What the phi symbol means
Phi (φ, capital Φ) is the 21st letter of the Greek alphabet. Its most famous job is the golden ratio: φ = (1 + √5) / 2 ≈ 1.618. Divide any Fibonacci number by the one before it and the result gets closer and closer to φ.
In geometry and physics, φ is a standard angle symbol, used for one of the two angles in polar and spherical coordinates. Physics and math books disagree on which angle is θ and which is φ, so check the convention in your textbook. Capital Φ stands for magnetic or electric flux, and φ also marks the phase of a wave and electric potential. In number theory, φ(n) is Euler's totient function.
Outside science, Φ appears in Phi Beta Kappa (ΦΒΚ), the American honor society founded in 1776, and in many fraternity and sorority names. See the other letters on the Greek letters page.
φ vs ϕ, and phi look-alikes
Small phi has two shapes. φ (U+03C6) is the open, looped form used in Greek text, and ϕ (U+03D5) has a straight stroke through a closed circle and is common in math. LaTeX trips people up here: \phi gives the straight ϕ and \varphi gives the looped φ.
Several slashed circles are not phi at all. ∅ is the empty set, ⌀ is the diameter symbol, and Ø is a Danish and Norwegian letter. ɸ is a phonetic symbol for an f-like sound made with both lips, as in Japanese "Fuji". Copy φ or ϕ when you mean phi, so math software and search engines understand you.
How to type φ
On Windows, hold Alt and type 237 on the number pad for φ or 232 for Φ. In Word, type 03C6 (or 03D5 for ϕ) and press Alt + X. On a Mac, use the Character Viewer (Control + Command + Space) or the Greek keyboard, where F types φ.
In LaTeX, use \phi, \varphi and \Phi. In HTML, use φ and Φ. For the golden ratio in plain text, copy φ ≈ 1.618 from the list above, and for roots and other operators see math symbols.