Lambda (; uppercase , lowercase ; , ''lám(b)da'') is the eleventh letter of the

Greek alphabet The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC. It was derived from the earlier Phoenician alphabet, and is the earliest known alphabetic script to systematically write vowels as wel ...

, representing the voiced alveolar lateral approximant . In the system of

Greek numerals Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, is 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 ...

, lambda has a value of 30. Lambda is derived from the Phoenician Lamed. Lambda gave rise to the

Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...

L and the

Cyrillic The Cyrillic script ( ) is a writing system used for various languages across Eurasia. It is the designated national script in various Slavic, Turkic, Mongolic, Uralic, Caucasian and Iranic-speaking countries in Southeastern Europe, Ea ...

El (Л). The ancient grammarians and dramatists give evidence to the pronunciation as () in

Classical Greek Ancient Greek (, ; ) includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archa ...

times. In

Modern Greek Modern Greek (, or , ), 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 language sometimes referred to ...

, the name of the letter, Λάμδα, is pronounced . In early Greek alphabets, the shape and orientation of lambda varied. Most variants consisted of two straight strokes, one longer than the other, connected at their ends. The angle might be in the upper-left, lower-left ("Western" alphabets) or top ("Eastern" alphabets). Other variants had a vertical line with a horizontal or sloped stroke running to the right. With the general adoption of the

Ionic alphabet The history of the Greek alphabet starts with the adoption of Phoenician letter forms in the 9th–8th centuries BC during early Archaic Greece and continues to the present day. The Greek alphabet was developed during the Iron Age, centuries ...

, Greek settled on an angle at the top; the Romans put the angle at the lower-left. NAMA Alphabet grec

Symbol

Upper-case letter Λ

Examples of the symbolic use of uppercase lambda include: * The lambda particle is a type of subatomic particle in subatomic particle physics. * Lambda is the set of logical axioms in the

axiomatic method In mathematics and logic, an axiomatic system is a set of formal statements (i.e. axioms) used to logically derive other statements such as lemmas or theorems. A proof within an axiom system is a sequence of deductive steps that establis ...

of logical deduction in first-order logic. * There is a poetical allusion to the use of Lambda as a shield blazon by the Spartans. * Lambda is the

von Mangoldt function In mathematics, the von Mangoldt function is an arithmetic function named after German mathematician Hans von Mangoldt. It is an example of an important arithmetic function that is neither multiplicative nor additive. Definition The von Mang ...

in mathematical

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

. * Lambda denotes the

de Bruijn–Newman constant The de Bruijn–Newman constant, denoted by \Lambda and named after Nicolaas Govert de Bruijn and Charles Michael Newman, is a mathematical constant defined via the zeros of a certain function H(\lambda,z), where \lambda is a real parameter ...

which is closely connected with

Riemann's hypothesis In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its Root of a function, zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important List of u ...

. * In

statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, lambda is used for the likelihood ratio. * In statistics, Wilks's lambda is used in multivariate analysis of variance (

MANOVA In statistics, multivariate analysis of variance (MANOVA) is a procedure for comparing multivariate sample means. As a multivariate procedure, it is used when there are two or more dependent variables, and is often followed by significance tests ...

analysis) to compare group means on a combination of dependent variables. * In the spectral decomposition of matrices, lambda indicates the

diagonal matrix In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagon ...

of the eigenvalues of the matrix. * In

computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...

, lambda is the time window over which a process is observed for determining the working memory set for a digital computer's

virtual memory In computing, virtual memory, or virtual storage, is a memory management technique that provides an "idealized abstraction of the storage resources that are actually available on a given machine" which "creates the illusion to users of a ver ...

management. * In astrophysics, lambda represents the likelihood that a small body will encounter a

planet A planet is a large, Hydrostatic equilibrium, rounded Astronomical object, astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The Solar System has eight planets b ...

or a

dwarf planet A dwarf planet is a small planetary-mass object that is in direct orbit around the Sun, massive enough to be hydrostatic equilibrium, gravitationally rounded, but insufficient to achieve clearing the neighbourhood, orbital dominance like the ...

leading to a deflection of a significant magnitude. An object with a large value of lambda is expected to have cleared its neighbourhood, satisfying the current definition of a planet. * In crystal optics, lambda is used to represent a lattice period. * In

electrochemistry Electrochemistry is the branch of physical chemistry concerned with the relationship between Electric potential, electrical potential difference and identifiable chemical change. These reactions involve Electron, electrons moving via an electronic ...

