Filed under: XTRAS

As a designer I use the Golden Ratio for almost every design project. That’s why I created this Golden Ratio Calculator. The use of the Golden Ratio will result in a more harmonious design. Often you can beautify a boring minimalistic design by following the Golden Ratio.

Enter a number in the calculator and get a sequence of Golden Ratio Numbers:

## The Golden Ratio in Modern Web Design

I used the Golden Ratio to calculate the proportion of the calculator box above. The standard width of my content area is 626 pixels. To calculate the height I used the following equation 626 pixels / Golden Ratio = 387 pixels. Also the sequence abcdefg follows the Golden Ratio.

For many more elements on this website I used the Golden Ratio. The proportion of font sizes between the three words that form my logo (‘Rado’, ‘Vleugel’ and ‘Media’) follow the Golden Ratio. The line height of this HTML text was calculated by font-size * Golden Ratio.

Of course there are limits in the use of the Golden Rule for web design. In print and in art you see always the whole object. On the web you are looking through a window (your screen) that obscures parts of the object (the webpage). It’s useful to apply the Golden Rule to the width of the columns of a website, the proportion of font sizes, the proportion of smaller images and boxes, but it’s less useful to apply it to the height of elements that are so large that they need to been scrolled.

## The Golden Ratio explained

Two quantities are in Golden Ratio if the ratio of the sum of the quantities to the larger one equals the ratio of the larger one to the smaller (a+b is to a as a is to b). The Golden Ratio is an irrational mathematical constant, approximately 1.6180339887. The Golden Ratio is often denoted by the Greek letter phi.

Other names used for the Golden Ratio are Golden Section (Latin: sectio aurea), Golden Mean, Divine Proportion, Divine Section (Latin: sectio divina), Golden Proportion, Golden Cut and Golden Number.

Some famous artists used the Golden Ratio. If you draw a rectangle around the face of Leonardo da Vinci’s Mona Lisa, the ratio of the height to width of that rectangle is equal to the Golden Ratio. Maybe Leonardo was introduced by the idea of the Golden Ratio by his friend Luca Pacioli, who published a three-volume treatise on the Golden Ratio in 1509 entitled Divina Proportione. Also my favorite painter Salvador Dali used the Golden Ratio in many of his paintings.

## The Golden Ratio and Fibonacci Numbers

The Golden Rule is closely related to Fibonacci numbers. Fibonacci numbers are named after the talented 13th Century mathematician, Leonardo of Pisa, (also known as Leonardo Pisano, Leonardo Bonacci, or Leonardo Fibonacci). Most people know Fibonacci numbers from The Da Vinci Code where the numbers are used to unlock a safe.

Fibonacci numbers approach the Golden Ratio, as the numbers get larger (try it yourself by using the Golden Ratio Calculator). Each new Fibonacci number is derived by adding the previous two numbers. This is an example of a Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987…

The Fibonacci sequence can be viewed as a spiral by drawing successive Fibonacci-proportioned squares. Start with a 1 x 1 square. Beside that square place another 1 x 1 square. Since 1 + 1 is 2, the next square will be a 2 x 2. And 1 + 2 is 3. So, the next square is 3 x 3, and so on. Each succeeding square is placed in a counter-clockwise position to the last square as they rotate around the initial 1×1 square.

Even today’s stock market is not immune of the influence of the Fibonacci Sequence. Some traders try to predict market reversals with Fibonacci Numbers. Maybe I’ll try this if I have earned more  money…

## 38 Responses to “Golden Ratio Calculator”

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On: March 7, 2014 at 10:40 am

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On: March 5, 2014 at 1:48 pm

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By: Tom

On: February 27, 2014 at 6:11 am

Really good calculator :) Thank You! :)

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By: Susan S

On: December 17, 2013 at 7:04 am

Thank you so much! I’m constructing some unusual and highly geometric knotwork designs, and your calculator was invaluable in scaling up some elements. I’ll have to apply it to other forms of design, too, like knitting and metalwork. This thing is invaluable, especially since it gives more than simply whole numbers. Sometimes I have to round, and it’s nice to be able to double check without having to go to a calculator.

By: Daniel Dou

On: December 13, 2013 at 8:18 pm

Thanks a lot for this cool calculator! :) I was thinking of what dimensions I should use for my pictures.

And so I thought, “Why not just go with the Golden Ratio?”

And the rest is history…

By: FP

On: November 16, 2013 at 4:05 am

How come your blog’s text is not set according to the golden ratio (You are using 19px as your Header size and 15 px as your paragraph text size – Should be 19-12 OR 24-15)?

