What Is the Golden Ratio & How Can You Apply It to Design?

Meet the Golden Ratio: 1.618…

The golden ratio, the divine proportion, spirals, curves, triangles, rectangles—there’s a lot to unpack when discussing the topic of what is often represented by the Greek symbol phi.

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Euclid & the Golden Rectangle

Let’s start with Euclidian geometry (hang tight). While Euclidian’s Elements doesn’t yet use the term “golden ratio,” it does introduce the concept of the golden rectangle: a rectangle whose sides are in the lengths of the golden ratio (1 and 1.618, respectively), and which can become more golden rectangles that exhibit the golden ratio with the addition (or subtraction) of a square inside the rectangle.

Fibonacci Series

Let’s fast forward from 300 BCE to the twelfth century, when Leonardo Fibonacci comes up with his Fibonacci series (which is also called the Fibonacci sequence and Fibonacci numbers). While he wasn’t the first to put this sequence together, it does bear his name. And it goes like this:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34…

And on and on in that fashion. Put another way:

• The first number (0), plus the second number (1), equals the third number (1), so
• The second number (1), plus the third number (1), equals the fourth number (2), so
• The third number (1), plus the fourth number (2), equals the fifth number (3)

You get the idea.

How did Fibonacci come up with this sequence? The speedy nature of bunny breeding. Really: The golden ratio came to be as a something of a joke, an idealized (but unnatural) month-by-month math problem to explain how rapidly a family of rabbits might reproduce. But so what? What’s this got to do with the golden rectangle? As the sequence continues along (for forever and ever), each number divided by its predecessor comes closer and closer to the golden ratio—roughly 1.618 (though it also goes on for forever).

Leonardo da Vinci & the Divine Proportion

By the time the Renaissance is in full swing, the golden ratio reappears under the name the divine proportion, thanks to the publication of mathematician Luca Pacioli’s book aptly titled De divina proportione, which was famously illustrated by da Vinci. This is when 1.618 takes on a bit of a magical, mystical quality—and when artists started to really take heed.

Real-World Examples of the Golden Ratio

Nautilus shells are popular examples of the golden ratio on full display in nature, but there are others to look out for as well:

• Bodies and body parts. It doesn’t always work out perfectly, but humans have spent hundreds of years looking at the ratio between the distance of the belly button to the feet versus the belly button to the top of the head, and yep—golden ratio. Check out your fingers—tip to wrist, then knuckles to wrist—and you’ll see it there again. A healthy uterus in a fertile person also has near-golden ratio dimensions.¹
• Flowers and plants. The seeds at the center of a sunflower or the swirl and number of the flower’s petals. The way a tree branch grows, then branches, then continues to branch. The spiral of a pinecone.
• Fruits and vegetables. Cauliflower florets, pineapples, the seeds embedded in an apple, and a slice of cucumber, to name a few.

Obviously not every fruit, flower, or body will display the golden ratio or Fibonacci spirals, but many do.

The Golden Ratio & Graphic Design

Here are some ways you might put the golden ratio to work in your designs:

• Design composition. Framing a subject in your camera’s lens before snapping a picture. Creating a logo for your brand. Sketching or painting or collaging. All of these can have 1.618 applied for a sense of balance.
• Layouts. From UX design and other wireframes to live show posters and magazines, if it can be designed with the help of a grid, it can be given a golden ratio go-’round.
• Typography. Working with typography comes with its own set of challenges, but when it comes to matters of kerning as well as matters of size, the golden ratio can help organize your typography in a logical way.

Detractors of Divine Proportion

Not everyone is so convinced that the golden ratio, no matter what it’s called or where it came from, is anything nearly as special as history has made it out to be. Some eschew the idea that the golden ratio is especially aesthetically pleasing or valuable when it comes to design. There have even been studies conducted that show that people don’t have a particularly strong affinity for divine proportions when given a choice.

So why use it?

Like any tool in your design repertoire, using the golden ratio is less a rule or law but more of a suggestion. With so many options ahead of you when you sit down to compose a new work, having an organizing principle like the golden ratio can be a helpful jumping off point. Ultimately, though, what your composition needs is up to you.