# Phi(Redirected from Φ)

Phi (/faɪ/; uppercase Φ, lowercase φ or ϕ; Ancient Greek: ϕεῖ pheî [pʰéî̯]; Modern Greek: φι fi [fi]) is the twenty-first letter of the Greek alphabet.

In Archaic and Classical Greek (c. 9th century BC to 4th century BC), it represented an aspirated voiceless bilabial plosive ([pʰ]), which was the origin of its usual romanization as ⟨ph⟩. During the later part of Classical Antiquity, in Koine Greek (c. 4th century BC to 4th century AD), its pronunciation shifted to that of a voiceless bilabial fricative ([ɸ]), and by the Byzantine Greek period (c. 4th century AD to 15th century AD) it developed its modern pronunciation as a voiceless labiodental fricative ([f]). The romanization of the Modern Greek phoneme is therefore usually ⟨f⟩.

It may be that phi originated as the letter qoppa (Ϙ, ϙ), and initially represented the sound /kʷʰ/ before shifting to Classical Greek [pʰ]. In traditional Greek numerals, phi has a value of 500 (φʹ) or 500,000 (͵φ). The Cyrillic letter Ef (Ф, ф) descends from phi.

As with other Greek letters, lowercase phi (encoded as the Unicode character U+03C6 φ GREEK SMALL LETTER PHI) is used as a mathematical or scientific symbol. Some uses[example needed] require the old-fashioned 'closed' glyph, which is separately encoded as the Unicode character U+03D5 ϕ GREEK PHI SYMBOL.

## Use as a symbol

### In lowercase

The lowercase letter φ (or often its variant, ϕ) is often used to represent the following:

### In uppercase

The uppercase letter Φ is used as a symbol for:

• The golden ratio conjugate −0.618... in mathematics.
• The cumulative distribution function (cdf) of standard normal distribution in statistics.
• The magnetic flux and electric flux in physics, with subscripts distinguishing the two.
• Quantum yield, the number of times a specific event occurs per photon absorbed by a system.
• In philosophy, Φ is often used as shorthand for a generic act. (Also in lowercase.)[citation needed]
• A common symbol for the parametrization of a surface in vector calculus.
• In Lacanian algebra, Φ stands for the imaginary phallus and also represents phallic signification; −Φ stands in for castration.[dubious ]
• The diameter symbol in engineering, , is often erroneously referred to as "phi", and the diameter symbol is sometimes erroneously typeset as Φ. This symbol is used to indicate the diameter of a circular section; for example, "⌀14" means the diameter of the circle is 14 units.
• A clock signal in electronics is often called Phi or uses the symbol.
• In emulsion and suspension science, Φ often denotes the volume fraction of the dispersed phase.
• Archaically used in chemistry for phenyl group.

## Computing

In Unicode, there are multiple forms of the phi letter:

Character Name Correct appearance Your browser LaTeX Usage
U+03A6 GREEK CAPITAL LETTER PHI ${\displaystyle \Phi \,\!}$ Φ ${\displaystyle \Phi }$ Used in Greek texts
U+03C6 GREEK SMALL LETTER PHI or φ ${\displaystyle \varphi }$ or ${\displaystyle \phi }$ Used in Greek texts
U+03D5 GREEK PHI SYMBOL ϕ ϕ (ϕ) ${\displaystyle \phi }$ Intended for use in modern (monotonic) Greek texts. Used italicized in mathematical and technical contexts when the "straight-line" variant glyph is preferred.
U+0278 LATIN SMALL LETTER PHI ɸ ${\displaystyle }$ 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" or "open" form), and less often with a glyph more like the representative glyph shown for U+03D5 (ϕ, the "stroked" or "closed" 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 those in the Porson family (used widely in editions of classical Greek texts), have a "stroked" glyph in this position (), most other typefaces have "loopy" glyphs. This also applies to the "Didot" (or "apla") typefaces employed in most Greek book printing (), as well as the "Neohellenic" typeface often used for ancient texts ().

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 ${\displaystyle \varphi }$ at U+03D5.

For use as a phonetic symbol in IPA, Unicode has a separate code point U+0278, LATIN SMALL LETTER PHI, because only the stroked glyph is considered correct in this use. 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 lowercase phi character entity references are &Phi; (Φ) and &phi; (φ), respectively.

In LaTeX, the math symbols are \Phi (${\displaystyle \Phi \,\!}$), \phi (${\displaystyle \phi \,\!}$), and \varphi (${\displaystyle \varphi \,\!}$).

The Unicode standard also includes the following variants of phi and phi-like characters:

Character information
Preview Φ φ
Unicode name GREEK CAPITAL LETTER PHI GREEK SMALL LETTER PHI COPTIC CAPITAL LETTER FI COPTIC SMALL LETTER FI
Encodings decimal hex dec hex dec hex dec hex
Unicode 934 U+03A6 966 U+03C6 11434 U+2CAA 11435 U+2CAB
UTF-8 206 166 CE A6 207 134 CF 86 226 178 170 E2 B2 AA 226 178 171 E2 B2 AB
Numeric character reference &#934; &#x3A6; &#966; &#x3C6; &#11434; &#x2CAA; &#11435; &#x2CAB;
Named character reference &Phi; &phi;
Character information
Preview ɸ
Unicode name LATIN SMALL LETTER PHI LATIN SMALL LETTER TAILLESS PHI
Encodings decimal hex dec hex
Unicode 632 U+0278 11383 U+2C77
UTF-8 201 184 C9 B8 226 177 183 E2 B1 B7
Numeric character reference &#632; &#x278; &#11383; &#x2C77;
Character Name Appearance
U+1D60 MODIFIER LETTER SMALL GREEK PHI
U+1D69 GREEK SUBSCRIPT SMALL LETTER PHI
U+1DB2 MODIFIER LETTER SMALL PHI
U+2CAA COPTIC CAPITAL LETTER FI
U+2CAB COPTIC SMALL LETTER FI
U+2C77 LATIN SMALL LETTER TAILLESS PHI
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 SANS-SERIF BOLD CAPITAL PHI 𝝫
U+1D785 MATHEMATICAL SANS-SERIF BOLD SMALL PHI 𝞅
U+1D78D MATHEMATICAL SANS-SERIF BOLD PHI SYMBOL 𝞍
U+1D7A5 MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL PHI 𝞥
U+1D7BF MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL PHI 𝞿
U+1D7C7 MATHEMATICAL SANS-SERIF BOLD ITALIC PHI SYMBOL 𝟇