There’s no need for us to find a reason or specific explanations when it comes to art. It can simply be Art for Art’s Sake, like many writers and artists believe(d).
Beauty exists. It’s everywhere, and it’s subjective. We don’t have to find completion in it. But, as humans, we do search for balance.
And here’s where the Golden Ratio comes to help whenever we want to create something harmonious.
The Golden Ratio is an example that math can help fine arts. This doesn’t mean that just using this theory will suddenly make everything look beautiful, but it will be of great help for everyone who’s looking to achieve equilibrium.
So, let’s dive right in, starting with the Golden Ratio definition.
B. The Golden Ratio & the Fibonacci sequence
C. Where does this term come from?
D. Where can you find the Golden Ratio?
E. How to create the Golden Ratio yourself
F. How to use the Golden Ratio in graphic design
G. Tools to help you use the golden ratio
A. What Is the Golden Ratio?
The Golden Ratio also referred to as the Golden Mean or Divine Proportion, is a mathematical ratio with its roots in the Fibonacci sequence. It’s used to create harmonious compositions in different fields, such as design projects, paintings, illustrations, photography, music, and other compositions that thrive on balance.
The Golden Ratio symbol is the Greek letter ϕ or τ.
So, since we have the Golden Ratio explained, and I also mentioned the connection between the Golden Ratio and the Fibonacci sequence, let’s look at their connection more closely.
B. The Golden Ratio & the Fibonacci Sequence
In the 1200s AD, the mathematician Leonardo Di Pisa (or Fibonacci) made some calculations, resulting in a series of numbers now called the Fibonacci sequence.
The sequence looks like this: 1, 1, 2, 3, 5, 8, 13, 21…
Starting with 0 and 1, you’ll get the next number from the sequence by adding the previous two numbers together. As the numbers in sequence get larger, the ratio between them gets closer to 1:1.618. This is considered to be the Golden Ratio number.
The Fibonacci sequence isn’t exactly the same as the Golden Ratio, but very similar. That’s why these two terms get mixed up quite often.
But there is a connection between them.
When we create the Golden Ratio scheme, we use separation to show its purpose. There’s a Golden Ratio calculation method that goes like this: we have to divide two quantities with their ratio the same as the ratio of their sum to the larger one of the two quantities.
That Golden Ratio number is 1.618, which is called Phi. That’s why the second Golden Ratio symbol you’ll often see is the letter Phi.
Here’s the Golden Ratio equation:
But we get the Fibonacci sequence differently. It starts from 0 and grows to larger numbers. So, that is the reason why the Golden Ratio scheme formed out of golden rectangles separated into squares has the Fibonacci numbers inside each one.
As you can see, after we divide the number, we don’t get an exact number. This is because the Golden Ratio is characterized by its extreme irrationality, which is also its beauty.
Irrational numbers can’t be represented by fractions, and they have an infinite increase. Therefore, the Golden Ratio formula is used to help us understand how it works.
These numbers are also difficult to observe in nature, but there are a few instances where the Golden Ratio can be spotted, usually as the Golden Ratio Spiral.
We’ll see a few examples later on in the article.
C. Where Does This Term Come From?
In 1815, the mathematician Martin Ohm coined the term Golden Ratio in his study “Die Reine Elementar-Mathematik” (The Pure Elementary Mathematics), where he addressed this for the first time as “goldener schnitt” (golden section).
Before this, the Golden Ratio was called the Divine Proportion by Luca Pacioli and Leonardo da Vinci.
Earlier I mentioned the Phi number, which comes from the Greeks. This number was first mentioned in Greek history in a book by Eukleides of Alexandria, where he called it the “extreme and mean ratio.”
Even though the Greeks are known for their mathematical calculations, the connection between the letter Phi and the Golden Ratio was made only in the 1900s.
D. Where You Can Find the Golden Ratio
Whenever you look for images that explain the Golden Ratio, you’ll find many Golden Ratio examples, including the Parthenon, the Mona Lisa, Leonardo da Vinci’s Vetruvian man, Salvador Dali’s Last Supper, and a lot of pictures from nature.
But the Golden Ratio can be found in modern times, too. There are painters closer to our era that used it, as we’ll see in a minute.
Also, some argue that even music can be created with this rule of balance in mind. For example, real fans of Tool analyzed their album Lateralus and made a clear connection with the Golden Ratio.
Some of the connections can be linked to this irrational number. Some of them are still up for debate, like the tie people made between the Parthenon and the Golden Ratio.
Before talking about this rule in graphic design, let’s see a few Golden Ratio examples from other places.
