Golden Ratio in logo designs.

Beauty and aesthetics have been praised from time immemorial. But little did people know that the most effective, perfectly balanced, and visually compelling creations followed the tid-bits of mathematics. At least not until 1860, when German physicist and psychologist Gustav Theodor Fechner proposed that a simple ratio, an irrational number defines the balance in nature. The Golden Ratio! Fechner’s experiment was simple: ten rectangles varying in their length-to-width ratios were placed in front of a subject, who was asked to select the most pleasing one. The results showed that the most favored choice was the “Golden Rectangle” (with ratio 1.618).

Golden Ratio

Golden Mean, Golden Section, Divine Proportion are all common names for what is known as the Golden Ratio which is based off the number phi (φ) = 1.61803398874… discovered by Italian Mathematician Fibonacci. Phi (φ) is the ratio between the number sequence 1, 1, 2, 3, 5, 8, 13, 21 etc. where the next number in the sequence is derived by adding 2 numbers together. So, 1+1 = 2, and 1+2 = 3, 2+3 = 5 and so on. When we divide two sequential numbers i.e. 5/3 = 1.67 and 21/13 = 1.615 Fibonacci Blocks and Fibonacci Spiral the ratio between these numbers soon become very close to φ (1.618). Fibonacci’s 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been described earlier in Indian mathematics, by Brahmagupta in 598 almost a thousand years earlier.

What’s so amazing about this number? Some believe that it is the most efficient outcome, the result of natural forces. Some believe it is a universal constant of design, the signature of God. Whatever you believe, the pervasive appearance of φ in all we see and experience creates a sense of balance, harmony and beauty in the design of all we find in nature. It should be no surprise then that mankind would use this same proportion found in nature to achieve balance, harmony and beauty in its own creations of art, architecture, colors, design, composition, space and even music. From the Parthenon to Monalisa, from the Egyptian pyramids to credit cards, φ has been there, always.

Logos with golden ratio

So, it was not surprising when I found the invasion of φ in logo designs. Let us have a look at some of the most popular brands which have used the golden ratio to induce the perfect harmony and balance in their logos.

National Geographic

Remember the yellow square in the National Geographic logo? Have you ever wondered why that simple logo appears to be so appealing? The answer is, as you might know, the Golden Ratio! The length and width of the square have a ratio of 1.61. It is quite fitting for an organization with a motto of “inspiring people to care about the planet” to have a logo based on the golden rectangle.
The yellow square in the National Geographic logo is a golden rectangle, with length:breadth = 1:1.61


The new logo of Pepsi has been much simpler and effective, characterized by spare, pure design. It looks intriguing and beautiful. Almost like a laughing emoticon in red and blue. But did you know that the underlying backbone of the Pepsi logo follows the golden ratio? The Pepsi brand is created by intersecting circles with a set proportion to each other. And, the proportion: Golden Ratio (φ) !
The two circles that form the backbone of the Pepsi logo have diameters with golden ratio, phi = 1.618


Apple is one of those very few companies that do not have the company name in their logo. Yet, the Apple logo is one of the most recognized corporate symbols in the world. The logo is perfectly balanced, and the outlines that map the logo are circles with diameters proportionate to the Fibonacci series. Did Rob Janoff really considered the Fibonacci series while designing it, or is it a coincidence? Well, somebody needs to ask Mr. Janoff. Interestingly, in a different context, in an interview, Rob Janoff said, “… and years later you find out supposedly why you did certain things. And, they are all BS. It’s a wonderful urban legend.”
The diameters of the circles that form the structure of the Apple logo has ratios according to the Fibonacci series (golden ratio). This image clarifies the circles used.


Another product from Apple, and again a masterpiece of design. The ripples on the cloud are made up of circles whose diameters are proportional to the you-know-what number. Also the containing rectangle, as shown below, is a golden rectangle. In fact, most of the Apple products, ranging from ipods to iPhone are golden rectangles. These amazing Apple designers!
The diameter that forms the ripples in the cloud of the logo follow golden ratio. The containing rectangle of the cloud form is also a golden rectangle (length:breadth=1:1.618)


BP is one of the world’s leading international oil and gas companies. They launched their new logo in 2000. What appears to be an attractive logo, however, turns out to be formed of concentric circles, again proportional to the Fibonacci sequence. Is it a mere co-incidence or a planned execution?
The diameter of the concentric circles that holds the petals in BP logo follow the Golden Ratio.


