About GoldenSpiral

The golden ratio and the Fibonacci sequence get mentioned constantly — in art classes, design tutorials, biology textbooks, and no shortage of documentaries — but the actual math behind those mentions is usually skipped over. What is φ, exactly, and how is a specific value like 1.6180339887 derived from one proportional relationship? Why does a sunflower’s seed head rotate by 137.5° instead of some rounder number? What does it actually mean for two lengths to be “in golden ratio,” and how do you compute that split for a real measurement? GoldenSpiral exists to answer questions like these with small, formula-driven calculators instead of another surface-level explainer.

The Fibonacci Calculatorcomputes any term of the Fibonacci sequence using Binet’s closed-form formula, alongside the full sequence and its running sum. The Lucas Number Calculator does the same for Fibonacci’s lesser-known sibling sequence, and verifies the identity that connects the two. The Golden Ratio Calculator splits any length into golden proportion and reports the matching golden-rectangle dimensions. The Modular Scale Generatorbuilds a typography or layout size scale from a base size and a ratio — φ by default, or any ratio you choose. The Golden Spiral & Phyllotaxis Calculator generates the sunflower-style seed pattern seen across many plants, using the same golden angle those plants’ growth follows. And the Golden Ratio Grid generates a rule-of-phi composition guide and crop suggestion for any frame size.

Beyond the calculators, the tools index lists every calculator in one place, the blogcarries original articles on the golden ratio and Fibonacci mathematics — including where the popular claims about both hold up and where they don’t — the learn section is a glossary sourced from Wikipedia, and the museumis a browsable, Wikipedia-sourced collection across four wings: The Golden Ratio in Nature, The Golden Ratio in Art & Architecture, Fibonacci & Mathematics, and Pattern & Proportion in Design.

A few things worth stating plainly. GoldenSpiral is an independent site, not affiliated with any university, museum, or standards body. It is supported by advertising, which is how the tools stay free with no account required. Every number a calculator produces — a Fibonacci or Lucas term, a golden-ratio split, a scale step, a spiral coordinate, a gridline position — comes from a standard, verifiable formula applied to the values you enter, not from a proprietary or unstated method. We also try to be direct about where popular golden-ratio claims are well-supported (like phyllotaxis in sunflowers) and where they're exaggerated or unsubstantiated (like many claims about specific historical buildings and artworks) — see the blogfor that distinction in more depth. If something looks off in a tool or an article, or there’s a calculator you wish existed, the contact page is the place to say so.