The kappa curve, also known as Gutschoven's curve, is a curve who shape resembles the letter κ.^[5]
Kappa statistics such as Cohen's kappa^[6]^[7] and Fleiss' kappa are methods for calculating inter-rater reliability.

Physics

In cosmology, the Einstein gravitational constant is denoted by κ.^[8]
In physics, the torsional constant of an oscillator is given by κ.^[9]
In physics, the coupling coefficient in magnetostatics is represented by κ.^[10]
In physics, the dielectric coefficient is represented by κ.
In fluid dynamics, the von Kármán constant is represented by κ.^[11]
thermal conductivity^[12]
In thermodynamics, the compressibility of a compound is given by κ.^[13]

Engineering

In 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 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.

Biology and biomedical science

In biology, kappa and kappa prime are important nucleotide motifs for a tertiary interaction of group II introns.
In biology, kappa designates a subtype of an antibody component.
In pharmacology, kappa represents a type of opioid receptor.^[14]

Psychology and psychiatry

In psychology and psychiatry, kappa represents a measure of diagnostic reliability.^[15]

Economics

In macroeconomics, kappa represents the capital-utilization rate.^[16]

Uppercase (Κ)

History

In textual criticism, the Byzantine text-type (from Κοινη, Koine, the common text).

Mathematics and statistics

In set theory, kappa is often used to denote an ordinal that is also a cardinal.

Chemistry

In chemistry, kappa is used to denote the denticity of the compound.^[17]
In pulping, the kappa number represents the amount of an oxidizing agent required for bleaching a pulp.

Unicode

U+039A Κ GREEK CAPITAL LETTER KAPPA (Κ)
U+03BA κ GREEK SMALL LETTER KAPPA (κ)
U+03F0 ϰ GREEK KAPPA SYMBOL (ϰ, ϰ)
U+2C94 Ⲕ COPTIC CAPITAL LETTER KAPA
U+2C95 ⲕ COPTIC SMALL LETTER KAPA
U+2CB8 Ⲹ COPTIC CAPITAL LETTER DIALECT-P KAPA
U+2CB9 ⲹ COPTIC SMALL LETTER DIALECT-P KAPA
U+1D6B1 𝚱 MATHEMATICAL BOLD CAPITAL KAPPA^[a]
U+1D6CB 𝛋 MATHEMATICAL BOLD SMALL KAPPA
U+1D6DE 𝛞 MATHEMATICAL BOLD KAPPA SYMBOL
U+1D6EB 𝛫 MATHEMATICAL ITALIC CAPITAL KAPPA
U+1D705 𝜅 MATHEMATICAL ITALIC SMALL KAPPA
U+1D718 𝜘 MATHEMATICAL ITALIC KAPPA SYMBOL
U+1D725 𝜥 MATHEMATICAL BOLD ITALIC CAPITAL KAPPA
U+1D73F 𝜿 MATHEMATICAL BOLD ITALIC SMALL KAPPA
U+1D752 𝝒 MATHEMATICAL BOLD ITALIC KAPPA SYMBOL
U+1D75F 𝝟 MATHEMATICAL SANS-SERIF BOLD CAPITAL KAPPA
U+1D779 𝝹 MATHEMATICAL SANS-SERIF BOLD SMALL KAPPA
U+1D78C 𝞌 MATHEMATICAL SANS-SERIF BOLD KAPPA SYMBOL
U+1D799 𝞙 MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL KAPPA
U+1D7B3 𝞳 MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL KAPPA
U+1D7C6 𝟆 MATHEMATICAL SANS-SERIF BOLD ITALIC KAPPA SYMBOL

^ The 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.

References

^ "kappa". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
^ Weisstein, Eric W. "Vertex Connectivity". mathworld.wolfram.com. Retrieved 2025-02-05.
^ Weisstein, Eric W. "Curvature". mathworld.wolfram.com. Retrieved 2025-02-05. Then the curvature κ, sometimes also called the "first curvature" (Kreyszig 1991, p. 47), is defined by...
^ "DLMF: §3.2 Linear Algebra ‣ Areas ‣ Chapter 3 Numerical Methods". dlmf.nist.gov. Retrieved 2025-01-31.
^ Weisstein, Eric W. "Kappa Curve". mathworld.wolfram.com. Retrieved 2025-02-05.
^ McHugh, Mary L. (2012). "Interrater reliability: The kappa statistic". Biochemia Medica. 22 (3): 276–282. doi:10.11613/bm.2012.031. PMC 3900052. PMID 23092060.
^ Gwet, Kilem Li (2014). Handbook of inter-rater reliability: the definitive guide to measuring the extent of agreement among raters (Fourth ed.). Gaithersburg, Md: Advances Analytics, LLC. p. 32. ISBN 978-0-9708062-8-4. Cohen's Kappa Definition
^ Carmeli, Moshe (1982). Classical fields: general relativity and gauge theory. New York: J. Wiley. p. 85. ISBN 978-0-471-86437-0. Here κ is some constant called Einstein's gravitational constant.
^ Halliday, David; Resnick, Robert; Walker, Jearl (2023). Principles of physics. International adaptation (Twelth ed.). Singapore: Wiley. p. 447. ISBN 978-1-119-82061-1. Here κ (Greek kappa) is a constant, called the torsion constant,
^ Stancil, Daniel D. (1993). Theory of magnetostatic waves. New York: Springer-Verlag. p. 200. ISBN 978-0-387-97969-4. The coupling coefficient (7.136) can now be written κ_ab =...
^ Monkewitz, Peter A.; Nagib, Hassan M. (2023). "The hunt for the Kármán 'constant' revisited". Journal of Fluid Mechanics. 967: A15. arXiv:2303.08071. doi:10.1017/jfm.2023.448. ISSN 0022-1120.
^ "Thermal Conductivity - Definition and Detailed Explanation". BYJUS. Retrieved 2025-02-05. It is generally denoted by the symbol 'k' but can also be denoted by 'λ' and 'κ'.
^ Transition metal and rare earth compounds. 3. Topics in current chemistry. Berlin Heidelberg: Springer. 2004. p. 5. ISBN 978-3-540-20948-5. The isothermal compressibility, κ ...
^ Spetea, Mariana; van Rijn, Richard M., eds. (2022). Opioids and Their Receptors: Present and Emerging Concepts in Opioid Drug Discovery II. Basel: MDPI - Multidisciplinary Digital Publishing Institute. ISBN 978-3-0365-4352-9. From a chemical standpoint, opioids comprise a diverse group of drugs, but they all share a common affinity towards μ,δ, and κ receptors
^ Sadler, John Z. (2005). Values and psychiatric diagnosis. International perspectives in philosophy and psychiatry. Oxford New York, NY: Oxford University Press. p. 118. ISBN 978-0-19-852637-7. ...the other (4b) involve the new (to psychiatry) use of the kappa statistic as a means of measuring diagnostic reliability.
^ "University of Hong Kong School of Business" (PDF). HKU.
^ Strohfeldt, Katja A. (2015). Essentials of Inorganic Chemistry: For Students of Pharmacy, Pharmaceutical Sciences and Medicinal Chemistry. Newark: John Wiley & Sons, Incorporated. p. 251. ISBN 978-0-470-66558-9. In terms of the nomenclature, the denticity of the of the ligand is denoted by the Greek letter κ (kappa)