The logo of Toyota consists of three ovals. “The two intersecting ellipses are intended to represent the customer and the product… and the importance of that relationship”, according to an e-mail from Mike Michels, VP of Communication at Toyota Motor Sales USA, Inc. “The outer ring represents the world and the global nature of our business.” On a closer look one can easily find a grid based on φ in their logo. The phi-grid is formed by gridlines at certain separation – the separations being in the ratio of the golden ratio φ.
This image shows the overlay of phi grid on the emblem of Toyota logo.

Grupo Boticário

The logo of the Brazilian company Grupo Boticário was designed by the Brazil office of Futurebrand. This logo uses a golden spiral. In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes. The golden spiral is very closely approximated by the Fibonacci spiral (shown above). The golden spiral is very common in nature, for example, the spiral galaxies and mollusc shells. Do you like the use of golden spiral in this logo?
Grupo Boticário logo derived from the golden spiral.

Golden Ratio in nature – a short film

I sincerely do believe that any discussion on golden ratio or the Divine Proportion (a name more appropriate) remains incomplete without showing how accurately the number φ finds its way into a plethora of natural creations. I found this nice and short video on the interwebs to do the job easier for me.






Iza  said on November 24, 2011


Thanks for the info. It seems that there is definitely something big in the golden ratio.
I’ll research more about it…


Shubho  said on December 2, 2011


Very well presented, Saikat! Loving your blog & your website :)


Ven  said on January 14, 2012


This is good article. Please introduce FB Like button on your articles.


Jeffrey  said on February 13, 2012


Hi, i measure the national geographic logo in their official website. The a/b is not the golden ratio oh… where is the info you found ?


banskt  said on February 14, 2012


Hi Jeffrey,

I am glad that somebody actually checked into these. The National Geographic logo is the one that led me to write this article. I found it out myself. After that I started searching for other logos, and I found that many others have found such interesting observations in different logos, but there was no compilation of this interesting fact on this world of web.

Well, now back to the logo. Here is one of the logos from national geographic website:

Here, the width is 26px, and the height is 42px – so that the exact ratio is 1.6153846153846….. (isn’t it close?). Please do check if you are getting the same numbers.


DSo  said on March 11, 2012


Felt like I was in a Robert Langdon’s class.. 😛

Micke  said on April 4, 2012


Thank you for this great article! Really well explained for a guy like me with crapy math skills. I do use the golden ratio in some logo design. It really is intriguing!

rsmithing  said on April 5, 2012


Great article, Saikat! Since this has been published, have you learned any more about whether the ratio actually did factor into the Apple logo?

banskt  said on April 5, 2012


While studying before writing this article and aftermath, I found that the Apple logo was not actually designed keeping the golden ratio in mind. However, its no wonder that the legendary logo – the beauty that it is – must have the golden proportion.

As it has been shown here, it falls into the golden grid quite neatly. I am still trying to find out who did it for the first time, I mean, who laid the grid on the Apple logo for the first time.

blablaspann  said on April 30, 2012


I am design student too … and justyesterday in the history of design class we were discussing Fibonacci , I’ve always believed that nat geo has the best logo as well.

it’s amazing, how you worked on deciphering this bit:) .Thank you very much , great coming across this bit . keep the mind working:)

Khuram Malik  said on May 3, 2012


Thank you for such a detailed and well researched post. It was very enlightening and well explained and has inspired me. May i ask you how is the angle of 36 degrees derived in the apple logo? I didn’t understand this bit?

