The golden ratio is a mysterious ratio that appears in nature and in art throughout history. Learning about the golden ratio in art can help you improve your composition.
After spending a whole week researching the golden ratio, here’s a few key points that can help with your art.
So let’s dive into it!
Table of Contents
What is the Golden Ratio?
The golden ratio is the ratio of 1 to 1.618. The greek letter Phi (Φ, φ, ϕ) represents the golden ratio. The number is an irrational number and does not repeat itself in a pattern, just like Pi. The first numbers up to ten decimal points of Phi are 1.6180339887…
To find the golden ratio, we start by dividing the line into two sections (you can look at the horizontal line on the rectangle above as a reference). If you measure the length of the whole line divided by the long part, it should be equal to the length of the long part divided by the short part.
Why should you learn about the golden ratio? Because this ratio improves your composition. Your eyes naturally find this ratio pleasing, similarly to the rule of thirds. Before diving into how to use the ratio, let’s look at a few examples first.
P.S. Don’t worry about the formula if you don’t get it! You can still use the golden ratio for your art. Just remember that it is a ratio of 1 to 1.618.
Golden ratio in art and architecture
One of the most famous examples of the golden ratio in art is Leonardo da Vinci’s Vitruvian Man. You can observe the ratio if you place the golden rectangle above vertically. The middle line perfectly lines up with the belly button. The forearm and hand of a person also line up with the golden ratio.
Another example of the golden ratio in art is found in Michelangelo’s The Creation of Adam at the Sistine Chapel. If you frame the golden rectangle horizontally, you can see that God’s finger and Adam’s finger meet right at the line.
There is also evidence that suggests the Egyptians built the Great Pyramid of Giza with the golden ratio in mind . But, it also could be a coincidence since there are many shapes and sizes of different pyramid structures. Later in the article, we talk about how some golden ratios you observe might just be an unrelated correlation.
There is plenty of evidence of the golden ratio out in the world and countless examples to choose from. Even the Ferrari has used the golden ratio in its design.
Golden ratio in modern art
The golden ratio has also been used in modern art. Piet Mondrian, a Dutch artist known for pioneering abstract art, used the golden ratio widely. In Composition with Red, Yellow and Blue, 1942, you can clearly see the golden ratio.
Salvador Dalí, a famous artist known for surrealism and bizarre images, also uses the golden ratio. In The Sacrament of the Last Supper, the top line of the table lines up with the golden ratio if you use the golden grid.
Who created the golden ratio?
Euclid, a very influential mathematician in the Greco-Roman era (around 300 BC), founded the golden ratio. He was widely known because of his book on Geometry, Elements.
In Book II of Elements, he mentions the golden ratio as “the section” . Artists and architects in the Renaissance later renamed the ratio “golden section”. Euclid also had other original works including the platonic solids, which are geometric shapes made from identical polygons.
How to create the golden rectangle
Here comes the fun part! To create the golden rectangle, follow these steps:
Step 1: draw a square and divide it in half.
Step 2: draw a diagonal line in the right half of the square from the bottom left corner to the top right corner.
Step 3: drop down the diagonal line to the right. This will be your new horizontal line for the width.
Step 4: complete the rectangle with the new horizontal line.
How to create the golden spiral
Creating a golden spiral is a bit more complicated so I have included a YouTube video to explain the process:
One interesting note is that you can fit a golden rectangle inside the next rectangle you create. You can keep repeating the pattern infinitely.
How to create the golden grid
The golden grid is very useful as a tool to improve your composition. Here are the steps to make it (you can also download my template for these):
Step 1: measure the width of your canvas/paper and divide it by 2.618. Draw your first vertical line (left vertical line).
Step 2: divide the width by 1.618. Draw your second vertical line.
Step 3: measure the height of your canvas/paper and divide it by 2.618. Draw your first horizontal line (top line).
Step 4: divide the height by 1.618. Draw your second horizontal line.
How to use the golden ratio in your art
You can use the golden ratio to improve the composition of your art. For example, you can place the horizon line on the second horizontal line of the golden grid. You can also place different objects of focus on intersections of the golden grid.
You can also create another grid inside the grid to have more reference points to place your horizon line and objects. For example, try placing the horizon line on the blue dotted line instead of the black line on top of it. Try out different compositions and find the best one you like.
What is the Fibonacci sequence? How is it relevant?
Fibonacci, an Italian mathematician, founded the Fibonacci sequence. It is a pattern of numbers where the next number is the sum of the two numbers before it. The pattern starts with 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on…
You can get an approximation to the golden ratio if you take one number and divide it by the number before it. The bigger the number is, the closer it is to the golden ratio. For example, 89 divided by 55 is 1.6181818… whereas 13 divided by 8 is 16.25.
As seen in the image above, the Fibonacci sequence fits into the golden rectangles used to create the golden spiral. You can repeat this pattern indefinitely.
Golden ratio in nature
You can observe the golden ratio in things like the human body and plants. Like in da Vinci’s Vitruvian Man, your forearm to hand ratio is the golden ratio.
In plants, leaves are arranged in a way that does not stack on top of each other. This creates an optimal way to absorb sunlight. The angle of rotation (golden angle) for the placement of each leaf is about 137.5 degrees. You can calculate this by (2 – Φ) x 360.
Caution about the golden ratio. Is it a correlation?
Some people claim that the Greeks built the Parthenon with the golden ratio. But, some experts also say that there is no actual evidence to link the Parthenon to the golden ratio . In fact, architectures have many points that you can measure to get the golden ratio. For example, the Eiffel Tower has many metal beams going across horizontally. If you carefully pick one, you are bound to find the golden ratio.
The golden ratio in a lot of cases could just be a spurious correlation, a correlation that looks like causation but actually is not. Here’s an example of a spurious correlation, the total revenue generated by arcades closely correlates to the computer science doctorates awarded in the US.
One common misconception about the golden ratio is related to logarithmic spirals. Things in nature like the nautilus shell actually are closer to the logarithmic spiral than the golden spiral.
Even if the golden ratio is just a spurious correlation, it is still very useful for art. It is a good way for you to compose your art and reframe your art in a different way.
What about the rule of thirds? How is it different?
You’ve most likely heard of the rule of thirds in photography and art. You can apply the rule of thirds by dividing your canvas horizontally and vertically into thirds. This should form a grid. The rule of thirds is like the golden ratio because you can use the grid to help make your art more visually interesting. Here are a few comparison photos for you to see if you can feel the difference between them.
Pros of the rule of thirds
- easier to use and eye-ball
- more symmetrical and easy to balance
Cons of the rule of thirds
- might feel a bit unnatural
- can become stale if all of your compositions are made from rule of thirds
Pros of the golden ratio
- more organic
- can give you more variety in composition, can stack ratios again
- can use it for objects (for example, a building in a landscape painting)
Cons of the golden ratio
- grids and spirals are harder to create (but can use templates)
- harder to use without grids and overlays
Both of them are very useful when you are planning your art and trying to find the right composition for it. There is no right answer when it comes to which is better. Try both out and see which one fits your next piece the best!
Tools and templates for download
Here are a few golden ratio templates I have created to help you compose your art. You can simply right-click and click “save image as” to download the template.
You can also get golden calipers if you are working with traditional art. It can save you a lot of time rather than measuring everything manually.
What to do next
Now that you know that the golden ratio is the ratio of 1 to 1.618, try it to see if it helps the composition of your art. Be sure to check out our article on beginner art techniques to improve your art.