, lambda denotes the "equivalent conductance" of an

electrolyte An electrolyte is a substance that conducts electricity through the movement of ions, but not through the movement of electrons. This includes most soluble Salt (chemistry), salts, acids, and Base (chemistry), bases, dissolved in a polar solven ...

solution. * In

cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe, the cosmos. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', with the meaning of "a speaking of the wo ...

, lambda is the symbol for the cosmological constant, a term added to some dynamical equations to account for the accelerating expansion of the universe. * In optics, lambda denotes the grating pitch of a Bragg reflector. * In

politics Politics () is the set of activities that are associated with decision-making, making decisions in social group, groups, or other forms of power (social and political), power relations among individuals, such as the distribution of Social sta ...

, the lambda is the symbol of Identitarianism, a white nationalist movement that originated in

France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...

before spreading out to the rest of

Europe Europe is a continent located entirely in the Northern Hemisphere and mostly in the Eastern Hemisphere. It is bordered by the Arctic Ocean to the north, the Atlantic Ocean to the west, the Mediterranean Sea to the south, and Asia to the east ...

and later on to

North America North America is a continent in the Northern Hemisphere, Northern and Western Hemisphere, Western hemispheres. North America is bordered to the north by the Arctic Ocean, to the east by the Atlantic Ocean, to the southeast by South Ameri ...

Australia Australia, officially the Commonwealth of Australia, is a country comprising mainland Australia, the mainland of the Australia (continent), Australian continent, the island of Tasmania and list of islands of Australia, numerous smaller isl ...

and

New Zealand New Zealand () is an island country in the southwestern Pacific Ocean. It consists of two main landmasses—the North Island () and the South Island ()—and List of islands of New Zealand, over 600 smaller islands. It is the List of isla ...

. The Identitarian lambda represents the Battle of Thermopylae.

Lower-case letter λ

Examples of the symbolic use of lowercase lambda include: * λ indicates the wavelength of any wave, especially in

physics Physics is the scientific study of matter, its Elementary particle, 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 whi ...

electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

, and

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

. * In evolutionary algorithms, λ indicates the number of offspring that would be generated from μ current population in each generation. The terms μ and λ are originated from Evolution strategy notation. * λ indicates the radioactivity decay constant in nuclear physics and radioactivity. This constant is very simply related (by a multiplicative constant) to the

half-life Half-life is a mathematical and scientific description of exponential or gradual decay. Half-life, half life or halflife may also refer to: Film * Half-Life (film), ''Half-Life'' (film), a 2008 independent film by Jennifer Phang * ''Half Life: ...

of any radioactive material. * In

probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...

, λ represents the density of occurrences within a time interval, as modelled by the Poisson distribution. * In

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

and

, λ is used to introduce anonymous functions expressed with the concepts of

lambda calculus In mathematical logic, the lambda calculus (also written as ''λ''-calculus) is a formal system for expressing computability, computation based on function Abstraction (computer science), abstraction and function application, application using var ...

. * λ indicates an eigenvalue in the mathematics of linear algebra. * In the physics of particles, lambda indicates the thermal de Broglie wavelength * In the physics of

electric field An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) descri ...

s, lambda sometimes indicates the linear charge density of a uniform line of

electric charge Electric charge (symbol ''q'', sometimes ''Q'') is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative''. Like charges repel each other and ...

(measured in coulombs per meter). * Lambda denotes a Lagrange multiplier in multi-dimensional calculus. * In solid-state electronics, lambda indicates the channel length modulation parameter of a

MOSFET upright=1.3, Two power MOSFETs in amperes">A in the ''on'' state, dissipating up to about 100 watt">W and controlling a load of over 2000 W. A matchstick is pictured for scale. In electronics, the metal–oxide–semiconductor field- ...

. * In

ecology Ecology () is the natural science of the relationships among living organisms and their Natural environment, environment. Ecology considers organisms at the individual, population, community (ecology), community, ecosystem, and biosphere lev ...

, lambda denotes the long-term intrinsic growth rate of a population. This value is often calculated as the dominant eigenvalue of the age/size class matrix. * In

formal language theory In logic, mathematics, computer science, and linguistics, a formal language is a set of string (computer science), strings whose symbols are taken from a set called "#Definition, alphabet". The alphabet of a formal language consists of symbol ...

and in computer science, lambda denotes the

empty string In formal language theory, the empty string, or empty word, is the unique String (computer science), string of length zero. Formal theory Formally, a string is a finite, ordered sequence of character (symbol), characters such as letters, digits ...