Svetlana  said on June 2, 2012


Thanks for discussing your ideas listed here. The other point is that if a problem develops with a laptop or computer motherboard, folks should not go ahead and take risk involving repairing the item themselves because if it is not done properly it can lead to irreparable damage to all the laptop. In most cases, it is safe just to approach your dealer of any laptop for the repair of the motherboard. They have got technicians who definitely have an competence in dealing with laptop computer motherboard difficulties and can get the right diagnosis and perform repairs.

banskt  said on June 3, 2012


Hi Svetlana, I do not understand your analogy here. :)

Stephen Christiansen  said on June 7, 2012


Have you applied the golden ratio to your own logo? :)

Paul Christian  said on August 10, 2012


Love this post man. This is awesome! I imagine a lot of measuring went into some of these logo’s thouhg…

jcburns  said on August 12, 2012


MUCH easier to just design a logo that ‘feels’ right and then retroactively say “look, it’s golden ratio-y, IF you do this, and this, and this…”

Jerkizé  said on August 12, 2012


You’re really reaching on the Apple ones, which is unsurprising given all the hero worship of Jobs and the lack of critical thinking applied to all things Apple. The BP one doesn’t looked planned, unless they intended for two of the four circles to not fit the ratio perfectly. I guess I’m echoing the JCBURNS comment. We humans love to create meaning from nothing, which is not meant as an indictment or anything.

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Andrew  said on August 15, 2012


This is such a great article! The combination of Art and Math is such a beautiful thing. Although I hear what some of the other people are saying, with regards to some of the logos you mentioned not being planned that way ahead of time… but, correct me if I’m wrong, it doesn’t seem like you are out to prove that these companies planned it, but more to reveal that there is inherent beauty (or popularity) in some of the brands that have the golden ratio. Maybe the thing to do, as JCBurns sort of alluded to, is to design a logo and when you think it is finalized, check it for any golden ratios.. if you find some, then it has good chance of being very successful!

DonaTions  said on August 17, 2012


I agree with Jerkizé above, humans read to much into everything. Could the fact that designers understand what is pleasing to the eye be the case why all these logos happen to fit the golden ratio? I would venture to guess that more company logos do not fit the golden ratio than do.

Kevin Barr  said on August 20, 2012


Very nice. I always come back to the golden ratio when I’m working on a web design layout. I don’t know why more designers make good use of this universal and proven formula for great design.

Johanne Daoust  said on September 1, 2012


To add to your Golden Section and Fibonacci references.

In my Visual Fundamentals Design class I lay the foundation by showing my students the following:

Great Book
The Geometry of Design, 2nd edition by Kimberly Elam?

Princeton Architectural Press, 2011-08-31 – 144 pages
At last, a mathematical explanation of how art works presented in a manner we can all understand. Kimberly Elam takes the reader on a geometrical journey, lending insight and coherence to the design process by exploring the visual relationships that have foundations in mathematics as well as the essential qualities of life. Geometry of Design takes a close look at a broad range of twentieth-century examples of design, architecture, and illustration (from the Barcelona chair to the paintings of Georges Seurat, from the Braun hand blender to the Conico kettle), revealing underlying geometric structures in their compositions. Explanations and techniques of visual analysis make the inherent mathematical relationships evident and a must-have for anyone involved in art, design, or architecture graphic arts. The book focuses not only on the classic systems of proportioning, such as the golden section and root rectangles, but also on less well known proportioning systems such as the Fibonacci Series. Through detailed diagrams these geometric systems are brought to life giving an effective insight into the design process.

Also track down the 1985 NOVA film entitled The Shape of Things

The introduction is on UTube but it is 55 minutes of Nature’s 6 basic shapes. Worth tracking down…
This is a film about patterns, structures and shapes in nature. Using plants, animals, crystals, fluids, and the ways in which they grow and move, the film explores how the intricate and beautiful geometries of nature are formed.

Believe it or not Disney produced a wonderful little Math film in 1959 aimed at grade seven students.
The first half explains the Golden Section

The last piece on Fibonacci is a 4 minute video produced in 1998 for a Math conference in Berlin. It is up on the net but unfortunately deejay4angles added a sacred geometry bent to the last half of this video.

