A tool for creating visually pleasing print borders using the golden ratio. You can calculate and preview the result for any picture or paper size.

Why did I start thinking about using the golden ratio for print borders? Actually, I was about to print one of my pictures. Looking at the screen preview of the print, I was trying to **figure out visually pleasing borders**.

Yes, I understand that this is a very subjective matter. But my goal was to create a **repeatable approach** for different picture and paper sizes.

In the past, I had used Martin Bailey’s print border calculations. He uses 10% of the shorter side of the paper as border size, but I find this too technical.

## 1.Golden ratio print borders

Then I remembered having read about the golden ratio (represented by the Greek letter phi: φ, or 1 : 1.6180339887…) and how **its proportions are considered aesthetically pleasing**. So I checked if someone has already tried this out. The only related post I was able to find was about how to optimize the picture-to-border ratio. The post explains how to calculate a border size for a given image size, using the golden ratio. What I wanted was the exact opposite – to calculate the borders for a given paper size.

In the end, I developed my own formula to calculate the border size for any given paper size. I decided to **make it available online so others can try and use it as well**. The header image at the top of this post is an example of how the result looks like on ISO sized paper.

The original version of the calculator could only **calculate the picture size for a given paper size**. With the latest update, you can also **calculate the paper size for a given picture size**. A **preview **will give you an idea of how the result looks like. Additionally, you can choose to **increase the lower border height** for a more dynamic off-center look or to leave some space for text.

## 2.The revised golden ratio calculator

**Update January 2021**: I have improved the calculator so **you can now enter numbers less than 10**. The number of decimal places is no longer fixed, but adjusted dynamically based on your input, which takes care of the precision issue. Thanks to everyone who provided feedback!

This is how the calculator works:

- Enter width and height – this can be any dimension: pixel, millimeter, inches, whatever you prefer. The results use the same dimension.
- Choose if width and height refer to picture size or paper size
- Select if you would like to place the picture off-center
- Click
*Calculate* - You will see a proportional visual representation of the resulting layout. Further below is a table with the complete list of dimensions.

### 2a.Resulting layout

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Thank you for this…I came across the Golden Ratio idea for framing on another site, but the explanation of how to calculate a Golden Rectangle (or the link to the Wikipedia page) based upon the photo dimensions was not helpful, even for someone who isn’t afraid of the math. I would still like to break open the “black box” as it were in figuring out how to do this calculation myself, but this gives an idea of what I’ll be looking at when it’s time to order canvases.

Btw how does the frame width factor into the calculations (or does it)? Is it included in the width of the border (=smaller mat), or is it entirely separate and irrelevant?

The calculations are all based on areas, not on individual dimensions.

Yes…but a frame adds to the overall area; so if one is calculating the “paper” size based on the picture, should the dimensions given include the picture + mat + frame, or is this assumed to be just the picture with the border/mat?

Basically it is whatever you want to use it for. I cannot tell you what is the “right” or “wrong” entry. Feel free to experiment and use whatever you feel comfortable with.

one could use the paper size calculated then use these dimensions as a picture size to get a frame size that would also be based on the golden ratio: as follows:

Picture (original) 18.01×6.87 gives a paper size 20.29×9.863, using this as a “new” picture size would result in a “new paper size” i.e. frame size of 23.94 x 13.52. The frame width would be 1.83″. (Then round up or down for easy cutting)

A2=A1*1.618;A2=W1*H1*1.618;W2*H2=1.618*W1*H1; W2=W1+dW1;H2=H1+dH1; ; (W1+dW1)*(H1+dH1)+1.618W1H1;let dW1=dH1 (note 2 x border size!).

(W1+dH1)*(H1+dH1)+1.618W1H1;

W1H1+W1*dH+dH1*H1+(dH*dh)+1.618*W1H1; We know H1 and W1, solve for dH by iteration (ie guess) till LHS=RHS;

Good luck and don’t stop trying! Tbh, it took me a while to figure out the formulas.

Hi Robert,

Thank you for this useful information and tool, I came across your page by accident, as I am not a photographer, although, I wish I were! I have always admired beautiful photography, and would someday love to learn more about the art, However, as a quilt designer, I found this tool extremely helpful in planning and designing the dementions for the borders of my current quilt projects.

The outcome is beautiful and very pleasing and balanced to my eye, just as I was hoping to create!

Now, I’m off to the cutting table and sewing machine!

Thank you, Sir

Hello Denise, thank you so much for letting me know about your ‘unusual’ way of using my golden ratio calculator! Your comment really made my day, I would never have thought this would be useful beyond framing pictures. Again, thank you and all the best!

Hi Robert

I like your calculations for margins but the way you do it the ratio Width/Height changes.

For example for a Paper with WxH 50x40cm (frequent frame size, Ikea for example), you have a Ratio of 1.25. With your calculations the result for the image is 40.51×30.51cm with the ratio 1.32 altering the proportion…

I normally do the calculations dividing each side by SQRT(Phi). So on the same example we have:

Paper WxH 50x40cm (Area 0.2 m2) >>> Image 39.3×31.4cm (0.1236 m2) >>> Margins Left/Right 5.35cm | Top/Bottom 4.3cm >>> Ratio W/H 1.25 in both Paper and Image >>> Areas Image/Borders Ratio = Phi.

Of course, all this depends on the format of the image we have to print …

What do you think/say about this?

Everything you have stated is correct. But what this calculator currently does is to ensure that the resulting

areasare in proportion, based on the golden ratioandthe border size is the same for all 4 (or at least 3) sides. As a result, the linear ratios will change. Personally, I don’t like the idea of having different vertical and horizontal border sizes, but as always, this is a matter of personal taste.Ok Robert

I can contribute with another resource about centering or not images in frame.

Introduces the concept of Optically Centered image that states that the bottom margin should be bigger than top margin.

http://www.russellcottrell.com/photo/centering.htm

Thank you, I will for sure have a look.

I would also think that for artwork above eye-level (e.g., over a fireplace) the bottom border needs to be wider in order to appear more proportional, as the angle of view would make a mathematically equal border appear to be narrower.

This calculator has an option to increase the lower border for exactly this purpose. Have you used it?

Yes – I did try it. I just meant to comment in support of L Matias’ post and suggest a reason that this feature would be needed.

Thank you. This is very helpful and handy. I too have tried Martin Baily’s calculations and your formula tends to give a slightly larger border for any paper size – but as you say it is a subjective matter of what pleases your eye. Cheers

Thank you for the comment Tahir, I am glad you find the calculations useful.

I would like to frame a picture that is 8 inches wide. The calculator does not allow any number less than 10. Should I change my calculations to centimeters?

You could either use centimeters (or millimeters) or multiply your input by 10 (use 80 instead of 8). Then, divide the resulting dimensions by 10 and you have the correct result. As I mentioned in an earlier comment, using numbers less than 10 would currently result in a loss of precision. Hope that helps.

Any reason why the dimensions are restricted to 10 minimum?

The reason is precision. Since the results are rounded to 2 decimals, allowing dimensions < 10 would impact the precision of the results. As a workaround, you can always use a different dimension (like mm instead of cm) or multiply your numbers by 10 before you calculate the results. Divide the results by 10 and use the benefit of increased precision (because now you have effectively 3 positions after the decimal point).

hey, thanks for this tool!

Thanks for the comment Laszlo!