Learn, apply and excel with Phi, the Golden Ratio

This site exists to help you appreciate the incredible beauty and design in the world around you and to excel in whatever you do by applying these same principles of design to your own creative works, following in the thoughts of many great minds before you, from ancient civilizations to the Renaissance to the best of class in all areas of today’s arts and design.

Applications of the Golden Ratio

GoldenNumber.Net explores the pervasive appearance of Phi, 1.618, the Golden Ratio, in mathematics, geometrylife and the universe and shows you how to apply it, and its applications are limitless:

Get started with an overview of the Golden Ratio

Select an area of interest from the categories to the right or begin with Phi for NeoPhites or the Golden Ratio Overview article.

Discussion on the Golden Ratio

Share your thoughts with others on the Discussion and Comments page or on any of the posts on specific topics listed above or to the right.

Goals of GoldenNumber.net

We’re dedicated to providing you with the best information and tools on this Golden Number, known as Phi, the Golden Ratio, Golden Section, Golden Proportion, Golden Mean or the Divine Proportion, and its mathematical cousin the Fibonacci Sequence (0, 1, 1, 2, 3, 5, 8, 13, 21 …)

Our goal is to present a broad sampling of phi-related topics in a visually engaging and easy-to-understand format, to provide an online community in which new findings about Phi can be shared and discussed and to offer tools and services (see the right side bar) to aid in your understanding and application of phi and the golden ratio in your work, passions or hobbies.

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Leave a Comment

{ 30 comments… read them below or add one }

Rachel June 2, 2013 at 3:11 pm

Why is the golden ratio called divine ratio?


Gary Meisner June 4, 2013 at 2:30 am

It’s more often called the Divine proportion, which is the English translation taken from the book “De divina proportione” (On the Divine Proportion), written in 1509 by Luca Pacioli and illustrated by Leonardo da Vinci. The title expresses the thought that this golden ratio proportion of design found in nature and in the human form is an expression of God, our Creator.


marko July 24, 2013 at 7:42 am

I first meet with this while I was reading The Da Vinci Code. I thought it isn’t true story about this phi. Now I am convinced


Pete August 11, 2013 at 2:17 pm

The widening and extension of a body, in line with identical and unchanging proportions.
Sir Darcy Thompson.

We even look through the golden ratio. As we walk away from something it shrinks while the bigger picture opens up.
So we look into and out of at the same time…thats impossible, yet we do.
Thanks for the post, I enjoyed reading through the fascinating connections everything has in common with the Fibonacci Golden Ratio of 1:1.618 ;)


Danny August 21, 2013 at 3:55 am

My personal discovery of the golden ratio has been very recent. It never fails to surprise me at just how often people experience that Eureka moment when something that you were previously blind to becomes so apparently clear, even though you may have been looking at it your entire life…the golden ratio is one such example!

In most design work I have done in the past there is a balance, you instinctively know what looks right and what doesn’t and until recently I hadn’t realized that it was this balance that I was applying to many different aspects of my life. Interesting stuff!


sanjay kumar August 22, 2013 at 3:41 am

i m agree with you sir


yasith September 11, 2013 at 5:38 am

It’s good to have a web site like this :D


Jeff September 14, 2013 at 3:45 pm

Back in the mid 1970′s in a college algebra class our professor introduced us to the “Golden Ratio” and some of it’s interesting properties. It’s something that’s stuck with me and mulled around in the back of my mind ever since. In the last 10 years or so (I’m writing this on 09-14-2013) many aspects of this ratio have appeared things like fractals and a very interesting book by Greg Braden – FRACTAL TIME, with many more subjects far too numerous to mention. There are so many implied and practical applications that it truly needs to be studied by scholars and non-scholars working together with a promise to open doors and present questions not yet imagined. Thank you for this website. Perhaps there are others out there interested in sharing thoughts. I’d be interested in correspondence with you. Thank you. FB –


Todd September 23, 2013 at 5:35 am

i like numbers. numbers make me smile. baruch attah adonoi, elochanu melech ha olam


Kim October 8, 2013 at 12:12 pm

Even flowers go by the golden ratio; rose petals are congruent 360 degrees to phi.


