Phi (Φ φ) in LaTeX
Phi is the twenty-first Greek letter. LaTeX gives it three forms in maths mode: \phi for the default lowercase glyph (a closed loop), \varphi for the open, cursive lowercase variant, and \Phi for the uppercase form.
LaTeX command
\PhiNot the symbol you meant? Draw it to find the command →
Phi is everywhere in mathematics and physics: the golden ratio, angles in spherical and polar coordinates (usually the azimuthal angle), electric and magnetic flux, and wave functions in some conventions. Because it is so common, many documents end up needing both the upright and curly forms to distinguish two related quantities.
\phi and \varphi are not the same glyph and not interchangeable by convention: \phi renders LaTeX's default closed-loop phi, while \varphi renders the open, more cursive shape that many mathematicians and most handwriting actually use for phi. Pick one per document and stay consistent, since mixing them for the same quantity reads as an inconsistency rather than a stylistic choice.
Uppercase \Phi has its own strong conventions: it is the standard symbol for the golden ratio in some traditions, for magnetic flux in electromagnetism, and for the cumulative distribution function of the standard normal distribution in statistics.
Other forms
\philowercase phi\Phiuppercase phi (Φ)\varphicurly / variant formExamples
$\phi$the default closed-loop lowercase phi
$\varphi$the open, cursive variant of lowercase phi
$\Phi$uppercase phi
$\Phi = \frac{1+\sqrt{5}}{2}$the golden ratio
$\Phi(x)$the standard normal cumulative distribution function
Tips and common mistakes
\phiand\varphiare visually different glyphs, not aliases; check which one your source or field actually uses before typing.- Physics texts commonly use
\varphifor the azimuthal angle in spherical coordinates, while pure maths texts often default to\phi. - Stick to one of
\phior\varphifor a given quantity throughout a document, switching partway through reads as a typo. \Phiis heavily overloaded across fields, golden ratio, magnetic flux, normal CDF, so define it explicitly the first time you use it.
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What is the difference between \phi and \varphi in LaTeX?
\phi produces LaTeX's default closed-loop lowercase phi glyph, while \varphi produces the open, cursive variant. They look different and are chosen independently; neither is more correct, but you should be consistent within a document.
Which phi symbol is the golden ratio?
Conventions differ; some texts write it as \varphi, others as \phi. Either renders correctly in LaTeX, what matters is stating your convention once.
How do I type phi in LaTeX?
Use \phi or \varphi for lowercase, and \Phi for uppercase, all inside maths mode, for example .
Is \Phi the same as the normal distribution CDF symbol?
Yes, \Phi(x) is the standard notation in statistics for the cumulative distribution function of the standard normal distribution.