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Phi (/faɪ/;^{[1]} uppercase Φ, lowercase φ or ϕ; Ancient Greek: ϕεῖ pheî [pʰéî̯]; Modern Greek: φι fi [fi]) is the 21st 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].^{[2]} 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, such as the golden ratio,^{[contradictory]} require the oldfashioned 'closed' glyph, which is separately encoded as the Unicode character U+03D5 ϕ GREEK PHI SYMBOL.
The lowercase letter φ (or often its variant, ϕ) is often used to represent the following:
The uppercase letter Φ is used as a symbol for:
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.
In Unicode, there are multiple forms of the phi letter:
Character  Name  Correct appearance  Your browser  LaTeX  Usage 

U+03A6  GREEK CAPITAL LETTER PHI  Φ  Used in Greek texts  
U+03C6  GREEK SMALL LETTER PHI  φ  or  Used in Greek texts  
U+03D5  GREEK PHI SYMBOL  ϕ  ϕ (ϕ)  Intended for use in modern (monotonic) Greek texts. Used italicized in mathematical and technical contexts when the "straightline" variant glyph is preferred.^{[7]}  
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" 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 (
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 at U+03D5.^{[7]}
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 Φ
(Φ) and φ
(φ), respectively.
In LaTeX, the math symbols are \Phi
(), \phi
(), and \varphi
().
The Unicode standard also includes the following variants of phi and philike characters:
Preview  Φ  φ  Ⲫ  ⲫ  

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 
UTF8  206 166  CE A6  207 134  CF 86  226 178 170  E2 B2 AA  226 178 171  E2 B2 AB 
Numeric character reference  Φ 
Φ 
φ 
φ 
Ⲫ 
Ⲫ 
ⲫ 
ⲫ 
Named character reference  Φ  φ 
Preview  ɸ  ⱷ  

Unicode name  LATIN SMALL LETTER PHI  LATIN SMALL LETTER TAILLESS PHI  
Encodings  decimal  hex  dec  hex 
Unicode  632  U+0278  11383  U+2C77 
UTF8  201 184  C9 B8  226 177 183  E2 B1 B7 
Numeric character reference  ɸ 
ɸ 
ⱷ 
ⱷ 
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 