Golden ratio calculator
Find the golden-ratio measures (φ ≈ 1.618) from one value — for design, art and layout.
In the golden ratio, larger ÷ smaller = total ÷ larger = φ ≈ 1.618. Widely used in design, photography and architecture for its pleasing look.
How the calculation works
The golden number is the constant φ = (1 + √5) / 2 ≈ 1.618. Two measures are in the golden ratio when the larger-to-smaller ratio equals the whole-to-larger ratio — both equal to φ:
larger ÷ smaller = (larger + smaller) ÷ larger = φ
Given one value, the others come from multiplying or dividing by φ.
Step-by-step example
Larger part = 100:
- Smaller: 100 ÷ 1.618 ≈ 61.8
- Whole: 100 × 1.618 ≈ 161.8
The Fibonacci link
In the Fibonacci sequence, the ratio of a number to the previous one approaches φ: 89 ÷ 55 ≈ 1.618.
Examples
- Larger = 50: smaller ≈ 30.9; whole ≈ 80.9.
- A golden rectangle 16 cm wide is ~9.9 cm tall (16 ÷ φ).
Frequently asked questions
Where does the golden ratio appear?
In plant and shell spirals, Renaissance art, and many modern logos and layouts.
Is φ really everywhere?
It appears often, but there is cultural exaggeration: not every pleasing proportion is exactly 1.618.
Exact value of φ?
It is irrational: 1.6180339887… — never ending or repeating.
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Updated on June 30, 2026 · by Rafael Rossi · Methodology & sources