Golden Ratio Calculator

Calculate the divine proportion (φ ≈ 1.618) for perfect design harmony. Create golden rectangles, spirals, and apply nature's favorite ratio to your projects.

Calculate Golden Ratio

Understanding the Golden Ratio

What is the Golden Ratio?

The golden ratio (φ = 1.618...) is a mathematical proportion that appears throughout nature and has been used in art and architecture for millennia. When a line is divided so the longer part divided by the smaller equals the whole divided by the longer part, you have the golden ratio.

Golden Ratio in Nature

  • Nautilus shells: Spiral growth pattern
  • Flower petals: Often in Fibonacci numbers
  • Human face: Proportions of features
  • DNA helix: 34 × 21 angstroms (Fibonacci)
  • Galaxies: Spiral arm formations

Famous Examples in Art & Architecture

Parthenon
Athens, Greece
Mona Lisa
Da Vinci
Great Pyramid
Giza, Egypt
Notre Dame
Paris, France

Modern Design Applications

  • Logo design: Apple, Twitter, National Geographic
  • Web layouts: Content to sidebar ratios
  • Photography: Rule of thirds alternative
  • Typography: Font size scaling
  • UI design: Card and button proportions

Design Tip: The golden ratio isn't a rigid rule but a guideline. Use it as a starting point for harmonious proportions, then adjust based on your specific needs. Combine it with other design principles like the rule of thirds, symmetry, and visual hierarchy for best results.

Quick Reference

φ (Phi)1.618034
1/φ0.618034
φ²2.618034
√φ1.272020

Common Dimensions

Business Card
3.5" × 2.16" (89 × 55mm)
HD Screen
1920 × 1080 ≈ 1.777:1
A4 Paper
297 × 210mm ≈ 1.414:1
Credit Card
85.6 × 53.98mm ≈ 1.586:1

Design Tools

  • Use golden grid for layouts
  • Apply to spacing and margins
  • Scale typography with φ
  • Compose photos using spiral