. * Lambda is a nonstandard symbol in the

International Phonetic Alphabet The International Phonetic Alphabet (IPA) is an alphabetic system of phonetic notation based primarily on the Latin script. It was devised by the International Phonetic Association in the late 19th century as a standard written representation ...

for the voiced alveolar lateral affricate . * Lambda denotes the

Lebesgue measure In measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of higher dimensional Euclidean '-spaces. For lower dimensions or , it c ...

in mathematical set theory. * The Goodman and Kruskal's lambda in

indicates the proportional reduction in error when one variable's values are used to predict the values of another variable. * Lambda denotes the oxygen sensor in a vehicle that measures the air-to-fuel ratio in the exhaust gases of an internal-combustion engine. * A Lambda 4S solid-fuel rocket was used to launch Japan's first orbital satellite in 1970. * Lambda denotes the

failure rate Failure is the social concept of not meeting a desirable or intended objective, and is usually viewed as the opposite of success. The criteria for failure depends on context, and may be relative to a particular observer or belief system. On ...

of devices and systems in

reliability theory Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability is defined as the probability that a product, system, or service will perform its intended funct ...

, and it is measured in failure events per hour. Numerically, this lambda is also the reciprocal of the mean time between failures. * In criminology, lambda denotes an individual's frequency of offences. * In

, lambda also denotes the ionic conductance of a given ion (the composition of the ion is generally shown as a subscript to the lambda character). * In neurobiology, lambda denotes the length constant (or exponential rate of decay) of the

electric potential Electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as electric potential energy per unit of electric charge. More precisely, electric potential is the amount of work (physic ...

across the cell membrane along a length of a nerve cell's

axon An axon (from Greek ἄξων ''áxōn'', axis) or nerve fiber (or nerve fibre: see American and British English spelling differences#-re, -er, spelling differences) is a long, slender cellular extensions, projection of a nerve cell, or neuron, ...

. * In the science and technology of heat transfer, lambda denotes the heat of vaporization per mole of material (a.k.a. its "latent heat"). * In the technology and science of celestial navigation, lambda denotes the longitude as opposed to the Roman letter "L", which denotes the

latitude In geography, latitude is a geographic coordinate system, geographic coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at t ...

. * A block style lambda is used as a recurring symbol in the Valve computer game series ''

Half-Life Half-life is a mathematical and scientific description of exponential or gradual decay. Half-life, half life or halflife may also refer to: Film * Half-Life (film), ''Half-Life'' (film), a 2008 independent film by Jennifer Phang * ''Half Life: ...

'', referring to the Lambda Complex of the fictional Black Mesa Research Facility, as well as making appearances in the sequel '' Half-Life 2'', and its subsequent prequel '' Half-Life: Alyx'' as an in-universe symbol of resistance. * In 1970, a lowercase lambda was chosen by Tom Doerr as the symbol of the New York chapter of the Gay Activists Alliance. The lambda symbol became associated with

gay liberation The gay liberation movement was a social and political movement of the late 1960s through the mid-1980s in the Western world, that urged lesbians and gay men to engage in radical direct action, and to counter societal shame with gay pride.Hoff ...

and recognized as an LGBTQ symbol for some time afterwards, being used as such by the International Gay Rights Congress in Edinburgh. * Golomb–Dickman constant

Litra symbol

The Roman and

Byzantine The Byzantine Empire, also known as the Eastern Roman Empire, was the continuation of the Roman Empire centred on Constantinople during late antiquity and the Middle Ages. Having survived the events that caused the fall of the Western Roman E ...

(), which served as both the pound mass unit and liter volume unit, were abbreviated in Greek using lambda with modified forms of the iota subscript ⟨λͅ⟩. These are variously encoded in Unicode. The Ancient Greek Numbers Unicode block includes 10183 (𐆃) as well as 𐅢, which is described as 10162 but was much more common as a form of the litra sign. A variant of the sign can be formed from 0338 and either 039B (Λ̸) or 03BB (λ̸).

Unicode

Unicode uses the (Modern Greek-based) spelling "lamda" in character names, instead of "lambda", due to "the pre-existing names in ISO 8859-7, as well as preferences expressed by the Greek National Body". Latin versions of lambda were added to Unicode in 2024 for the Salishan and Wakashan languages in

Canada Canada is a country in North America. Its Provinces and territories of Canada, ten provinces and three territories extend from the Atlantic Ocean to the Pacific Ocean and northward into the Arctic Ocean, making it the world's List of coun ...

. * * * * * * * * * * * * * * * * * *

References