|Use in other languages|
Phi (/faɪ/; 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]. 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 old-fashioned '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 "straight-line" variant glyph is preferred.|
|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.
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 (), and
The Unicode standard also includes the following variants of phi and phi-like characters:
|Unicode name||GREEK CAPITAL LETTER PHI||GREEK SMALL LETTER PHI||COPTIC CAPITAL LETTER FI||COPTIC SMALL LETTER FI|
|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||Φ
|Named character reference||Φ||φ|
|Unicode name||LATIN SMALL LETTER PHI||LATIN SMALL LETTER TAILLESS PHI|
|UTF-8||201 184||C9 B8||226 177 183||E2 B1 B7|
|Numeric character reference||ɸ
|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 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|