Golden Ratio Calculator

Calculate golden ratio proportions using phi (1.618...). Perfect for design, art, architecture, and typography.

Golden Rectangle Visualization

ABA + B (total length)

The golden rectangle divides into a square (A) and a smaller golden rectangle (B). The spiral approximates the golden spiral.

Fibonacci Sequence

01123581321345589144233377

As Fibonacci numbers grow, the ratio between consecutive numbers approaches phi (1.618...).

Ratio of last two terms:377 / 233 = 1.6180257511

Applications in Design

  • -Typography: Line heights, font size ratios
  • -Layout: Column widths, margins, padding
  • -Images: Cropping, composition guidelines
  • -UI Elements: Button sizes, card proportions

Golden Ratio in Nature

  • -Spiral patterns in shells and galaxies
  • -Leaf and petal arrangements in plants
  • -Proportions of the human body
  • -DNA molecule structure

Golden Ratio Formulas

Definition

phi = (1 + sqrt(5)) / 2

1.6180339887...

Relationship

A / B = (A + B) / A = phi

The golden proportion

Given A, find B

B = A / phi

Divide by 1.618...

Given B, find A

A = B * phi

Multiply by 1.618...

Given A+B, find A

A = (A+B) / phi

Total divided by phi

Reciprocal Property

1 / phi = phi - 1

0.6180339887...