If I purchase a scenic photo from Shutterstock that says 5586px x 3724px, and 18.6" x 12.4" @ 300 dpi, can this photo be enlarged to a huge 40ft x 6ft banner without appearing extremely pixelated? This banner will be used outdoor and will mostly be viewed from a 10ft to 15ft distance.

I asked the actual printer, they told me to open photoshop and insert the photos at 50 dpi and view it at 100%, if that is acceptable then that's how it would print on the banner.

Since this is not a graphic design, I'm assuming a photo can not be vectorized, so What is the general rule for enlarging photos to extreme large sizes? what are the formulas to calculate how big can you enlarge without loosing the pixilation too much?

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    Images do not get rasterized with nearest neibourhood sampling, when printing. So the result is never really pixelated as such they just blurr in interesting ways. – joojaa May 18 '17 at 7:11

Lets say a 150dpi image looks good at arms length, about 2.5 feet. 10-15 feet is 4-6 times this, so you'd want an effective DPI of 25-37.5 dpi.

This image would have an actual DPI of about 12 DPI (5586 / (40ft x 12in)), but the image conversion up to that size would somewhat mitigate the negative hit from this. Still, that's not stellar.

So for this specific case, I'd look for an image 2-3 times that width to start getting into 'good' range.

That said, sub-par background resolutions can look fine on banners, as long as the text and logos on top of the background image are vectorized and perfectly crisp. The background image is visual, but the text and features of your banner are generally the important part so if those look great you can usually get away with a lot.

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