Golden Ratio Calculator

Enter any value to find its golden ratio pair — instantly

φ = 1.6180339887...

Fibonacci & Golden Ratio

Consecutive Fibonacci numbers converge toward φ = 1.618…

nF(n)F(n+1)F(n+1) / F(n)

Golden Ratio in Design

📐 Typography

Set body font at 16px → heading at 16 × 1.618 = 26px. Or line-height at 16 × 1.618 = 25.9px for optimal readability.

🖼️ Logo proportions

If your logo icon is 40px wide, the text beside it should be 40 × 1.618 = 64.7px wide for harmonious proportion.

📱 UI layout

Split a 1000px layout: sidebar = 1000 ÷ 2.618 = 382px, main content = 618px. Exactly φ proportion.

📷 Photography

The rule of thirds is an approximation of the golden ratio. Place key subjects at 38% (1/φ) from the edges.

🏛️ Architecture

The Parthenon, Notre-Dame cathedral, and many modern buildings use golden ratio proportions in facade dimensions.

🎨 Art composition

Place the horizon at 38% or 62% from the top to achieve golden ratio balance in landscape paintings.

Frequently Asked Questions

The golden ratio (φ, phi ≈ 1.618) describes a proportion where a/b = (a+b)/a. It appears throughout nature, art, and architecture and is widely considered aesthetically pleasing.

Enter any value in either field. If you enter in field A, field B = A × 1.618. If you enter in field B, field A = B ÷ 1.618. The results panel shows both values and their sum.

φ = (1 + √5) / 2 = 1.6180339887498948482... It's an irrational number — its decimal expansion never repeats. The reciprocal is 1/φ = φ − 1 ≈ 0.618.

The ratio of consecutive Fibonacci numbers (1,1,2,3,5,8,13,21…) approaches φ as numbers grow. F(10)/F(9) = 55/34 ≈ 1.6176. F(20)/F(19) ≈ 1.61803. The convergence is remarkably fast.

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