# human visual: relation of Distance and DPI

I was told that human's visual sharpness is 60 pixels per degree. As such, pixel per inch is approximately given by:

PPI = 1/ (Distance * tg((1/60*pi/180) )


Is this formula fully correct? (I saw similar, but slightly different versions). How is this formula derived? Maybe some step by step description?

• Could you either include a link to the source of this formula, or define what the terms in it refer to? – trichoplax Aug 5 '17 at 21:05

According to a review by Legge & Bigelow the arc or degrees of visual angle ($\alpha$) is,

$$\alpha = 57.3 \times S/D,$$

where S is height of object and D is distance to object. [1] $S/D$ is the small angles approximation of $2 \times arctan(S/2D)$ which follows form geometry.

Image 1: the equation comes straight from trigonometric definitions.

Since humans continuously scan the page with the fovea, small angles assumption is a good approximation for entire pages. The factor $57.3$ is simply $180/\pi$ or conversion form radians to angles.

So given that we do not know the nature of $tg$, then its hard to say. Looks a bit fishy, but if tg is some sort of inversion of S then its plausible.

[1] G. Legge & C Bigelow. 2011. Jornal of vision. Does print size matter for reading? A review of findings from vision science and typography.