Phi

Phi is the twenty-first letter of the Greek alphabet. Its uppercase form looks like Φ, and it has two lowercase forms: φ and ϕ. In ancient times, Phi represented a special sound made by combining a breathy "p" sound with a soft "h" sound, which is why it is often written as "ph" in English words.

Over many centuries, the way people said Phi changed. By the time of ancient Rome and later Greece, it began to sound more like the "f" we use today. This change continued into the Byzantine era, and today, Greek speakers simply say Phi as "fi."

Phi also has importance beyond language. Like other Greek letters, the lowercase Phi is used in math and science to represent many ideas and formulas. There is even a special symbol called the "closed" Phi, used in some older writings, which looks slightly different.

Use as a symbol

In lowercase

The lowercase letter φ (or its variant, ϕ or ɸ) is often used in many areas:

• The letter phi is used in physics for wave functions in quantum mechanics.
• It represents the golden ratio in mathematics, art, and architecture, which is about 1.618.
• It is used for Euler's totient function in number theory.
• It shows the number of electrical phases in electrical engineering, like 1ϕ for single phase and 3ϕ for three phase.
• In probability theory, it is the probability density function of the standard normal distribution.
• It can mean an angle, like the phase of a wave in signal processing or the polar angle in spherical coordinates.
• It is used for the work function of a surface in solid-state physics.
• It is a short way to show an aromatic group in organic chemistry.
• In perceptual psychology, it describes the phi phenomenon, which is the feeling of motion when looking at still images, like in movies.
• In linguistics, it shows features such as number and gender where words agree with each other.

In uppercase

The uppercase Φ is used as a symbol for:

• The cumulative distribution function (cdf) of the standard normal distribution in statistics.
• The magnetic flux and electric flux in physics.
• Quantum yield in physics, which measures how often an event happens when a photon is absorbed.
• A common way to show the shape of a surface in calculus.
• The diameter symbol, often called "phi", used to show the width of a circle, like "⌀14" meaning a diameter of 14 units.
• A clock signal in electronics.
• In science, it can mean the amount of one substance mixed in another.
• In older chemistry, it was used for a certain type of phenyl group.
• Integrated information theory, a model for understanding consciousness.

Unicode

In Unicode, the Greek letter phi has many different forms.

In normal Greek writing, the character U+03C6 φ is used. This letter can look different depending on the font, sometimes with a loop and sometimes without.

For special uses like math and language studies, Unicode has extra versions of phi. For example, U+03D5 is used in math when a special shape is needed, and U+0278 is used for phonetic symbols.

Unicode includes many versions of phi for different purposes, such as bold or italic styles used in math.

IPA, LaTeX, and Porson are mentioned in the source but are not rewritten here to keep the text simple for younger readers.

Character	Name	Correct appearance	Your browser	LaTeX	Usage
U+03A6	GREEK CAPITAL LETTER PHI		Φ	Φ {\displaystyle \Phi }	Used in Greek texts
U+03C6	GREEK SMALL LETTER PHI		φ	φ {\displaystyle \varphi } or ϕ {\displaystyle \phi }	Used in Greek texts
U+03D5	GREEK PHI SYMBOL		ϕ (ϕ)	ϕ {\displaystyle \phi }	Intended for use in modern (monotonic) Greek texts. Used italicized in mathematical and technical contexts when the "straight-line" variant glyph is preferred.
U+0278	LATIN SMALL LETTER PHI		ɸ	{\displaystyle }	Used in IPA to denote a voiceless bilabial fricative