1. In nature
Although it’s said that an irrational number can’t be easily found, we can still spot the Golden Ratio in nature.
For example, the Fibonacci sequence is linked to how the population grows and the shapes from certain plants or things from nature that fit perfectly together.
The most popular examples of Golden Ratio in nature are the ones characterized by the Golden Ratio Spiral. We can find such a sequence in the sun flower’s spirals:
Or in certain plants’ leave arrangements, like succulents.
Another example of the Golden Ratio in nature, which you’ll most probably find a lot when looking for this scheme, is the nautilus shell chambers that seem to adhere to it perfectly. You don’t even need to place the spiral over the image to see it.
You’ll find the Golden Ratio in nature even near you, in the smallest things, like a pinecone. You just have to watch it from the top down.
If you need a bigger scale to place the Golden Ratio on, we can go farther than this (at least mentally) and search for the scheme in the spiral galaxies.
2. In paintings
The likeliness of finding the Golden Ratio in paintings is higher compared to its natural appearings in our surroundings.
While some painters used the sequence in their paintings intentionally, working from the very beginning with this rule in mind, some artists didn’t leave any indications that this was their work method.
- The Mona Lisa by Leonardo da Vinci
We don’t know if da Vinci really worked with the Golden Ratio in mind when he painted his widely famous painting. Still, this is one of the most famous Golden Ratio examples. Moreover, if we place the Golden Ratio spiral over the Mona Lisa, you’ll see that the body placement adheres to these proportions.
The idea is that even if we don’t place the spiral over the painting, our eyes are naturally drawn to where the spiral’s center would be, which is her face.
Thus, the constant connection between Mona Lisa and the Golden Ratio.
It’s said that Leonardo da Vinci was the first proven artist that used the Golden Ratio in his work, Vitruvian Man, illustrating the proportions of the human body. But this could be just pure speculation since the connection between da Vinci and the Golden Ratio can’t be found in any of his writings. Moreover, the association came after he collaborated with Luca Pacioli, the author of the Divine Proportion.
- The Great Wave Off Kanagawa by Hokusai
It seems that one of the most recognized works of Japanese art, Katsushika Hokusai’s The Great Wave off Kanagawa, adheres to the golden mean, too.
- The Sacrament of The Last Supper by Salvador Dali
While in other cases we don’t know for sure if the artist used the Golden Ratio in their art, but their works are perfectly balanced, so we can assume it, Salvador Dali used the phi grid to create his most famous depiction of the Golden Ratio: The Sacrament of The Last Supper.
Dali also placed a dodecahedron above the table. A dodecahedron has the Golden Ratio rooted in its shape, so the painting is showing all the more evidence that it’s Golden Ratio compliant.
- The works of Le Corbusier
Le Corbusier was a Swiss-French architect and painter who was a real advocate of the Golden Ratio, as he used it in both these fields.
His interest in the simple forms, natural phenomenon, and the mathematical order of the universe are pointed out in the balance with which his architectural works are done.
And not only.
He also developed the Modulor, being inspired by Leonardo da Vinci’s Vitruvian Man.
The Modulor is a fictional human body divided into divine proportions, which was made as a system for designers and architects as guidance to create balanced proportions. It is made to illustrate the human Golden Ratio.
Le Corbusier’s discoverings in the mathematical proportions of the human body (i.e., the human Golden Ratio) were meant to guide him in other areas of his work, such as the appearance and balance in architecture.
For example, the UN Secretariat Building and the dividing lines of its façade are believed to be based on the Golden Ratio.
- Composition in Red, Blue, and Yellow by Piet Mondrian
Piet Mondrian started his career with landscape paintings, but then he switched to an abstract style, believing that lines, geometric shapes, and primary colors encapsulate logic and nature.
This idea can be found in his paintings Composition in Red, Blue, and Yellow, which have a common theme built on the golden rectangle.
E. How to Create the Golden Ratio Yourself
Because the Golden Ratio is approximately equal to a 1:1.61 ratio, it can be illustrated using a Golden Ratio Rectangle.
From a mathematical point of view, you can take a square and multiply one side by 1.618, and you’ll get a balanced rectangle.
You can also create it out of shapes.
I’m going to show you how.
Since the golden rectangle sides match the Golden Ratio, more interlocked golden rectangles create the golden spiral.
Let’s take it step by step.
The Golden Ratio Rectangle has the shape from which if you cut off a square with its side length equal to the shortest side of the rectangle, the part of the rectangle that’s left has the same proportions as the original rectangle.
You can do this action as many times as you wish, and the rectangle ratio will still be the same.
Alternatively, you can add a square with its sides equal to the longest side of the rectangle.
