This is a guide covering the golden ratio.
We’ll be covering the following topics (click on a bullet point to jump to that section):
- Definition of golden ratio
- Why is it called the golden ratio
- What is special about the golden ratio
- What is the golden ratio used for
- Who invented the golden ratio and when
- And more
Let’s dive in!
What is the Golden Ratio?
In mathematical terms, the Golden ratio equals 1.618, and Phi (Ф) – a Greek letter – represents it. It’s also called the Greek letter Phi, Golden Mean, and Divine Proportion – after how much it’s found in nature. However, when we talk about design, the Golden ratio definition is to make organic or natural designs that are pleasing to look at with the proportions or elements being in harmony with each other.
The Golden ratio is a great tool to make images and objects more appealing.
In design, the Golden ratio meaning is that the elements are balanced, but are still aesthetic.
When we use it in designs, it gives them an artistic edge that has always appealed to human eyes.
The Golden ratio is special because we can find it everywhere, from mathematical geometry, arts, and buildings to our bodies. It’s seamlessly built into our everyday life. It was first called “golden” in the 1800s and over the years, its relation with phi has become known.
It has many uses, and you can use it in typography, images, logo design, and when planning layouts for your ads or website.
The Golden ratio can be found anywhere in our world, in nature, painting, music, and architecture.
The ratio and the number behind it were derived using the Fibonacci sequence. So, what’s the Fibonacci Sequence?
Simply, the Fibonacci Sequence is a set of numbers that exist in nature, e.g., the total sides of a banana (unpeeled), and the petals in some flowers are Fibonacci.
The Fibonacci sequence begins with 0 and 1. Let’s take the next number as x You’ll get the value of x by adding the two numbers before x.
Right now, the previous numbers are 0 and 1 so x equals to 0 + 1 = 1. You can get consecutive numbers when you add the two numbers before that number.
Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21… to infinity.
To make the ratio, we take two consecutive numbers n and n+1 from the Fibonacci Sequence and divide n+1 with n – the bigger number with the smaller number.
The resulting answer comes close but doesn’t exactly equal to 1.618, for example, 3/2 = 1.5, 5/3 = 1.667, and 21/13 = 1.615.
Why is it Called the Golden Ratio?
The Golden ratio is as old as the world itself and it’s prevalent in the world around us.
It was called by a few other names before it was dubbed as ‘golden’ by Martin Ohm in the 1800s.
In his textbook, Die rein Elementar Mathematik, he described Euclid’s “diving a line in the extreme and main ratio” theory as the “golden section”.
The value 1.618 is called the Golden ratio, and it can make any shape, logo, and typography, and image pleasing to look at and give it hierarchy.
What is Special About the Golden Ratio?
The Golden ratio meaning is linked with a line – the simplest shape in nature.
When we divide a line into two uneven parts and take the larger part ‘a’ and divide it with the smaller part, b we get the ratio of 1.618.
The ratio, and the derived Golden rectangle, and the Golden spiral are all found in nature, in the form of flowers, ferns, hurricanes, and seashells.
It helps to make images more appealing.
The Golden spiral is typically used in designing logos, and cropping and resizing pictures, etc.
But what exactly is the Golden spiral? The Golden spiral comes about when you multiply the horizontal side of a square with 1.618.
You’ll get a rectangle, then put the square on the rectangle.
Then, take the rectangle not covered with the square and cover it with a square – divide the horizontal side with 1.618 to find the dimensions of the square.
The vertical side or the width should stay the same for both the square and rectangle.
Then, cover the rectangle with the square. Repeat this process with the square part until you get three small squares.
The overlapping of these two shapes gives you the Golden rectangle.
Start to draw the spiral arch from a small square that is adjacent to the second square you used.
Take the arch to the second smaller square and into the square below. Then, extend it into the second square you used and take it into the uncovered part of the rectangle.
Finish the spiral arch at one edge of the square that covers the rectangle. The Golden spiral covers the overlapping Golden rectangle.
Anything made with the Golden ratio becomes the most picturesque image for the human eyes.
This characteristic of the Golden mean makes it special, and we can use it in arts and design, architecture, website building (layouts, typography, etc) to design elements that appeal to human nature.
To further explore the concepts of the golden ratio, we recommend this video by DavidsonArtOnline:
What is the Golden Ratio Used For?
The Golden ratio has been used throughout our history in paintings, architecture, and even music more aesthetically pleasing to the human eye.
People like Leonardo Da Vinci used it in his work, and the Mona Lisa painting was made with this ratio in mind too. In our everyday life, it also has many uses.
The Golden ratio definition dictates that it equals 1.618, and you can use this number to set the hierarchy of your typography – the art of writing.
