Yes there is a formula for working out the required resolution and it is all based on viewing distance.
With good eyes and good light the formula is :
Print resolution in ppi = 2/(distance x 0.000291)
where "distance" is the viewing distance in inches, and ppi is pixels per inch
Here is an article which discusses resolution requirements
all in inches?
Yes that formula uses inputs in inches and gives resolution in pixels per inch
A few examples.
First a print in an album to be viewed from 2 feet = 24 inches.
ppi required = 2/(24*.000291) = 286ppi so approx. 300ppi
Second a wall print to be viewed from 4 feet = 48 inches.
ppi required = 2/(48 x 0.000291) = 143 pixels per inch
Third a billboard poster to be viewed at 10 yards = 30 feet =360 inches
ppi required = 2/(360 x .000291) = 19ppi
Anything above those resolutions will not be visible, i.e. is wasted, at those viewing distances
I hope that helps you
So, the distance i have to guess
Standard rule of thumb is 300dpi. Most images we get for large or grand format are 300dpi at 100% size because you can't guess viewing distance. For Grand and up 150 works for the very large graphics over 10 ft.