Golden Ratio Calculator
Apply the golden ratio (φ ≈ 1.618) to any size.
Designers use the golden ratio (φ ≈ 1.618) for pleasing proportions in layouts, typography and spacing. Enter a size to get the larger and smaller value in golden proportion.
Formula / method
Examples
161.80 / 61.80
25.89 / 9.89
The ratio behind the tool
The golden ratio, written with the Greek letter phi, is approximately 1.618. Two lengths are in the golden ratio when the larger divided by the smaller equals their sum divided by the larger. Give this tool one measurement and it returns the golden partners: multiply your value by 1.618 to get the next size up, and divide by 1.618 to get the next size down.
Chaining those steps produces a harmonious sequence of sizes, each one about 1.618 times the last, which is why designers use it to build scales rather than picking numbers at random.
Where designers apply it
The ratio guides layout proportions, image crops, logo geometry and typographic scales. A common use is setting body text and heading sizes so the jump between them feels balanced, or dividing a page into a wider content area and a narrower sidebar.
Treat phi as a helpful starting point, not a rule that guarantees beauty; plenty of excellent design uses simpler ratios like 3:2 or 4:3. When you translate the resulting sizes into a stylesheet, the PX to REM Converter helps you express them in scalable units.
Where it's used
- Building a typographic scale from body text up to headings
- Setting balanced content and sidebar column widths
- Sizing images and crops in pleasing proportion
- Guiding logo and icon geometry
- Creating a spacing system for a UI
Real-world examples
- 100 gives 161.80 (larger) and 61.80 (smaller)
- A 16px base font suggests a heading of about 25.9px
- A 960px layout splits into roughly 593px of content and 367px of sidebar
- Chaining the ratio builds a size sequence where each step is about 1.618× the last
A bit of history
The Greek letter φ (phi) as the symbol for the golden ratio was introduced by Mark Barr in the early 20th century (around 1910), naming it after the Classical sculptor Phidias.
Did you know?
Mark Barr chose 'phi' to honour Phidias on the belief the sculptor used the ratio — yet Barr himself later wrote that he thought it unlikely Phidias actually did.
FAQ
Where is the golden ratio used?
In typography scales, column widths, image crops and spacing systems — proportions based on φ tend to feel balanced and harmonious to the eye.