Golden Ratio Calculator

A rectangle whose side lengths are in the golden ratio (φ:1). When you remove a square from a golden rectangle, the remaining rectangle is also a golden rectangle. This self-similar property creates the golden spiral, found in nautilus shells and galaxies.

Multiplying a base font size by φ at each level creates a harmonious type scale. Starting from 16px: 16, 25.9, 41.9, 67.8px. This produces heading sizes that feel naturally proportioned relative to body text.

Divide a page or screen into sections using the golden ratio for sidebar-to-content ratios (e.g., 382px sidebar, 618px content area on a 1000px layout). This creates balanced, visually appealing compositions used in web design, photography, and print layouts.

The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21...) converges to the golden ratio. The ratio of consecutive Fibonacci numbers approaches φ as the sequence grows. This pattern appears in sunflower seed arrangements, pinecone spirals, and leaf phyllotaxis.

Reality: While popular, this claim depends on which measurements you choose. The Parthenon's proportions are close to several simple ratios (9:4, 7:3), not exclusively φ. The golden ratio was not formally described until after the Parthenon was built.

Reality: Studies on aesthetic preference show mixed results. While φ-based proportions are often rated favorably, cultural context, individual taste, and other ratios (like the rule of thirds) also produce pleasing results. It is one useful tool among many.

Reality: They are related but distinct. The Fibonacci sequence is a series of integers; the golden ratio is an irrational number. The ratio of consecutive Fibonacci numbers converges to φ, but it never exactly equals φ for any finite pair.

Select "Calculate" mode. Choose which segment you know (whole, longer, or shorter) and enter the value. The calculator derives the other two segments using φ and shows a visual proportion bar.

Switch to "Rectangle" mode. Enter either the width or height. The calculator computes the other dimension so that width/height = φ, along with area and diagonal length.

Select "Typography" mode. Set a base font size (e.g., 16px) and the number of scale levels. Each level is multiplied by φ, producing a harmonious heading hierarchy with a live preview.

Switch to "Sequence" mode. Enter a starting value and the number of terms. The calculator produces a sequence where each term is the sum of the two preceding terms, with ratios that converge to φ.