Phi (Upper) in LaTeX (\Phi)

Where it is used

Uppercase Greek Phi, used for the standard normal CDF, magnetic flux, and potentials.

Statistics writes the standard normal cumulative distribution function as \Phi(z), with lowercase \phi(z) for the density. Physics uses \Phi_B for magnetic flux and \Phi for electric potential, while engineering uses it for flux in general. In linear algebra and optimization \Phi can name a design matrix of basis functions. Capital Greek is upright in LaTeX; \varPhi gives the italic variant. Do not confuse \Phi with \emptyset or with the circled \oslash. Its inverse \Phi^{-1} gives normal quantiles such as z_{0.975} \approx 1.96.

Minimal compilable example

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

\documentclass{article}
\begin{document}
Phi (Upper): $\Phi$

\[ P(Z \le z) = \Phi(z) = \int_{-\infty}^{z} \phi(t)\,dt \]
\end{document}

Related symbols

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

Frequently asked questions

How do I write Phi (Upper) in LaTeX?

Type \Phi in math mode, for example $P(Z \le z) = \Phi(z) = \int_{-\infty}^{z} \phi(t)\,dt$. 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).