Phi (uppercase Φ, lowercase or ; Ancient Greek: ϕεῖ, pheî, [pʰé͜e]; modern Greek: φι, fi, [fi]; English: /f/) is the twenty-first letter of the Greek alphabet. In Ancient Greek, it represented an aspiratedvoiceless bilabial plosive ([pʰ]), which was the origin of its usual romanization as "ph". In modern Greek, it represents a voiceless labiodental fricative ([f]) and is correspondingly romanized as "f". Its origin is uncertain but it might be that phi originated as the letter qoppa 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.

Phi is additionally used as a symbol for the golden ratio and on additional occasions in maths and science. This use is separately encoded as the Unicode glyph ϕ. The modern Greek pronunciation of the letter is at times encountered in English (as /f/) when the letter is being used in this sense.

Use as a symbol

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

The upper-case letter Φ is used as a symbol for:

The diameter symbol in engineering, , is often incorrectly 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:

CharacterNameCorrect appearanceYour browserUsage
U+03A6GREEK CAPITAL LETTER PHIΦused in Greek texts
U+03C6GREEK SMALL LETTER PHI or φused in Greek texts
U+03D5GREEK PHI SYMBOLϕused in mathematical and technical contexts. Here 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, at times 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 a few Greek typefaces, most notably "Porson" typefaces (used widely in editions of classical Greek texts), have a "stroked" glyph in this position (), most additional 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 a few 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 might still show a loopy form at U+03D5.

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 maths symbols are Phi (), phi (), and varphi ().

The Unicode standard additionally 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