# Phi

Phi (/f/;[1] uppercase Φ, lowercase φ or ϕ; Ancient Greek: ϕεῖ pheî [pʰé͜e]; 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 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 is used as a mathematical or scientific symbol. Some uses, such as the golden ratio, require the old-fashioned 'closed' glyph, which is separately encoded as the Unicode character U+03D5 ϕ GREEK PHI SYMBOL.

## Use as a 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.

## Computing

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

U+03A6GREEK CAPITAL LETTER PHI${\displaystyle \Phi \,\!}$ΦUsed in Greek texts
U+03C6GREEK SMALL LETTER PHI or φUsed in Greek texts
U+03D5GREEK PHI SYMBOL${\displaystyle \phi \,\!}$ϕ (ϕ)Used in mathematical and technical contexts.[4] (Italicized.)
U+0278LATIN SMALL LETTER PHIɸUsed 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). Unicode makes an effort to distinguish the two by generally calling the loopy form "small letter phi" or "small phi", and by calling the stroked form "phi symbol", but this isn't exclusively true on all variants.

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 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 goes for the "Didot" (or "apla") typefaces employed in most Greek book printing (), as well as for 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.[4]

For use as a phonetic symbol in IPA, Unicode has a separate code point 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 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:

CharacterNameAppearance
U+1D60MODIFIER LETTER SMALL GREEK PHI
U+1D69GREEK SUBSCRIPT SMALL LETTER PHI
U+1DB2MODIFIER LETTER SMALL PHI
U+2CAACOPTIC CAPITAL LETTER FI
U+2CABCOPTIC SMALL LETTER FI
U+2C77LATIN SMALL LETTER TAILLESS PHI
U+1D6BDMATHEMATICAL BOLD CAPITAL PHI𝚽
U+1D6D7MATHEMATICAL BOLD SMALL PHI𝛗
U+1D6DFMATHEMATICAL BOLD PHI SYMBOL𝛟
U+1D6F7MATHEMATICAL ITALIC CAPITAL PHI𝛷
U+1D711MATHEMATICAL ITALIC SMALL PHI𝜑
U+1D719MATHEMATICAL ITALIC PHI SYMBOL𝜙
U+1D731MATHEMATICAL BOLD ITALIC CAPITAL PHI𝜱
U+1D74BMATHEMATICAL BOLD ITALIC SMALL PHI𝝋
U+1D753MATHEMATICAL BOLD ITALIC PHI SYMBOL𝝓
U+1D76BMATHEMATICAL SANS-SERIF BOLD CAPITAL PHI𝝫
U+1D785MATHEMATICAL SANS-SERIF BOLD SMALL PHI𝞅
U+1D78DMATHEMATICAL SANS-SERIF BOLD PHI SYMBOL𝞍
U+1D7A5MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL PHI𝞥
U+1D7BFMATHEMATICAL SANS-SERIF BOLD ITALIC SMALL PHI𝞿
U+1D7C7MATHEMATICAL SANS-SERIF BOLD ITALIC PHI SYMBOL𝟇