So start at 0:36 and at end at 4;10

Recent published book:
The Man of Numbers, Fibonacci’s Arithmetic Revolution by Keith Devlin

As for Apple designers…let us please give credit where credit is due…Dieter Rams and his designs for Braun are truly the basis for Apple products.

Sunny A Padiyar  said on September 11, 2012


The golden ratio is not valid on the apple logo, its a hoax which was posted by some mysterious blogger. Please check your references or put some next time you post something. I think you can refer ‘design by nature’ by Maggie Macnab


Chandan Kumar Singh  said on September 14, 2012


Greatly impressed by your post on golden ratio. I’ve come across one Logo Designing Company in India ,they indeed keep the ratio aspect in mind while developing a logo design. Good Work and keep it Up!

Dan Dumitrache  said on September 26, 2012


I have to admit that I didn’t know about “golden-ratio”. Very interesting and well presented. I see some grid lines on this website’s background. Do they have anything to do with the “golden-ratio”? Is “golden-ratio” the key to success?

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Benin Maningman  said on September 30, 2012


Aesthetics is belong to the eyes of beholder, so how do we know whether the golden ratio really effects us as we think it does ?


Rajesh  said on October 11, 2012


Really excellent presentation, Thanks!

Carlos  said on October 17, 2012


Hello! Great job and research about logos. I have one question, how did you get to Apple logo? I mean how do you made the golden ratio grid? Which way did you take? I don’t get it :(


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This is *hard*, “scientific” evidence for the existence of God–but you may keep calling it “evolution” until you die, if you want. And you do.


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Jessica  said on November 17, 2012


Really interesting topic.

eric neuman  said on December 18, 2012


Hey there nicework

Bruce  said on December 20, 2012


The iCloud logo does NOT follow a 1:1.6 ratio AT ALL. I could tell by looking, but, to be sure, I downloaded the image and measured for myself. The two “circles” on the left work out to a ratio of about 1:1.77, and the two “circles” on the right are about 1:1.215.

Also, the NatGeo logo is a ratio of about 1:1.44.

Logos are, for the most part, designed to look good. Later, it’s easy to say, oh they used this ratio, or oh they copied that pattern, when in fact, they simply made something that looked good, to their own eyes. Do things that look good often fall into a similar ratio as this? Yes, because it’s pleasing to the eye, just as a I-IV-V progression in music is pleasing to the ear. It’s as simple as that.

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Jan  said on January 24, 2013


I’d rewrite the introduction if I were you… not only you’ve mistaken the creator of the term, who was Martin Ohm 25 years earlier, but also, quite curiously, in your research you haven’t stumbled upon the fact that it was well known and consciously used since ancient times in mathematics and works of art.

Pitagoras, Euclid, and sculptor Phidias – the creator of one of Seven Wonders of the Ancient World – to name but a few. It had different names (mean and extreme ratio, the divine proportion), but nonetheless it was still the good old Golden Ratio 1:1.618


Radu  said on February 7, 2013


Here’s another example of my personal monogram perfectly fit to circles in a golden ratio:

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Sarven Capadisli  said on March 22, 2013


This doesn’t fascinate me. There are patterns everywhere in nature. Golden ratio in particular is no more special than any other. People use or create patterns in their designs. I’ve used the ratio in the past myself, not because it is somehow pleasing to look at but as a matter of convenience to stick to a bunch of points and their relationships to one another. While it is fun, and sometimes aesthetically pleasing when done in a simple and decipherable way, it is not overly special.

IMHO, designs which employ the golden ratio are not necessarily pleasing to look for that reason alone but that the final design (with so many other variables) is well put together.

It is a trivial exercise to point out bad design using any pattern for that matter.

Umair  said on March 24, 2013


I happened to have written an article on the same topic. Its an amazing idea. Its actually a positive angle to subliminal marketing

Pat Nottingham  said on April 8, 2013


Really interesting post – I never realised there was such a science to logo design

Sprecheragentur  said on April 28, 2013


Nice article, we like it.

Tzvi  said on May 9, 2013


Amazing article! I am going to start following those rules in my graphic designs.
Amazingly I realized that I naturally use those rules in my designs, astounding!