You can use this ratio to find the font size that would fit your headings and subheadings according to the body text size.
Assume that you have got an 11px (pixel) body text size, and you want to know what size the heading of the blog should be.
Simply, multiply 11px with 1.618 and the answer will be 17.798 so you should use a font size of 18-19px for the headings.
For 12px body text size, the answer will be 19.416 when you multiply 12 with 1.618 so a 19-20px size would be good.
To further explore the use of golden ratio in typography, we recommend this video by Anton Reyes:
The Golden ratio is an effective tool for cropping or resizing pictures. You can use the Golden spiral for this job.
The Golden spiral is closely associated with the Golden ratio and by placing it on an image, you can find the portion that you want to keep or the focal section of the image.
With the Golden spiral, you can find the harmony that the various elements that the images need.
When you overlay the Golden spiral on your picture, the part with the highest number of details should be in the tiniest rectangle in the spiral, but this part doesn’t need to be in the center.
It can be in any part of the image, but you’ll need to change the spiral based on where the most details are.
By trying out a few spiral overlays, you can make sure that the focal/highlight point of your image is at the center of the spiral.
Moreover, you can move the objects around until the spiral shows the harmony it should in your image.
To further explore the use of the golden ratio in photography, we recommend this video by Reg:
3. Logo Designing
You need a well-designed logo that can deliver your brand’s message in just a glance. The Golden ratio can help you find the correct alignment and the best foundation for your logo.
Many big brands that are trending nowadays used Divine proportions to make their logos, e.g., Pepsi, Twitter, and Apple.
You can use the ratio to find the right width and height that fits your logo and what proportions work well for the internal objects in the logo design.
To make the logo, you can take the numbers in the Fibonacci Sequence and draw circles against each number. You can use these circles to make a grid on which you can make your logo design.
Twitters used this method to make the tweet bird that represents Twitter.
With the Golden rectangle, you can position all the objects in a harmony with each other or use the Fibonacci circles as the foundation for the logo.
You can also use both the Golden rectangle (the overlapping rectangles and squares without the spiral) and the Fibonacci circles to make a grid for your logo – Apples used both for their logo.
To further explore the use of golden ratio in logo design, we recommend this video by Dansky:
With the ratio, you can design layouts that are appealing to your audience.
For example, if you want to create something for your website or blog that has the main message and then a sub-message, you can use the ratio to calculate the number of pixels for both.
For your infographics, if you want to create the main sidebar of width 667px, simply divide it with 1.618 to find the width of the sidebar that would suit that particular layout.
The ratio may not provide the exact lengths in some cases but it can give you an estimate of where to place what element to make the whole layout more pleasing to look at.
Moreover, you want to focus the important element of your poster, ad, or image in the middle of the Golden spiral because that is the place where your audience’s eye will land first.
Who Invented the Golden Ratio and When?
Even before Martin Ohm, a German mathematician, named the divine proportion as ‘golden’ in the 1800s, accounts in history state that it was used by the Greeks and the Egyptians.
The Great Pyramid and the Parthenon are said to have been designed with phi in mind.
Artists and mathematicians like Phidias, and Plato used the Golden ratio in their work and worked on it.
Similarly, Euclid, who lived from 300 BC to 365 BC, explained that a line divided at 0.6180399 is referred to as “diving a line in the extreme and main ratio’’, which he later dubbed as the Golden mean. In 1200 AD, Leonardo Fibonacci discovered the Fibonacci Sequence.
Fast forward to 1500 AD, Leonardo Da Vinci used the Golden mean or the Divine proportions, as was called during that era, in his artwork, e.g., in his ‘The Last Supper’ painting.
Later in the 1900s, Mark Barr, an American mathematician, designated phi, a Greek letter, for the Divine proportion.
Phi is the Greek letter for the alphabetical letter, F, which also happens to be the first letter of the Fibonacci series, and phi is the first half of Phidias, who is known to have used the Golden ratio in the sculptures he made.
Phi or the Golden ratio is used nowadays in mathematics, arts and design, architecture, and it’s even associated with spirituality.
The Golden ratio equals 1.618, and the ratio is a result of the Fibonacci Sequence, and when the consecutive number in the series is divided, they equal 1.618.
This number is also called Greek Phi and is an essential part of the world around us.
You can find the ratio in the world around us, in nature, art and architecture, and even our bodies.
You can use it to make the Golden rectangle and Golden spiral.
These two are used in logo designing, image resizing, and designing layouts for ads, websites, and infographics.
Jon has been a passionate photographer for 10+ years. Fun fact is that he has a collection of around 300-400 cameras that his family has collected over the years. Outside of photography, he has a Masters Degree in Engineering and has 13 years experience working in the industry across the globe.