I recently reached a milestone in my photography printing journey with the realization that, unless I was printing a photo specifically for framing, my prints were really just “test prints.” Mostly I was simply printing the photos to see how they would look on paper; rather than creating a print designed to present the image to the viewer.
The solution to this issue is to print the photo on the page in an aesthetically pleasing manner such that the printed image is surrounded by a suitable border that frames the image on the page and provides some room for the viewer to hold the paper without covering the photo. Of course, this then begs the question of what is a suitable border? Is it some percentage of the short or long side of the image? Is it based on a standard for a certain size of print? And how do I determine this quickly for a particular photo?
A search for the answers to these questions returns diverse opinions on the matter. Many are based on determining the appropriate mat size to fit within standard frame dimensions. Others are based on high level principles of art and how the human eye perceives space and something about Greek columns. Others are very simple-Martin Bailey offers a spreadsheet calculator based on the using a border that is 10% of the length of the short edge of the image (but this percentage must be adjusted as the page size increases).
I fumbled around for a few hours working on an Excel spreadsheet to calculate some type of “optimal” image size and borders for a given image aspect ratio and page size. However, once my calculator was working, I quickly discovered that there is no optimal size to print images on a standard letter-size sheet for anything other than the 2×3 aspect ratio. For all others, the top/bottom and side borders will be different and, therefore, ugly.
Back to the internet and I soon discovered the answer, apparently conceived long ago in 2010 by an American in Spain, which is to base the size of the borders on the Golden Ratio. I printed a photo to try it and realized that I had found perfection.
Golden Ratio Print Borders
If one sets the ratio of the image area to the area of the borders equal to the Golden Ratio, then the border size will be visually pleasing for any size of image. The Golden Ratio, or divine proportion φ (~1.618:1), is found everywhere in nature and is often considered an aesthetic ideal for design and proportions in visual composition. It has been used for centuries to create harmony and balance in art and architecture including DaVinci’s Last Supper, the Sistine Chapel, and the design of the Parthenon.
Robert Reiser has developed an online Golden Ratio Print Borders calculator, and after experimenting with his calculator for several image sizes, I was sold. Robert sums it up nicely:
The real beauty of the golden ratio approach reveals itself if you look at the resulting ratios. The ratio of the paper area to the picture area is φ, as expected. But additionally, the ratio of the picture area to the border area is φ. And if you have chosen to increase the lower border, the ratio of the lower border to the other borders is also φ.Robert Reiser
Robert’s calculator can be used to calculate the size of the image for a given page size or vice-versa, but is too cumbersome to use for my objective since neither the image aspect ratio nor page size can be set as fixed constraints. I needed a calculator to determine the maximize size of the printed image at a particular aspect ratio for a given size of paper, e.g., what is the largest 4×5 image that can be printed on 8.5×11” paper according to the Golden Ratio?
Being an engineer, I created my own Golden Ratio print borders calculator, again in Excel, this time using an iterative technique to find the solution. The calculator allows me to enter the aspect ratio of the photo and the page size, then finds the dimensions of the largest size image that can be printed on that size of paper.
So, what is the largest 4×5 image that can be printed on 8.5×11” paper according to the Golden Ratio? The answer is 7.9″ wide and 6.3″ tall with a border of 0.8″ on the top and sides and 1.33″ on the bottom as shown below. The page will have to be trimmed down on one side after printing, but the finished print will be perfectly balanced.
The optimal image size can be calculated using an equal width for all borders or “optically centering” the image by extending the bottom border. I prefer the optically centered print, and again the Golden Ratio provides a pleasing result with the bottom border being 1.618x larger than the others.
I used my calculator to determine the optimal print dimensions for a number of common image aspect ratios (2:3, 4:5, 5:7, 16:9, 1:1) and paper sizes (letter, A3+, and half sizes of each) for both portrait and landscape orientations. These have been compiled into tables to provide a quick reference for use when printing.
Update (November 2023): After finally getting a quality paper cutter (Dahle 18″ guillotine trimmer) to trim my prints, I went through my stack of prints from the last six months and trimmed every print that could be trimmed so that the top and side borders were uniform with the bottom border larger. I am absolutely astounded at the difference that this step makes for a printed photograph. Photos that were previously just randomly printed on a letter-size page now look like they were intentionally printed with specific dimensions. I really cannot overstate the importance of using appropriate borders around printed images.