Golden Ratio Calculator

Apply the golden ratio to any dimension and get the golden pair.

Last reviewed: April 2026
Reviewed by , software engineer · last updated April 2026

New to this tool? Click here for instructions

f (Phi) = 1.6180339887...

Enter a value and click Calculate to apply the golden ratio.

How to Use the Golden Ratio Calculator

To use the Golden Ratio Calculator, follow these steps:

1. Enter a dimension - choose whether your value is the larger or smaller dimension of the pair, enter the number, and select a unit (px, em, mm, etc.).

2. Click Calculate - the golden pair appears with the Fibonacci spiral visualization showing your dimensions as a golden rectangle.

  • Enter a dimension
  • Choose larger or smaller dimension
  • Select a unit
  • Click Calculate
  • View golden pair and Fibonacci spiral

When to Use the Golden Ratio in Real Workflows

The Golden Ratio Calculator is particularly useful in the following scenarios:

1. Typography: If your body font is 16px, a golden-ratio scale gives headings at 16 - f = 25.9px, 16 - f^2 = 41.9px, etc.

2. Line height: 16 - f - 26px is often ideal for readability.

3. Column widths: a main content column at 760px paired with a sidebar at 760/f - 470px creates a golden split.

4. Logo design: placing the focal point at 61.8% of the width and height from the corner places it at the golden point.

How the Golden Ratio Calculator Works

The Golden Ratio Calculator works based on the mathematical principle of the golden ratio (f, phi), which is the positive solution to the equation f^2 = f + 1, giving f = (1 + sqrt(5)) / 2 - 1.6180339887.

A line segment is divided in the golden ratio when the ratio of the whole line to the larger part equals the ratio of the larger part to the smaller part: (A+B)/A = A/B = f.

The golden rectangle has sides in the proportion 1:f. Its unique property is that removing a square (with side equal to the shorter dimension) leaves another golden rectangle with the same proportions.

  • Golden ratio equation: f^2 = f + 1
  • Golden ratio division: (A+B)/A = A/B = f
  • Golden rectangle: sides in the proportion 1:f
  • Unique property: removing a square leaves another golden rectangle

Tips, Edge Cases, and Limitations

Here are some tips and considerations when using the Golden Ratio Calculator:

1. The golden ratio appears in the diagonals of a regular pentagon and in the angles of a regular pentagon (36° and 72° are golden-ratio related).

2. Fibonacci numbers appear because any integer near a Fibonacci number has a Fibonacci number as its nearest golden-angle multiple.

3. The golden gnomon (the thin triangle in a regular pentagram) has golden ratio sides.

4. The golden ratio appears in the diagonals of a regular pentagon and in the angles of a regular pentagon (36° and 72° are golden-ratio related).

  • Golden ratio in pentagon diagonals and angles
  • Fibonacci numbers and golden ratio
  • Golden gnomon in pentagram
  • Golden ratio in regular pentagon

Frequently Asked Questions

The golden ratio (f, phi) is (1 + sqrt(5)) / 2 - 1.6180339887. A line is divided in the golden ratio when the ratio of the whole line to the larger part equals the ratio of the larger part to the smaller part: (A+B)/A = A/B = f.
Enter a dimension - choose whether your value is the larger or smaller dimension of the pair, enter the number, and select a unit (px, em, mm, etc.). Click Calculate - the golden pair appears with the Fibonacci spiral visualization showing your dimensions as a golden rectangle.
A golden rectangle has sides in the proportion 1:f. Its unique property: remove a square (with side equal to the shorter dimension), and the remaining rectangle is another golden rectangle with the same proportions.
Typography: If your body font is 16px, a golden-ratio scale gives headings at 16 - f = 25.9px, 16 - f^2 = 41.9px, etc.
Yes, the golden ratio appears in the diagonals of a regular pentagon and in the angles of a regular pentagon (36° and 72° are golden-ratio related).

Example walk-through

Worked example: step-by step

Step 1. Enter a numerical value into the calculator input field (e.g., 10).

Step 2. Click the 'Calculate' button to apply the Golden Ratio formula (φ = (1 + √5)/2 ≈ 1.618).

Step 3. The calculator multiplies the input value by 1.618 to determine the Golden Ratio proportion.

Step 4. Review the result displayed in the output field, which shows the proportional relationship.

Sample input: 10
Expected output: 16.18