Lowercase phi

Phi takes its meaning from the word or formula. In Greek writing, read it as part of the word. In mathematics and physics, look for the author's definition of the variable—the quantity the letter stands for. The golden ratio, also called the golden section, is one use of the phi symbol, not its meaning in every equation.

Why does phi look different?

Fonts vary; φ and ϕ are also separate characters. A font can change φ's outline without changing the underlying text. Unicode also encodes ϕ separately for technical use, allowing mathematical writing to distinguish the forms.

Match your source formula rather than choosing the prettier curl. The author's definitions—not appearance alone—tell you whether two phis represent different quantities.

Where did the phi symbol come from?

Phi began as a Greek sound letter, not a proportion. Ancient Greek used it for a p sound released with a puff of breath. Its letterform's origin is debated: a 2018 scholarly discussion considers a connection with qoppa, another ancient Greek letter. That is proposed ancestry, not an established family tree.

The golden-ratio notation came much later. A 1914 account credits Mark Barr with proposing φ for the proportion and links his choice to the sculptor Phidias. This dates an account of the notation, not the discovery of the proportion or the Greek letter's origin.