Phi

The twenty-first Greek letter, used for the golden ratio and magnetic flux.

Also known as: Greek letter phi, Phi symbol, Golden ratio symbol, φ

ScientificMathematicalEngineering & technicalStandard profile

Meanings

Phi names the golden ratio, approximately 1.618, and magnetic flux in electromagnetism. The golden ratio use is the one most people meet, and it arrives attached to a large body of claims about art and nature that are far less settled than they are usually presented.

Common modern usageVerified fact
Is a letter of the Greek alphabet before it is a symbol: what it denotes is fixed by the field it appears in, not by the character itself. The uses below are the documented conventions, not competing definitions.
Contexts: Mathematics
Common modern usageVerified fact
In mathematics, denotes the golden ratio, approximately 1.618.
Contexts: Mathematics
Common modern usageVerified fact
In electromagnetism, denotes magnetic flux.
Contexts: Mathematics
Common modern usageVerified fact
In spherical coordinates, denotes the azimuthal angle.
Contexts: Mathematics
Common modern usageVerified fact
In number theory, denotes Euler's totient function, in its capital form.
Contexts: Mathematics
Common modern usageDisputed claim
Attracts widely repeated claims that the golden ratio governs classical architecture, Renaissance painting and the proportions of the human body. These are largely retrospective and have been repeatedly challenged; the mathematical properties of the ratio are not in doubt, but the aesthetic claims are.
Recorded as contested rather than settled. Symbolwise states that the dispute exists and does not adjudicate it.
Contexts: Mathematics

Visual description

A vertical stroke running the full height, passing through a circle or oval centred on it.

Symmetry: bilateral
Orientation: upright

Visually similar to: Theta
Both are a rounded form crossed by a stroke; theta's bar is horizontal and inside, phi's is vertical and extends beyond.

Confidence

IdentityHigh confidence: High confidence because the identity is defined by a current official standard, but multiple independent sources agree.
Historical originModerate confidence: Moderate confidence because the historical origin is documented in encyclopedic references, but multiple independent sources agree, but early or supporting evidence is limited, but the regional or cultural match to this specific claim is not precise.
Current useHigh confidence: High confidence because the current use is documented in encyclopedic references, but multiple independent sources agree.
Visual matchHigh confidence: High confidence because the visual match is defined by a current official standard, but multiple independent sources agree.

Sources

Unicode Code Chart: Greek and Coptic (U+0370–U+03FF)
The Unicode Consortium · retrieved 2026-07-30
Authoritative for the character's code point, name and block only. Unicode assigns identity; it does not define what a symbol means in use.
Greek alphabet
Wikipedia · retrieved 2026-07-31
Tertiary reference. Used for the widely-agreed uses of the letter across fields and for its history. Not used to assert that any one use is the letter's definitive meaning — no body defines that, and the record says so.
Phi
Wikipedia · retrieved 2026-07-31
Tertiary reference. Used for the widely-agreed uses of the letter across fields and for its history. Not used to assert that any one use is the letter's definitive meaning — no body defines that, and the record says so.
Greek letters used in mathematics, science, and engineering
Wikipedia · retrieved 2026-07-31
Tertiary reference. Used for the widely-agreed uses of the letter across fields and for its history. Not used to assert that any one use is the letter's definitive meaning — no body defines that, and the record says so.

Last reviewed 2026-07-31