Phi (uppercase Φ, lowercase φ, or math symbol ϕ, also fi), pronounced // or sometimes // in English,^{[1]} and [ˈfi] in modern Greek, is the 21st letter of the Greek alphabet. In modern Greek, it represents [f], a voiceless labiodental fricative. In Ancient Greek it represented [pʰ], an aspirated voiceless bilabial plosive (from which English ultimately inherits the spelling "ph" in words derived from Greek). In the system of Greek numerals it has a value of 500 (φʹ) or 500,000 (͵φ). The Cyrillic letter Ef (Ф, ф) arose from Φ.
Use as a symbol
The lowercase letter φ (or often its variant, ϕ) is often used to represent the following:
 The golden ratio $\backslash tfrac\{1\; +\; \backslash sqrt\{5\}\}\{2\}\; \backslash approx$ 1.618033988749894848204586834... in mathematics, art, and architecture.
 Euler's totient function φ(n) in number theory; also called Euler's phi function.
 In algebra, group or ring homomorphisms
 In probability theory, ϕ(x) = (2π)^{−½}e^{−x2/2} is the probability density function of the normal distribution.
 In probability theory, φ_{X}(t) = E[e^{itX}] is the characteristic function of a random variable X.
 An angle, typically the second angle mentioned, after θ (theta). Especially:
 The work function in electronics.
 A shorthand representation for an aromatic functional group in organic chemistry.
 The fugacity coefficient in thermodynamics.
 The ratio of free energy destabilizations of protein mutants in phi value analysis.
 In cartography and navigation, latitude.
 In combustion engineering, equivalence ratio. The ratio between the actual fuel air ratio to the stoichiometric fuel air ratio.
 A sentence in firstorder logic.
 Porosity in geology and hydrology.
 Strength (or resistance) reduction factor in structural engineering, used to account for statistical variabilities in materials and construction methods.
 The symbol for a voiceless bilabial fricative in the International Phonetic Alphabet (using the straight line variant character)
 In economics, this is usually an additive term.
 In flight dynamics, the roll angle.
 In philosophy, φ is often used as shorthand for a generic act. (Also in uppercase.)
The uppercase letter Φ is used as a symbol for:
The diameter symbol in engineering, ⌀, is often incorrectly^{[citation needed]} referred to as "phi". This symbol is used to indicate the diameter of a circular section, for example "⌀14", means the diameter of the circle is 14 units.
Computing
In Unicode, there are multiple forms of the phi letter:
Character 
Name 
Correct appearance 
Your browser 
Usage

U+03A6 
GREEK CAPITAL LETTER PHI 
$\backslash Phi\backslash ,\backslash !$ 
Φ 
used in Greek texts

U+03C6 
GREEK SMALL LETTER PHI 

φ 
used in Greek texts

U+03D5 
GREEK PHI SYMBOL 
$\backslash phi\backslash ,\backslash !$ 
ϕ 
used in mathematical and technical contexts^{[3]}

U+0278 
LATIN SMALL LETTER PHI 

ɸ 
used in IPA to symbolise a voiceless bilabial fricative

In ordinary Greek text, the character U+03C6 φ is used exclusively, although this character has considerable glyphic variation, sometimes represented with a glyph more like the representative glyph shown for U+03C6 (φ, the “loopy” form) and less often with a glyph more like the representative glyph shown for U+03D5 (ϕ, the “straight“ form).
Because Unicode represents a character in an abstract way, the choice between glyphs is purely a matter of font design. While some Greek typefaces, most notably "Porson" typefaces (used widely in editions of classical Greek texts), have a "stroked" glyph in this position ().
It is necessary to have the stroked glyph available for some mathematical uses, and U+03D5 GREEK PHI SYMBOL is designed for this function. Prior to Unicode version 3.0 (1998), the glyph assignments in the Unicode code charts were the reverse, and thus older fonts may still show a loopy form $\backslash varphi$ at U+03D5.^{[3]}
For use as a phonetic symbol in IPA, Unicode has a separate codepoint U+0278, LATIN SMALL LETTER PHI, because in this use only the stroked glyph is considered correct. It typically appears in a form adapted to a Latin typographic environment, with a more upright shape than normal Greek letters and with serifs at the top and bottom.
In HTML/XHTML, the upper and lower case phi character entity references are Φ (Φ) and φ (φ) respectively.
In LaTeX, the math symbols are \Phi ($\backslash Phi\backslash ,\backslash !$), \phi ($\backslash phi\backslash ,\backslash !$), and \varphi ($\backslash varphi\backslash ,\backslash !$).
The Unicode standard also includes the following variants of phi and philike characters:
Character 
Name 
Appearance

U+1D60 
MODIFIER LETTER SMALL GREEK PHI 
ᵠ

U+1D69 
GREEK SUBSCRIPT SMALL LETTER PHI 
ᵩ

U+1DB2 
MODIFIER LETTER SMALL PHI 
ᶲ

U+2CAA 
COPTIC CAPITAL LETTER FI 
Ⲫ

U+2CAB 
COPTIC SMALL LETTER FI 
ⲫ

U+2C77 
LATIN SMALL LETTER TAILLESS PHI 
ⱷ

U+1D6BD 
MATHEMATICAL BOLD CAPITAL PHI 
𝚽

U+1D6D7 
MATHEMATICAL BOLD SMALL PHI 
𝛗

U+1D6DF 
MATHEMATICAL BOLD PHI SYMBOL 
𝛟

U+1D6F7 
MATHEMATICAL ITALIC CAPITAL PHI 
𝛷

U+1D711 
MATHEMATICAL ITALIC SMALL PHI 
𝜑

U+1D719 
MATHEMATICAL ITALIC PHI SYMBOL 
𝜙

U+1D731 
MATHEMATICAL BOLD ITALIC CAPITAL PHI 
𝜱

U+1D74B 
MATHEMATICAL BOLD ITALIC SMALL PHI 
𝝋

U+1D753 
MATHEMATICAL BOLD ITALIC PHI SYMBOL 
𝝓

U+1D76B 
MATHEMATICAL SANSSERIF BOLD CAPITAL PHI 
𝝫

U+1D785 
MATHEMATICAL SANSSERIF BOLD SMALL PHI 
𝞅

U+1D78D 
MATHEMATICAL SANSSERIF BOLD PHI SYMBOL 
𝞍

U+1D7A5 
MATHEMATICAL SANSSERIF BOLD ITALIC CAPITAL PHI 
𝞥

U+1D7BF 
MATHEMATICAL SANSSERIF BOLD ITALIC SMALL PHI 
𝞿

U+1D7C7 
MATHEMATICAL SANSSERIF BOLD ITALIC PHI SYMBOL 
𝟇

See also
References
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