BYTETOOLS

Golden Ratio Calculator

Split any length into golden sections with phi = 1.6180339887, build a golden rectangle and spiral, and generate a golden typographic scale for design work.

1.6180339887
φ (phi)
0.6180339887
1/φ
61.8034
Longer section
38.1966
Shorter section

Golden sections of your length

  • Total length = 100
  • Longer part a = L/φ = 61.803399
  • Shorter part b = L - a = 38.196601
  • a / b = 1.6180339888 (this is φ)
  • Extended: L × φ = 161.803399
  • Reduced: L / φ = 61.803399
  • Golden rectangle from this length: 100 × 61.803399

Golden rectangle and spiral

Cutting the largest possible square off a golden rectangle always leaves a smaller golden rectangle. Joining opposite corners of each square with a quarter circle traces the golden spiral.

Golden typographic scale

StepSize (px)Preview
-19.89Aa
base16Aa
+125.89Aa
+241.89Aa
+367.78Aa
+4109.67Aa
+5177.44Aa

Each step multiplies the previous size by φ. The preview column is capped at 48 px so the table stays readable.

Fibonacci ratios converging on φ

nFₙFₙ / Fₙ₋₁
11—
211
322
431.5
551.666666667
681.6
7131.625
8211.615384615
9341.619047619
10551.617647059
11891.618181818
121441.617977528
132331.618055556
143771.618025751
156101.618037135
169871.618032787

The ratio of consecutive Fibonacci numbers alternates above and below φ and converges on it — 987/610 already matches to six decimal places.

What is the Golden Ratio Calculator?

The ByteTools Golden Ratio Calculator divides a length into its golden sections, a = L/φ and b = L - a, so that the whole is to the larger part as the larger is to the smaller.

  • Splits any length into golden sections and extends it by phi
  • Golden rectangle dimensions from the length you entered
  • Nested-square golden rectangle drawing with the quarter-arc spiral traced through it
  • Golden typographic scale with a live size preview per step
  • Fibonacci ratio table showing convergence on phi
  • Runs entirely in your browser — private and offline-capable

How to use the Golden Ratio Calculator

  1. 1

    Enter the length you want to divide into golden sections.

  2. 2

    Set a base font size and how many steps of type scale you want.

  3. 3

    Read phi, its reciprocal and both golden sections in the summary tiles.

  4. 4

    Check the golden rectangle dimensions and the spiral drawing.

  5. 5

    Use the type scale table for your design system, and copy the results.

About the Golden Ratio Calculator

The ByteTools Golden Ratio Calculator divides a length into its golden sections, a = L/φ and b = L - a, so that the whole is to the larger part as the larger is to the smaller. It also extends a length by multiplying by φ = (1 + √5)/2 = 1.6180339887, and gives the matching golden rectangle dimensions.

For designers there is a golden typographic scale: pick a base font size and a number of steps, and each step multiplies the previous size by φ, with a live preview beside every value. A drawing shows a golden rectangle subdivided into nested squares with the golden spiral traced through them by quarter arcs.

A Fibonacci table shows consecutive ratios closing in on φ from alternating sides — 987/610 already matches to six decimal places. Everything is computed in your browser, so nothing is uploaded and the tool works offline.

Frequently asked questions

What is the golden ratio?

It is the number φ = (1 + √5)/2 ≈ 1.6180339887, the unique proportion where the whole divided by the larger part equals the larger part divided by the smaller. It satisfies φ² = φ + 1, which is why so many of its relationships are self-similar.

How do you divide a length by the golden ratio?

Divide the total by φ to get the longer section, then subtract that from the total for the shorter one. A 100-unit length splits into 61.803 and 38.197, and 61.803 ÷ 38.197 is φ again — the ratio repeats at every scale.

What are the dimensions of a golden rectangle?

Its long side divided by its short side equals φ, so a rectangle 100 units wide is 61.803 units tall. Cutting the largest possible square off one end always leaves another golden rectangle, which is exactly what the nested-square drawing shows.

How is the golden ratio used in typography?

Multiply a base font size by φ for each step up to build a modular scale. A 16 px base gives roughly 25.9 px, 41.9 px and 67.8 px, which produces a clear visual hierarchy. Many designers prefer gentler ratios such as 1.25 for body-heavy layouts.

How is the golden ratio related to Fibonacci numbers?

Divide any Fibonacci number by the one before it and the answer gets closer to φ each time, alternating above and below. 8/5 is 1.6, 13/8 is 1.625, and by 987/610 you are at 1.618033, accurate to six decimal places.

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