What is the golden ratio?

The golden ratio (phi, φ ≈ 1.6180339887) is the proportion a/b = (a+b)/a. It appears in the Fibonacci sequence, natural spirals, classical architecture, and is widely used in design for its perceived visual harmony.

How is the larger dimension calculated?

If you know the smaller value, multiply it by phi (1.618033...) to get the larger. If you know the larger value, divide by phi to get the smaller.

What is the minor segment?

When you split the larger dimension at the golden ratio point, you get two parts: the minor segment (smaller part) and the major segment (larger part). Their ratio equals phi, and the major/total ratio also equals 1/phi.

Is this the same as the 60/40 rule in design?

Not exactly. The 60/40 rule is an approximation used in color and layout. The true golden ratio split is approximately 61.8% / 38.2%, which is more precise and mathematically grounded.

Can I use this for font size scales?

Yes. If your body text is 16px, the golden ratio gives a heading size of about 25.9px (16 × 1.618). Many typographic scales use phi or a close approximation for visual hierarchy.

Does phi work for any unit?

Absolutely — pixels, points, ems, centimeters, inches, or any other unit. The ratio is dimensionless, so the units carry through unchanged.

Golden Ratio Calculator Design

Enter a width or height and instantly get the matching golden ratio dimension using phi (1.618033...).

Enter a Dimension

Type any value and pick whether it is the larger or smaller side.

Value

Unit label (optional)

My value is the...

Larger value Smaller value

phi (φ) = 1.6180339887... | 1/φ = 0.6180339887...

Enter a dimension on the left to see golden ratio results.

Proportion Preview

61.8%

38.2%

Major (larger part) Minor (smaller part)

Larger —

Smaller —

Minor Segment —

Formula Used

Design Scale from Your Value

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Summary

The golden ratio (phi, ≈ 1.618033) is a mathematical proportion found throughout nature, art, and architecture. Designers use it to create visually balanced layouts, determine type scale, and set harmonious spacing. Enter any known dimension and this tool derives the complementary value — plus shows the minor segment of the split for three-way breakdowns.

How it works

Enter a dimension (width, height, or any length) in the input field.
Choose whether the value is the larger or smaller part of the ratio.
The calculator multiplies or divides by phi (1.618033...) to find the complementary dimension.
The minor segment (the smaller portion when splitting the larger) is also shown.
Copy any result to your clipboard with a single click.

Use cases

Setting image or banner dimensions for a page hero section.
Defining typographic scale — body size to heading size.
Calculating sidebar width from a main content column.
Spacing and padding that feel naturally balanced.
Cropping photos using the golden section as a guide.
Laying out card grids with phi-proportioned aspect ratios.
Architectural or product sketching with harmonious proportions.
Generating a three-part layout split using the minor segment.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu