How to calculate viewing distance for a print size?

Question

I'm working on a photomontage (35mm landscape). The client is asking for what size they should print it at and what is the viewing distance.

I'm planning to print the final image on either A1 or A2 sized paper.

I have read numerous guides on how to work out the viewing distance. But none of them make much sense. The advice note from the Landscape Institute suggests it is not guess work by I'm more confused by it.

The Diagonal x 1.5 rule seems to produce a large viewing distance. I thought a value of around 400mm for an A1 print would be more suitable, but looking for a way calculate it rather than guessing it. Any help is appreciated.

Answer 1

The viewing distance of an image is based on two factors; first is the diagonal image size and second are the pixels per inch required at that distance to give a sharp image.

Firstly the rough rule of thumb is that the viewing distance should be 1.5 to 2 times the diagonal length. This will give you an optimal viewing distance for the overall printed size based on the human eye's ideal viewing angle. You have to understand, however, that for a landscape this may not be optimal as you may actually want the viewer to pan around the image, and you may want the size of features within the image to be the basis of this calculation. This is an artistic decision though, based on the composition of your image.

Secondly for the image to look good at the distance you choose, there need to be sufficient pixels per inch (ppi) to fool the eye into seeing a smooth image that isn't pixelated. The minimum ppi needed for a print with acceptable quality is calculated by dividing the value 3438 by the viewing distance. Anything above this ppi will look good at the distance chosen.

So: minimum ppi = 3438/Viewing Distance

With viewing distance in inches, and where 3438 is a constant for human vision, which was derived as follows:

1/ppi = 2 x Viewing Distance x tan(0.000290888/2)

1/ppi = Viewing Distance x tan(0.000290888)

ppi = 3438/Viewing Distance

where 0.000290888 radians (1 arc minute) is known as the 'visual acuity angle' and represents how much resolution a human can see.

Answer 2

This sounded easy to test, I have a slightly larger than A1 (it's almost exactly B1 size) picture hanging in my living room so I took a tape measure and started measuring.

At 400mm I couldn't even see the edge of the picture, I might look from this distance if I want to "zoom in" on a feature in the image (so you may want to use it for PPI calculation) but it's obviously not a comfortable viewing distance.

Around 1m is the minimum distance that I could see the whole picture at once - but it was still to close to feel comfortable.

At around 2m (between x1.5 to x2 of the diagonal, what a surprise) I felt comfortable viewing the picture.

So to x1.5-x2 rule seems to work.

All measurements are from the tip of my nose to the middle of the picture (they are approximately the same height and I didn't feel like poking myself in the eye)