Golden Ratio Calculator

Fast, accurate, and free online Golden Ratio Calculator tool that runs directly in your browser.

Secure (SSL)

Client-Side Processing

100% Free

Go to tool

Instructions

1

Enter data
Enter content, paste text or load a file from disk.
2

Click the button
The tool will immediately process your data in the browser.
3

Get the result
Copy the finished text or save the file to your device.

                                                function runTool() {

                                                  return "Result ready in 0.1s";

                                                }

Settings

Unit

Mode

Value

Number of decimal places

Proportion ladder Tool Option

Number of steps

Include SVG Tool Option

Result

phi: 1.6180339887499 mode: line_total unit: mm decimals: 2 input: 210 total: 210 long: 129.78713763748 short: 80.212862362522 gold point: 129.78713763748 svg: <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 960 160" width="100%" height="160" role="img" aria-label="Golden Ratio Visualization"><rect x="0" y="0" width="960" height="160" fill="none"/><g font-family="ui-sans-serif, system-ui, -apple-system, Segoe UI, Roboto, Arial" font-size="14"><line x1="60" y1="82" x2="900" y2="82" stroke="currentColor" stroke-width="3" opacity=".85"/><line x1="60" y1="64" x2="60" y2="100" stroke="currentColor" stroke-width="3" opacity=".85"/><line x1="900" y1="64" x2="900" y2="100" stroke="currentColor" stroke-width="3" opacity=".85"/><line x1="579.14855054991" y1="60" x2="579.14855054991" y2="104" stroke="currentColor" stroke-width="4"/><text x="579.14855054991" y="52" text-anchor="middle">Golden Ratio Point</text><text x="60" y="134" text-anchor="start">Start</text><text x="900" y="134" text-anchor="end">Koniec</text><text x="319.57427527496" y="114" text-anchor="middle">Longer</text><text x="739.57427527496" y="114" text-anchor="middle">Shorter</text></g></svg> text: Golden ratio calibrator (phi φ ≈1.6180339887) Jednostka: mm Input value:210.00 mm Total length:210.00 mm Longer section:129.79 mm Shorter section:80.21 mm Golden Ratio Point:129.79 mmfrom the beginning Phi proportion ladder (step k → value × φ^k): -6 11.70 mm -5 18.94 mm -4 30.64 mm -3 49.57 mm -2 80.21 mm -1 129.79 mm 0 210.00 mm 1 339.79 mm 2 549.79 mm 3 889.57 mm 4 1439.36 mm 5 2328.94 mm 6 3768.30 mm

Rate this tool:

Related tools

Other tools you may find useful

Golden Ratio (φ) Calculator – Harmony in Dimensions

The Golden Ratio (φ = 1.618033...) is a mathematical ratio that appears in nature, art and architecture. The tool calculates dimensions according to the golden ratio: you enter one value, the calculator calculates the other so that the ratio is φ.

golden ratio calculator golden ratio phi golden ratio calculator golden rectangle dimensions

Golden ratio - definition

φ (phi) = (1+√5)/2 ≈ 1.6180339887. Definition: a/b = (a+b)/a = φ. Where a > b. Properties: 1/φ = φ-1 ≈ 0.618. φ² = φ+1 ≈ 2.618. Fibonacci sequence (1,1,2,3,5,8,13,21,34...): the quotient of neighbors tends to φ. F(n)/F(n-1) → φ with n→∞.

Golden Rectangle

A rectangle whose sides have a ratio of 1:φ. Dimension A known: B = A/φ = A×0.618. Dimension B known: A = B×φ. A golden rectangle can be divided into a square + a smaller golden rectangle (recursively). Cutting out squares: a spiral approximating the golden spiral (logarithmic).

Applications in design

Typography: header and paragraph size in the proportion φ (e.g. 32px header, 20px text: 32/20=1.6 ≈ φ). Photographic composition: rule of thirds ≈ golden ratio (similar but not identical). Logo: Apple, Twitter, Toyota - component proportions based on φ. Architecture: Parthenon in Athens (debatable), Le Corbusier Modulor.

Fibonacci sequence and φ

Fib(1)=1, Fib(2)=1, Fib(3)=2, ..., Fib(10)=55, Fib(11)=89. 89/55=1.6182 ≈ φ. Nature: number of flower petals (3,5,8,13 - Fibonacci), spirals of sunflower seeds, pineapple, pine cones. This is not perfect in all cases, but the pattern is statistically significant.

FAQ

Is the golden ratio really "perfect" aesthetically?

Scientific research is inclusive. Classic experiments (Fechner, 1876): people prefer rectangles close to φ. More recent research: preferences depend on cultural and individual context. The golden ratio is not the only "beautiful" proportion - other ratios (5: 4, 3: 2) are also aesthetically attractive.

What is the difference between the rule of thirds and the golden ratio?

Rule of Thirds: Divides the image into 3 equal parts. Golden ratio: divides in the proportion 0.618: 0.382 (not equal). Golden ratio ratio ≈ 1.618, third ratio ratio = 1.5. In photographic practice, both produce similar compositions - both are correct.

How to use the golden ratio in CSS?

Set font-size: 1rem (16px) for content. Header h1: 16 × 1.618² ≈ 42px. h2: 16 × 1.618 ≈ 26px. line-height: 1.618 for optimal readability. Sidebar width: content × 0.618. Outer margin: content × 0.382.

Does φ appear in music?

In some compositions by Bartók and Debussy: division into sections according to φ. Pentatonic scale: 5 notes (Fibonacci number). Bach: spiral motifs. However, most of the "golden ratio in music" is post-hoc rationalization.

How to calculate the golden spiral?

Golden spiral = logarithmic spiral with a growth factor of φ. Equation: r = φ^(θ×2/π). In practice: draw a golden rectangle, cut out a square, draw a quarter circle in the square, repeat. The spiral does not go exactly through the corners of the squares.

Related tools: aspect ratio calculator, right triangle calculator and SVG blob generator.