Rho (uppercase Ρ, lowercase ρ or ; el, ῥῶ) is the 17th letter of the

^{+}, ρ^{−}, ρ^{0})
** General quantum states
**

Greek letters

Greek alphabet
The Greek alphabet has been used to write the Greek language since the late ninth or early eighth century BC. It is derived from the earlier Phoenician alphabet, and was the first alphabetic script in history to have distinct letters for vowels ...

. In the system of Greek numerals
Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a numeral system, system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal number (linguistics), ordi ...

it has a value of 100. It is derived from . Its uppercase form uses the same glyph
The term glyph is used in typography
Typography is the art and technique of arranging type to make written language
A written language is the representation of a spoken or gestural language
A language is a structured system o ...

, Ρ, as the distinct Latin
Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Roman Republic, it became ...

letter ; the two letters have different Unicode encodings.
Uses

Greek

Rho is classed as aliquid consonant
In phonetics
Phonetics is a branch of that studies how humans produce and perceive sounds, or in the case of s, the equivalent aspects of sign. Phoneticians—linguists who specialize in phonetics—study the physical properties of speech. Th ...

(together with Lambda
Lambda (; uppercase , lowercase ; el, λάμ(β)δα, ''lám(b)da'') is the 11th letter of the Greek alphabet, representing the sound Dental, alveolar and postalveolar lateral approximants, /l/. In the system of Greek numerals, lambda has a ...

and sometimes the nasals Mu and Nu), which has important implications for morphology
Morphology, from the Greek and meaning "study of shape", may refer to:
Disciplines
* Morphology (archaeology), study of the shapes or forms of artifacts
* Morphology (astronomy), study of the shape of astronomical objects such as nebulae, galaxies ...

. In both Ancient
Ancient history is the aggregate of past eventsWordNet Search – 3.0

"History" from ...

and "History" from ...

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 l ...

, it represents a trilled or .
In polytonic orthography
Greek orthographyThe orthography of the Greek language ultimately has its roots in the adoption of the Greek alphabet in the 9th century BC. Some time prior to that, one early form of Greek, Mycenaean language, Mycenaean, was written in Linear ...

, a rho at the beginning of a word is written with a rough breathing
In the polytonic orthography
Greek orthographyThe orthography of the Greek language ultimately has its roots in the adoption of the Greek alphabet in the 9th century BC. Some time prior to that, one early form of Greek, Mycenaean language, My ...

, equivalent to ''h'' ( ''rh''), and a double
Double may refer to:
* Look-alike, a person who closely resembles another person
* Double (filmmaking), someone who substitutes for the credited actor of a character
* Doppelgänger, ghostly double of a living person
* Polish Enigma doubles, repl ...

rho within a word is written with a smooth breathing
The smooth breathing ( grc, ψιλὸν πνεῦμα, psilòn pneûma; ell, ψιλή ''psilí''; la, spīritus lēnis) is a diacritical mark
A diacritic (also diacritical mark, diacritical point, diacritical sign, or accent) is a glyph adde ...

over the first rho and a rough breathing over the second ( ''rrh''). That apparently reflected an aspirated or voiceless
In linguistics
Linguistics is the science, scientific study of language. It encompasses the analysis of every aspect of language, as well as the methods for studying and modeling them.
The traditional areas of linguistic analysis include ...

pronunciation in Ancient Greek
Ancient Greek includes the forms of the Greek language
Greek ( el, label=Modern Greek
Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the diale ...

, which led to the various Greek-derived English words starting with ''rh'' or contain ''rrh''.
The name of the letter is written in Greek as (polytonic) or ρω/ ρο (monotonic).
Other alphabets

Letters that arose from rho include Roman and Cyrillic Er (Р).Mathematics and science

The characters ρ and are also conventionally used outside the Greek alphabetical context inscience
Science () is a systematic enterprise that builds and organizes knowledge
Knowledge is a familiarity or awareness, of someone or something, such as facts
A fact is something that is truth, true. The usual test for a statement of ...

and mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ...

.
*In the physical sciences
Physical science is a branch of natural science
Natural science is a branch
A branch ( or , ) or tree branch (sometimes referred to in botany
Botany, also called , plant biology or phytology, is the science of plant life and a b ...

to represent:
**Densities: mass density
The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its mass per unit volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter Rho (letter), rho), although the L ...

, air density The density of air or atmospheric density, denoted ''ρ'' (Greek#REDIRECT Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece
Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Sout ...

or charge density
In electromagnetism
Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is c ...

(''ρ'')
**Resistivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...

(''ρ'')
**Rho meson
In particle physics
Particle physics (also known as high energy physics) is a branch of physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department ...

(ρHammett Equation
The Hammett equation in organic chemistry describes a linear free-energy relationship relating reaction rates and equilibrium constants for many reactions involving benzoic acid derivatives with meta- and para- substituents to each other with ...

, ρ is used to represent the reaction constant, this is independent of the position and nature of the substituents of the benzene ring.
*In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ...

to represent:
**A length coordinate in polar
Polar may refer to:
Geography
Polar may refer to:
* Geographical pole, either of two fixed points on the surface of a rotating body or planet, at 90 degrees from the equator, based on the axis around which a body rotates
*Polar climate, the clim ...