If you keep cutting the Golden Ratio rectangle to get squares out of it, you’ll end up with progressively smaller squares, which will be your base for the Golden Ratio spiral.
Now, all you have to do is to draw an arch in each square to get the Golden Spiral, like this:
You can even draw circles inside the squares, and they’ll all be in balance with each other, following the 1:1.618. This means we get Golden Ratio circles. We’ll see later on why they are important for your design.
If you want to see a quick video of how the Golden Ratio is created, you can see it here.
You can go even further and choose a golden triangle as guidance for your compositions. A golden triangle is an isosceles triangle with two equal sides that are in Golden Ratio to the third one.
If you keep cutting the golden triangle into smaller triangles, you can even create the golden spiral based on the diagram you’ll get.
The alternative way to create the Golden Ratio
If you need a faster way to create a skeleton that will help you with your balanced compositions, you can use the Rule of Thirds.
This rule is based on dividing an area into equal thirds, both vertically and horizontally. Once you have those spaces between the lines, you can use any of them as your focal point. This method works really well for photographers, but it can also be used in page layouts, designs made for print, or web design.
You can apply the rule of thirds to any shape, but when you use it on a rectangle similar to that we saw earlier (with proportions close to 1:1.6), you’ll almost get a Golden Rectangle.
F. How to Use the Golden Ratio in Graphic Design
Now that you have a few examples of the Golden Ratio in mind and you even know how to create the ratio, we can see how it can be applied in a few areas of design to reach a perfectly balanced composition.
There are several ways in which you can do this, as the Golden Ratio can also be simplified. You can use:
- The golden rectangle
- The golden spiral
- The golden triangle
- The phi grid
With these shapes, you can get the golden spiral or Golden Ratio circles, as we’ve seen previously. They will also help your design compositions.
1. The Golden Rectangle
This is the golden rectangle, which I mentioned earlier. It’s the simplest guide to use for your design compositions.
By overlaying this over your designs, you can create a focal point and have enough white space to balance it. These squares can coordinate everything from the rectangle.
2. The Golden Spiral
You can use the Golden Spiral in the same way as the Golden Rectangle, but the spiral’s line will probably offer you even more guidance regarding your design’s elements.
Follow the spiral’s direction, and your creative will have a clear center of attention and surrounding elements in perfect harmony.
If you’re planning to have a more complex design, and you need to place more elements on it, you can take the golden spiral further and put two golden spirals together. They will create the shape of a heart.
You can also place them like this and get a perfect focus for your design.
3. Golden Triangles
This method may seem a little bit more complicated than using a golden rectangle, but it’s a great way to create balanced compositions that have diagonal elements.
This guide consists of a line that goes from one corner of the composition to the opposite corner.
Then another two lines fall perpendicularly from the middle line to each of the two remaining corners.
After you draw these lines, they’ll create four triangle frames, making your job easier at aligning the elements.
4. The Phi Grid
This is yet another way to make your creatives, similar to the rule of thirds.
The difference between the two is that the Phi grid has the lines placed in such a way so that the middle shapes will be narrower than the upper and lower rectangles.
This alignment places the focal object even more to the center than the Rule of Thirds.
Applying the Golden Ratio
You can create the Golden Ratio in design, sometimes even without realizing it. This is because the human eye thrives for harmony in visuals.
Still, let’s see a few instances where we can apply the Golden Ratio in design intentionally, in order to create the perfect arrangement.
In photography & images
A balanced, eye-pleasing composition is vital. When starting to work on your design, which can be for your ads campaign, website, or blog, you most probably need to include images.
You can choose these images from a premium stock photo library. If you do this, you need to consider a few best practices for stock photos so that people won’t say they’re in bad taste.
Alternatively, you can take your own photos. Either way, you can apply the Golden Ratio in photography to start on the right foot and get perfectly equilibrated compositions.
Consider the rule of thirds or the phi grid to create your designs.
Here’s how you can do it with the phi grid.
Split the picture into three unequal sections, then use the lines and the spaces between them to create your image. The ratio of 1:1.168 is already very close to 35mm film and digital camera dimensions, which means you can place your image details while taking the photo without adjusting the image size.
The ratio is 1: 0.618: 1, like this:
Another way to apply the Golden Ratio in photography is by using the Rule of Thirds. All you have to do is divide the image with lines vertically and horizontally to 1:1:1 so that you’ll get four equal spaces.
You can also use the Golden Ratio in photography through cropping after your photos are already taken. Place the spiral over the photo and see where the focus should be. This will guide your way into cropping the image to make it look equilibrated.
