Golden Ratio & Fibonacci Calculators & Tools
Free, formula-driven calculators for the Fibonacci sequence, the golden ratio, and the proportion math behind nature, art, and design.
Fibonacci Calculator
Compute any term of the Fibonacci sequence with Binet's closed-form formula, plus the full sequence up to that term and its running sum.
Golden Ratio Calculator
Split any length into golden proportion (a ÷ b = φ), and see the matching golden-rectangle dimensions.
Modular Scale Generator
Generate a typography or layout size scale from a base size and a ratio — φ by default, or any custom ratio.
Golden Spiral & Phyllotaxis Calculator
Generate a sunflower-style seed pattern using the golden angle (137.5°) and Vogel's phyllotaxis model, with exact coordinates for any seed count.
Lucas Number Calculator
Compute the Lucas sequence (2, 1, 3, 4, 7, 11, 18…) and verify the Fibonacci–Lucas identity L(n) = F(n−1) + F(n+1).
Golden Ratio Grid
Generate rule-of-phi gridlines and a golden-rectangle crop suggestion for any frame or canvas size.
Fibonacci & Lucas Convergence Reference
Every term from F(0) to F(30) and the matching Lucas number, alongside the ratio F(n+1)/F(n) and its error against φ — the one popular golden-ratio claim that is not just approximately true, it's exactly provable
Reference
Not a calculator you enter your own numbers into — a precomputed table showing the one golden-ratio claim that’s not just approximately true, it’s exactly provable.