Thanks for the tool.

By: ILIEV

On: October 9, 2013 at 10:42 pm

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

By: ILIEV

On: October 9, 2013 at 10:42 pm

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

By: Greg

On: September 26, 2013 at 2:15 am

Thanks for this awesome tool.

By: Trevor Avichènnya Zénaïde

On: September 19, 2013 at 5:25 pm

Aloha! I completely agree with your supposition that using the Golden Ratio improves aesthetics. Your calculator is a great tool!

I have used the Golden Ratio constantly in my art and design work for 25+ years. Now, I rely heavily on it when I’m designing typefaces, which has been my hobby for the past several years since I retired as an Art Director when I was 32.

By: Gustavo Meano

On: September 15, 2013 at 4:47 am

That’s a great whey to see things. Golden ratio is amazing for me and lots of people that discover the existence in art, nature, maths, etc. Your calculator is a strong machine. Thanks a lot.

By: Kevin Dee

On: August 22, 2013 at 3:56 pm

This is the best… I use it constantly. You are a saint.

By: Ann

On: August 9, 2013 at 2:01 am

Hi,
I have used divine proportion GS for 20 years in architecture and design, I really think that with constant use, you automatically have an eye for intuitive natural proportion. You cultivate a visional dictionery
In property I believe the essence of a house or building is really enhanced or has happier feel for its occupants when propotion is perfected. I also love to break the rules and experiment with proportion, just to make sure I have not be o e a slave to a particular design process.
Love the site , did you know that brands like Apple have used the golden section to develop the logo

Perhaps being so true to nature are what make the GS calculations so divine. !
Best Wishes
A

By: Olga

On: June 10, 2013 at 7:07 pm

Thank you for the calculator. It’s just got added to my bookmarks, and will be used frequently. I’m a cosmetic dentist so I know the value of a Golden proportion very well.

By: Alex

On: February 9, 2013 at 11:52 am

Hi, thanks for being another designer to consider the greatest aesthetic principle known. These n00bs above saying how it has nothing to do with design are just uber myopic.

By: Lonny

On: December 30, 2012 at 3:58 pm

Just what I was looking for today. I am a woodworker who has built uncounted cabinets, chests, shelves,ect.. The quality is always the same but some just look more pleasing than others……… Gee, using the golden proportion seems to make sence! Funny how a small dimension change makes a noticeable difference!,,,

By: Josh

On: November 28, 2012 at 9:08 am

Please don’t ever take this down! I use it all the time :)

By: ian nicely

On: September 17, 2012 at 12:16 pm

I dont get it… maybe im just mentally deficient…doesn’t make a lick of sense to me.

By: Rene Espinoza

On: August 3, 2012 at 6:34 am

very useful this calculator in Mining engineering

By: Jordan

On: July 5, 2012 at 10:09 pm

Also as a web designer, why are you using the golden ratio in web design? The golden ratio has no notable aesthetic properties, which would be the only reason to be using it in design.

By: ?

On: May 28, 2012 at 4:56 pm

How does this work if I’m trying to figure out the best height of a rectangle with width 2?

By: Meeksoul

On: October 6, 2011 at 9:58 am

Thanks for the tool! Do you have any ideas on volumetric (spatial and/or flow pattern) relationships that could be defined and predicted by the GR?

By: Johanas Berg

On: October 1, 2011 at 9:07 am

Thanks for the calculator. It’s very helpful!

By: Paolo

On: July 14, 2011 at 6:21 pm

How about the whole sequence:…+13,-8,+5,-3,+2,-1,+1,0,1,1,2,3,5,8,13… It does not begin with a zero!

By: Fiona

On: May 24, 2011 at 4:29 pm

I went looking for a Golden Ratio calculator just now, and was disturbed to discover that all the websites I visited would only calculate the ratio to nearest whole number! So I was pleased to find your site, where more significant figures are given.

By: Geoff

On: October 21, 2009 at 11:58 am

Every month or two I find myself on my bookmarks list looking for your calculator. Thank you for putting this together: I love the multiple returns!

By: Maria C

On: August 1, 2009 at 4:12 am

Can you make an interface where you can upload a portrait so you can calculate the golden ratio of a face. I was searching for a golden ratio face calculator and landed on this page. The golden ratio calculator you have here is certainly helpful for designers, but for a beauty queen like me a golden ratio face calculator would be very appreciated.

By: Josh

On: July 30, 2009 at 7:29 am

Thanks for this calculator and the useful information regarding it’s origin.