In logo design
Understanding the logo design’s importance is vital for your brand. A well-made logo helps you create brand identity, brand recognition and stand out from the crowd.
Once you understand what exactly defines your brand and you know how your logo should look, the Golden Ratio will help you gain harmony for your logo’s proportions.
Many brands used the Golden Ratio to create their logos. A few examples would be Pepsi, Apple, and Twitter.
So, this means that if you want a round-shaped logo, you can use the Fibonacci sequence to create a series of circles that are in perfect ratio to each other and place them to form a grid as a base for your future logo design.
Look how the Twitter bird logo was made based on Golden Ratio circles.
Placing the elements on a layout by keeping in mind the importance of spacing and balance of the overall composition is important in order to have a pleasing UI that everyone enjoys.
Your job can turn into an easier task when you apply the Golden Ratio rule.
Many websites follow the simple two-column layout. The thing is to know how to make it look good and where to place the important information.
So, without overcomplicating the grid that’s going to help with the arrangement of your elements, you can simply take the golden rectangle and let it guide you.
The Speedy website follows this rule.
If your layout is more complex, you can apply the golden spiral heart, which we’ve seen earlier.
For typography hierarchy
When we use the Golden Ratio, it’s usually for a design or photography composition. But, we can apply it for typography as well.
Here’s how easy it is to get that perfect balance for your text sizing and arrangement by applying the Golden Ratio formula.
Pick a dimension for your body text, then multiply it by 1.618. The final number could be your headline’s size.
So, if you choose 12 pt for the body text size and multiply it by 1.618, you’ll get 19.416, but you can round it up to 19 or 20. And just like that, you’ll get the harmony you wanted.
You can go the other way around, too. You can start with the headline and then calculate the body text size. This means you’ll take the header’s size and divide it by 1.618.
There’s also the arrangement and hierarchy of your copy, which is essential in design, whether it’s for your website, ads, blog, or printed materials.
In this case, once you establish the size of the copy, you can still apply the Golden Ratio rule for the layout, just as we’ve seen before.
Image ads have all the elements we’ve talked about previously: images, typography, and logos. This means they need the right layout to make it all come together nicely.
They have to be eye-candy for anyone who comes across them in order to catch their attention. And besides the right colors and copy, this includes balance too.
When designing your image ads, it’s important to place everything in the right way so that your message gets across.
If you’re not a professional designer and you’re not doing this intuitively already, the Golden Ratio rule can help you with that.
You don’t even need to overcomplicate things. Just use the Rule of Thirds.
G. Tools to Help You Use the Golden Ratio
If math scares you, there are almost always workarounds. At least there are a few tools to help you with the Golden Ratio calculation.
This app is made for artists and designers who want to check if their work is Golden Ratio compliant by placing overlays on their designs.
Remember how I said you could calculate the size of the fonts you use in your designs or blog? There’s a calculator for that.
Enter the font size, content width, or both, and get your Golden Ratio Typography.
With this calculator, you can calculate the shorter and longer sides of a shape and their combined lengths to determine the Golden Ratio.
- Golden Ratio Calipers
Even if you work and create digital compositions, there may be times when you’re going the classical way and designing something on paper. If that’s the case, you can use Golden Ratio calipers to measure the proportions of your work on the page.
Despite its irrationality, you can find the Golden Mean in nature or create a Golden Ratio composition yourself to reach that state-of-the-art balance.
The Golden Ratio is a mathematical tool, which proves to us that there’s also science in art, but at the same time that this formula is not here to create something instantaneously beautiful.
The Golden Ratio is used in design to reach the equity that anyone appreciates.
Hi Amalia, I must say you are a true professional in the field of design, Amazing concept of golden ration in graphic designing.
A brief history of the Divine “Φ” [Phi] and Golden Ratio origins.
Ancient Greek mathematicians first studied the Golden Ratio because of its frequent appearance in geometry the division of a line into “extreme and mean ratio” (the Golden section) is important in the geometry of regular pentagrams and pentagons. According to historical accounts, 5th century BC Greek philosopher and mathematician Hippasus discovered that the Golden Ratio was neither a whole number nor a fraction but an irrational number, like Pythagoras’ “π” [Pi], meaning that its terms go on forever after the decimal point without repeating. Euclid, the Greek mathematician and father of geometry, in his Elements works (c.300BC) provides several propositions and their proofs employing the Golden Ratio, and contains its first ever known definition.
Copious article but falls rather short of mentioning the all too important historical origins and to give credit where credit is due.
A M X Tolis
Thank you for these great insights! We didn’t go into too much detail regarding the Golden Ratio origins because we wanted to keep the focus on how it can be used in graphic design.