, cylindrical
A cylinder (from ) has traditionally been a Solid geometry, three-dimensional solid, one of the most basic of curvilinear geometric shapes. Geometrically, it can be considered as a Prism (geometry), prism with a circle as its base.
This traditi ...

, spherical
of a sphere
A sphere (from Greek language, Greek —, "globe, ball") is a geometrical object in three-dimensional space
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values ...

, and toroidal coordinate systems, and toroidal and poloidal
Image:Toroidal coord.png, 250px, A diagram depicting the poloidal (\theta) direction, represented by the red arrow, and the toroidal (\zeta or \phi) direction, represented by the blue arrow.The terms toroidal and poloidal refer to directions relativ ...

coordinates of the Earth's magnetic field.
**The correlation coefficient
A correlation coefficient is a numerical measure of some type of correlation and dependence, correlation, meaning a statistical relationship between two variable (mathematics), variables. The variables may be two column (database), columns of a give ...

of a population parameter
**The spectral radius
''Spectral'' is a 2016 American military science fiction action film
Action film is a film genre in which the protagonist or protagonists are thrust into a series of events that typically include violence, extended fighting, physical feats, ...

of a matrix $A$ denoted as $\backslash rho(A)$
**The plastic number
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...

**The prime constant
**The sensitivity to interest rates of a pricing function
**The expected return of a given policy ($\backslash pi$) in reinforcement learning
Reinforcement learning (RL) is an area of machine learning
Machine learning (ML) is the study of computer algorithms that can improve automatically through experience and by the use of data. It is seen as a part of artificial intelligence. M ...

, denoted $\backslash rho^\backslash pi$
*In economics
Economics () is a social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and interact ...

to represent the discount rate of future pence cash flows
*In molecular biology
Molecular biology is the branch of biology
Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, P ...

to represent the Rho protein responsible for termination of RNA synthesis. In such occasions, it is often represented as , to avoid confusion with the Latin letter ''p''
*In molecular biology
Molecular biology is the branch of biology
Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, P ...

to represent the Rho family of GTPases
The Rho family of GTPases is a family of small (~21 kDa) signaling G proteins, and is a subfamily of the Ras superfamily. The members of the Rho GTPase family have been shown to regulate many aspects of intracellular actin dynamics, and are found ...

, important for cytoskeletal dynamic regulation.
*In ecology
Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms
In biol ...

to represent the population damping ratio where ρ = λ1 / , λ2, .
*In computer programming
Computer programming is the process of designing and building an executable computer program to accomplish a specific computing result or to perform a particular task. Programming involves tasks such as analysis, generating algorithms, Profilin ...

**The lower-case rho "⍴" means reshape in the APL programming language
APL (named after the book ''A Programming Language'') is a programming language
A programming language is a formal language comprising a Instruction set architecture, set of instructions that produce various kinds of Input/output, output. Pr ...

, and by extension also queries shape
**The lower-case rho "ρ" is used for the unary rename operation in relational algebra
In database theory, relational algebra is a theory that uses algebraic structures with a well-founded semantics for modeling data, and defining queries on it. The theory has been introduced by Edgar F. Codd.
The main application of relational ...

*In statistics
Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data
Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...

to represent Spearman's rank correlation coefficient 300px, When the data are roughly elliptically distributed and there are no prominent outliers, the Spearman correlation and Pearson correlation give similar values.
In statistics
Statistics is the discipline that concerns the collection, orga ...

, commonly known as Spearman's rho
*In options theory to represent the rate of change of a portfolio with respect to interest rates
An interest rate is the amount of interest
In finance
Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and inves ...

Chi Rho

The letter rho overlaid withchiThe initialism CHI may refer to:
Health
*Catholic Health Initiatives
Catholic Health Initiatives (CHI) is a national Catholic healthcare system, with headquarters in Englewood, Colorado. CHI is a nonprofit, faith-based health system formed, in 19 ...

forms the ''Chi Rho
The Chi Rho (; also known as ''chrismon'') is one of the earliest forms of christogram, formed by superimposing the first two (capital) letters—chi (letter), chi and rho (ΧΡ)—of the Greek word (Christ (title), Christos) in such a way th ...

'' symbol, used to represent Jesus Christ
Jesus, likely from he, יֵשׁוּעַ, translit=Yēšūaʿ, label=Hebrew
Hebrew (, , or ) is a Northwest Semitic languages, Northwest Semitic language of the Afroasiatic languages, Afroasiatic language family. Historically, it i ...

.
Rho with stroke (ϼ)

The rho with a stroke through its tail is used for abbreviations involving rho, most notably in γϼ for γράμμα as a unit of measurement.Character encodings

Greek rhoUnicode Code Charts

Greek and Coptic (Range: 0370-03FF)

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Greek rho symbols

Coptic ro

Functional symbol

Mathematical rho

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.See also

* Р, р - Er (Cyrillic) * *References

{{Wiktionary, Ρ, ρ