Golden Calculators

The Golden Ratio (φ ≈ 1.618) and the Golden Angle (≈ 137.5°) are found throughout nature, art, and architecture. These calculators allow you to apply these divine proportions to your own designs and projects with mathematical precision.

The Golden Ratio (φ)

The ratio is defined such that the ratio of the sum of two quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one:

(a + b) / a = a / b = φ

Included Calculators

• Golden Section — Split any length into two segments that follow the golden ratio.
• Golden Rectangle — Calculate the dimensions of a rectangle where the ratio of the sides is φ.
• Golden Angle — Partition a circle using the angle that creates the most efficient packing (seen in sunflowers and pinecones).
• Sunflower Phyllotaxis — Explore the divergence angle in nature with an interactive spiral pattern generator.
• Gothic Rose Window — Visualize the “Sacred Geometry” of medieval cathedrals, where φ governs concentric proportions.
• Fibonacci Sequence — Generate and explore the sequence that converges to the golden ratio.

Mathematical Constants

• Golden Ratio (φ): 1.6180339887…
• Golden Angle: 137.507764…° (or 360° / φ²)

[!TIP] Use the Golden Angle for creating organic-feeling distributions and patterns in your visual compositions. It’s the “angle of least overlap.”