Golden Ratio Calculator - Free Phi Calculator & Golden Rectangle Generator
Golden Ratio Calculator
Calculate golden ratio proportions (ฯ = 1.618...), create golden rectangles, and explore the divine proportion in design and nature.
The Golden Ratio
ฯ = 1.618033988749895
(1 + โ5) / 2
Find Golden Ratio Partner
Enter a value to find its golden ratio partner. If A and B are in golden ratio, then A/B = ฯ
Results
Total Length (A + B)
Larger Segment (A)
Smaller Segment (B)
Golden Ratio Verification
Width
Height
Area
Perimeter
Fibonacci Sequence
Ratio Convergence to ฯ
Golden Ratio Applications
Design & Art
- โข Logo design and branding
- โข Photography composition (Rule of Thirds)
- โข Typography and layout
- โข Web design spacing
Nature & Architecture
- โข Nautilus shells spiral
- โข Flower petal arrangements
- โข The Parthenon proportions
- โข Human body proportions
How to use this calculator
โจ How to Use the Golden Ratio Calculator
- Choose a calculation type: Proportion, Rectangle, or Fibonacci
- For proportions: Enter a value and select if it's the larger or smaller segment
- For rectangles: Enter width or height to create a golden rectangle
- For Fibonacci: Enter the number of terms to generate
- View visual representations and mathematical relationships
๐ Understanding the Golden Ratio
The golden ratio (ฯ or phi) is approximately 1.618033988749895. It appears when a line is divided into two parts so that:
(a + b) / a = a / b = ฯ โ 1.618
Where 'a' is the larger segment and 'b' is the smaller segment.
Mathematical Definition:
ฯ = (1 + โ5) / 2
๐ Golden Ratio in Practice
Design Applications
- โข Logo design: Apple, Twitter, Pepsi logos use golden proportions
- โข Web layouts: Sidebar to content ratio of 1:1.618
- โข Typography: Font size hierarchies based on ฯ
- โข Photography: Golden spiral for composition
Architecture
- โข The Parthenon in Athens
- โข Notre Dame Cathedral
- โข The Great Pyramid of Giza
- โข Modern buildings by Le Corbusier
๐ก Pro Tips
- โข The golden ratio is often approximated as 8:13 or 5:8 for practical use
- โข In design, use 61.8% for main content and 38.2% for sidebar
- โข The golden angle is approximately 137.5ยฐ (used in plant growth)
- โข Credit cards often have golden rectangle proportions
- โข The rule of thirds in photography is derived from golden ratio
- โข Fibonacci numbers converge to ฯ: each term รท previous term โ ฯ
โ ๏ธ Common Misconceptions
- โข Not everything in nature follows the golden ratio exactly
- โข The golden ratio isn't always the "most beautiful" proportion
- โข Many claimed examples are approximations, not exact
- โข Don't force designs to fit - use it as a guide, not a rule
- โข The ratio 1.6:1 is often close enough for practical purposes
About this calculator
Calculate golden ratio proportions, find golden rectangle dimensions, and explore Fibonacci sequences. Visual tools for design and art.
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