ILIEV October 10, 2013 at 12:51 am

Life on Planet Earth is based on the Water (HOH) and hydrocarbon molecular compounds which are arranged in a beautiful mathematical order of the “golden section”.
  (a + b) / a = a / b = 1.6180033


angiladie October 11, 2013 at 6:21 am

My personal discovery of the golden ratio has been very recent. It never fails to surprise me at just how often people experience that Eureka moment when something that you were previously blind to becomes so apparently clear, even though you may have been looking at it your entire life…the golden ratio is one such example! http://ebrandingexperts.com


Geoffrey October 15, 2013 at 3:48 pm

Love the site! I first heard about PHI in the movie called “PI”. Great flick! Then I ran across Mario Livio’s book “The Golden Ratio”. Great book! What amazes me is:
1) The neat, tidy number theory. Phi can expressed in so many ways.
2) The presence of Phi in nature – the way plants branch, the growth of pineapples, multiplication of rabbits & many other examples.
It is my impression that Phi is a natural evolution of what works best as a scaling & growth factor.
I recommend pulling up a spreadsheet and playing with some the equations – it is SO COOL when the right numbers fall my own fingertips!


N J Smith February 25, 2014 at 7:41 pm

Agreed. Trivia: Note on one of the promotional posters Pi is written:

3.1415926538… should be …535…

Takes nothing from the brooding genius, of course.



Alberto de Victoria November 3, 2013 at 10:22 pm

This site its awesome.


Eugen November 4, 2013 at 4:27 pm

Is anyone else interested in this number because of the da vinci code :D ?


Rachel Nickles November 22, 2013 at 12:19 pm

The Da Vinci Code brought me here also! This proportion amazes me.


Vince Lin December 3, 2013 at 1:51 am



Sarab January 29, 2014 at 11:32 am

Me 2


Laxman February 19, 2014 at 7:05 am

Mee too… I got here in the middle of reading Da Vinci Code

Ron Giddings December 1, 2013 at 3:20 pm

The website io9.com has a guy supposedly finding Golden Ratios in shots from the film “There Will Be Blood”. First thing I noticed was that he placed spirals wherever he wanted (sometimes more than one per shot), with no relation whatsoever to the border/frame. Surely without a relationship to the border and format of an image, the Golden Ratio could be found anywhere we look and is therefore meaningless. I mean, if I’m measuring an object with a ruler, and keeping moving the ruler around arbitrarily, how can it possibly work?
I drink your milkshake, io9.


chris December 4, 2013 at 1:28 pm

This magical mathematical mystery is prevalent in all that is beautiful; i.e. LIFE. Here are some movies that I have come across that show the majesty of this number:

Inner Worlds Outer Worlds part 2 – the Spiral

Secrets in Plain Sight by Scott Onstott (Website is the same name)

The Pyramid Code

Live, Laugh, Light, Love


Ernest Smith December 7, 2013 at 1:39 pm

Formula that gives the nth Fibonacci number
f(n)=1/(5^1/2)((1+(5^1/2))^n – (1-5^1/2)^n)
Give it a try. I have written a short program that uses this formula and it works.


Henry Norman January 9, 2014 at 11:44 am

Gave it a try in Excel. Does not work. Try it out!


Tuomo January 20, 2014 at 6:10 am

(Please excuse my bad english, but I feel I have to write a message below :-)

When I was young(er), I needed to figure out if God exist using math, physics, theology and cosmology. Never understood it before I heard about golden ratio half years ago. Thanks to this website, I understand now the Phi and whole “cake” better, putting slice of life together.

I still need to work with art and design but hoping one day “the cake” has made.

Thank you for so much of this website and God bless you!


Science Man January 27, 2014 at 12:56 pm

Yes, this was a very helpful info page for the golden ratio. i am doing a science project on it so this help a lot. :D


jon January 28, 2014 at 2:00 pm

O this website is the best. i have done 28 science projects with this website and it hasn’t failed me yet. I would like to have a discussion with you about your science project. I think it is interesting to see how people interpret this theory.


isaacson yak February 16, 2014 at 8:14 am

jst met this number in the davinci code book..perfact.


isaacson yak February 16, 2014 at 8:17 am

davinci code book brought me here..


Hailey April 1, 2014 at 9:53 pm

Hello! I am a junior in college, and a math major, writing a 10 page paper for my Modern Geometry class on the golden ratio and honestly this website was all I needed. Broke everything down very nicely, was very easy to navigate, made sense, and used good diction, I was very impressed in such a website. It clearly states where the information is from for my Works Cited, I love this whole web page! Thanks for all your help!