Wasim Raja Khan  said on May 13, 2013


Awesome guide for designers.

Bruce morris  said on June 11, 2013


First of all i want to thank you for sharing such a wonderful article.
Your blog is really very informative. I am a daily visitor of your blog and everyday I found many new things to know. Your logo design is very creative and it’s sign of professional graphic designer.

John Schneider  said on June 18, 2013


Amazing! Thank you for putting together this very nice post.


Brand logo  said on July 31, 2013


thanks for sharing such a nice article for logo here as there are several websites are there for the logo design, this blog provides several information for us.

Logo Design Online  said on September 26, 2013


woow! i like the way you written, thanks a lots admin, from where are you getting these all designing info i am lookin for this :)


Roby  said on October 11, 2013


Fantastic very useful. Does architecture use the same ratio? Like the Colosseum for example?

Alexander  said on October 12, 2013


Wowww nice, inspiring post!! I love the way you write and the design of your website is awesome too. Love it!

om  said on October 20, 2013


Hey thank you so much for all this stuff man, just want to know how to construct logo using golden ratio ? will you share this secret ?

shazee  said on December 9, 2013


what is the music play on this page?
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loulwa etri  said on February 9, 2014


I am a graphic student , how much amazing using the amazing the golden ratio in our designs.

GG  said on April 13, 2014


nice blog.I like people like you graphic designer.

ScienceFreak  said on May 11, 2014


Nice explanation. Though I like the golden ratio symmetry. I just feel the Pepsi logo is a bit…off. It seems like they asked a 5-year old kid to draw a curvy line but he messed. But Pepsi was like “Nah, it looks good”.

Or if you’ve ever used the Pen tool, you’ll see the Pepsi logo line is what you usually get when you’re manually adjusting a line and you mess up.

yo mama  said on May 14, 2014


wow I love this stuff

ronald  said on June 3, 2014


i never knew there was a golden ratio for logo designs.

i will definitely keep this in mind on my next logo project.

NIKOS  said on July 15, 2014


Nice explanation but the Golden Ratio wasn’t discovered by Fibonacci. Fibonacci just mentioned the numerical series now named after him. Look at Wikipedia.

“Ancient Greek mathematicians first studied what we now call 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. Euclid’s Elements (Greek: Στοιχεῖα) provides the first known written definition of what is now called the golden ratio: “A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.”[12] Euclid explains a construction for cutting (sectioning) a line “in extreme and mean ratio”, i.e., the golden ratio.[13] Throughout the Elements, several propositions (theorems in modern terminology) and their proofs employ the golden ratio.[14]”

Vidhit  said on August 9, 2014


Hi Saikat,

Thanks for the interesting facts and information.
Recently, I have designed a logo and for the first time applied golden ratio in it. Is there any possible way I can get my logo checked for the same.


ichih  said on August 11, 2014


Great article but i really don’t understant the 36 degree in the pepsi logo.

i don’t what to do with 36 and how it was messured.
Can anyone answer my question here??

banskt  said on August 12, 2014


The 36 degree in the Pepsi logo has nothing to do with the golden ratio. It is just a measurement for proper usage and construction of the logo.

jacky  said on September 4, 2014


Your thing is awesome and I think you should do one on music

ff  said on November 5, 2014




Priyanka Kamble  said on December 1, 2014


The Nlog is very well wresearched and written Saikat. Thanks for the info on the GOlden Ratio

Remaja  said on December 24, 2014


you’re awesome and very good in this one. I love this blog too, very catchy :)
keep up thegreat works.

Mr. A  said on March 27, 2015


Simply awesome

Love this Pepsi Logo :)

Kiril Peychev  said on April 11, 2015


Apple’s logo designers didn’t used the golden ratio. It’s a famous myth.

juvia Loxar  said on May 7, 2015



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sandeep  said on August 11, 2015


Thanks. Now i understood how they build the logo

SAM  said on August 12, 2015


Wow! This was simply amazing.Thank you so much for sharing

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Love this Logo

Manasa  said on September 2, 2015


Wow! This was simply amazing.

Raji  said on September 2, 2015


Love this

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