Phi in LaTeX (\phi)

Where it is used

Lowercase Greek phi, used for angles, the golden ratio, Euler's totient function, and feature maps.

\phi gives the closed, stroked form, while \varphi gives the open, loopy form; many authors choose \varphi for functions and keep \phi for angles. Number theory writes Euler's totient as \varphi(n) or \phi(n), the golden ratio is \phi = (1 + \sqrt{5})/2, and spherical coordinates use \phi for an angle. Machine learning uses \phi(x) for a feature map in kernel methods, and physics uses it for scalar potentials and wavefunctions. Do not confuse \phi with \emptyset or the Scandinavian Ø.

Also listed under: Trigonometry

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Phi: $\phi$

\[ \phi = \frac{1 + \sqrt{5}}{2} \approx 1.618 \]
\end{document}

Related symbols

• Phi (Upper)\Phi
• Upsilon (Upper)\Upsilon
• Chi\chi
• Upsilon\upsilon
• Psi\psi
• Tau\tau

Frequently asked questions

How do I write Phi in LaTeX?

Type \phi in math mode, for example $\phi = \frac{1 + \sqrt{5}}{2} \approx 1.618$. It works in plain LaTeX without loading any package.

Which package do I need for \phi?

None. \phi is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \phi in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\phi$ in running text. If you only need the glyph in text, paste the Unicode character ϕ instead (with XeLaTeX or LuaLaTeX and a font that has it).