[18] The 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.

[1] "kappa". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)

[2] Weisstein, Eric W. "Vertex Connectivity". mathworld.wolfram.com. Retrieved 2025-02-05.

[3] Weisstein, Eric W. "Curvature". mathworld.wolfram.com. Retrieved 2025-02-05. Then the curvature κ, sometimes also called the "first curvature" (Kreyszig 1991, p. 47), is defined by...

[4] "DLMF: §3.2 Linear Algebra ‣ Areas ‣ Chapter 3 Numerical Methods". dlmf.nist.gov. Retrieved 2025-01-31.

[5] Weisstein, Eric W. "Kappa Curve". mathworld.wolfram.com. Retrieved 2025-02-05.

[Mary2012-6] McHugh, Mary L. (2012). "Interrater reliability: The kappa statistic". Biochemia Medica. 22 (3): 276–282. doi:10.11613/bm.2012.031. PMC 3900052. PMID 23092060.

[7] Gwet, Kilem Li (2014). Handbook of inter-rater reliability: the definitive guide to measuring the extent of agreement among raters (Fourth ed.). Gaithersburg, Md: Advances Analytics, LLC. p. 32. ISBN 978-0-9708062-8-4. Cohen's Kappa Definition

[8] Carmeli, Moshe (1982). Classical fields: general relativity and gauge theory. New York: J. Wiley. p. 85. ISBN 978-0-471-86437-0. Here κ is some constant called Einstein's gravitational constant.

[9] Halliday, David; Resnick, Robert; Walker, Jearl (2023). Principles of physics. International adaptation (Twelth ed.). Singapore: Wiley. p. 447. ISBN 978-1-119-82061-1. Here κ (Greek kappa) is a constant, called the torsion constant,

[10] Stancil, Daniel D. (1993). Theory of magnetostatic waves. New York: Springer-Verlag. p. 200. ISBN 978-0-387-97969-4. The coupling coefficient (7.136) can now be written κ_ab =...

[11] Monkewitz, Peter A.; Nagib, Hassan M. (2023). "The hunt for the Kármán 'constant' revisited". Journal of Fluid Mechanics. 967: A15. arXiv:2303.08071. doi:10.1017/jfm.2023.448. ISSN 0022-1120.

[12] "Thermal Conductivity - Definition and Detailed Explanation". BYJUS. Retrieved 2025-02-05. It is generally denoted by the symbol 'k' but can also be denoted by 'λ' and 'κ'.

[13] Transition metal and rare earth compounds. 3. Topics in current chemistry. Berlin Heidelberg: Springer. 2004. p. 5. ISBN 978-3-540-20948-5. The isothermal compressibility, κ ...

[14] Spetea, Mariana; van Rijn, Richard M., eds. (2022). Opioids and Their Receptors: Present and Emerging Concepts in Opioid Drug Discovery II. Basel: MDPI - Multidisciplinary Digital Publishing Institute. ISBN 978-3-0365-4352-9. From a chemical standpoint, opioids comprise a diverse group of drugs, but they all share a common affinity towards μ,δ, and κ receptors

[15] Sadler, John Z. (2005). Values and psychiatric diagnosis. International perspectives in philosophy and psychiatry. Oxford New York, NY: Oxford University Press. p. 118. ISBN 978-0-19-852637-7. ...the other (4b) involve the new (to psychiatry) use of the kappa statistic as a means of measuring diagnostic reliability.

[16] "University of Hong Kong School of Business" (PDF). HKU.

[17] Strohfeldt, Katja A. (2015). Essentials of Inorganic Chemistry: For Students of Pharmacy, Pharmaceutical Sciences and Medicinal Chemistry. Newark: John Wiley & Sons, Incorporated. p. 251. ISBN 978-0-470-66558-9. In terms of the nomenclature, the denticity of the of the ligand is denoted by the Greek letter κ (kappa)

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[a]