Golden Ratio Calculator
Calculate golden ratio values. Find phi (φ) relationships between numbers.
The Golden Ratio (φ)
φ = 1.6180339887...
(1 + √5) / 2
Try:
Golden Ratio in Nature & Art
• Fibonacci sequence ratios approach φ
• Nautilus shell spirals
• Parthenon architecture
• Leonardo da Vinci's art
How to Use
- Select which value you know (longer segment, shorter segment, or whole length)
- Enter the value
- Click "Calculate Golden Ratio"
- View all related golden ratio measurements
What is Golden Ratio Calculator?
The golden ratio (φ, phi) is approximately 1.618033988749... It's a special number found when a line is divided so that the whole length divided by the longer part equals the longer part divided by the shorter part. This ratio appears throughout nature, art, and architecture.
Formula
Golden Ratio Definition:
φ = (1 + √5) / 2 ≈ 1.6180339887...
Golden Ratio Property:
(a + b) / a = a / b = φ
Examples
- If a = 10: b ≈ 6.18, total ≈ 16.18
- If b = 5: a ≈ 8.09, total ≈ 13.09
- If total = 100: a ≈ 61.8, b ≈ 38.2
FAQ
Where is the golden ratio found in nature?
The golden ratio appears in spiral arrangements of leaves, flower petals, seed patterns in sunflowers, nautilus shells, hurricanes, and even the proportions of the human body.
How is the golden ratio related to Fibonacci numbers?
As the Fibonacci sequence progresses (1, 1, 2, 3, 5, 8, 13...), the ratio between consecutive numbers approaches the golden ratio. For example, 13/8 ≈ 1.625, which is close to φ.
Is the golden ratio used in art and design?
Yes! Artists and architects have used the golden ratio for centuries. It's found in the Parthenon, Leonardo da Vinci's works, and modern logo designs for companies like Apple and Twitter.
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