What is the golden ratio
Updated on June 30, 2026 · by Rafael Rossi
The golden ratio is φ = (1 + √5) / 2 ≈ 1.618, also called the golden number. Written with the Greek letter φ (phi), it appears with surprising frequency in nature, art and design.
The definition
A line is divided in the golden ratio when the larger part divided by the smaller equals the whole divided by the larger — and both ratios equal exactly φ (1.618).
How to calculate
Given the larger part:
- smaller part = larger ÷ φ
- whole = larger × φ
Example: larger = 100 → smaller ≈ 61.8, whole ≈ 161.8.
The Fibonacci link
The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21…) has a beautiful property: the ratio of a number to the previous one approaches φ as it goes. 89 ÷ 55 ≈ 1.618.
Where it appears
In shell, sunflower and hurricane spirals; in Renaissance art; in photography (the rule of thirds approximates it); and in modern logos and layouts seeking visual balance.
FAQ
Is φ really everywhere? It appears often, but there's cultural exaggeration: not every "pleasing" proportion is exactly 1.618.
Exact value of φ? It's irrational: 1.6180339887… — never ending or repeating.