Reference pixels

6 June 2026

Calculations

A practical way to put it is to say that 1 inch equals 96 pixels, 72 points and 6 picas.
1 ″ = 96 px = 72 pt = 6 picas.
A logical pixel or reference pixel is independent of the physical pixels present in a screen, but is tied to physical sizes.

More precisely, this binding to the inch is valid for a sight distance of 28 inch or about 70 cm. At a wider viewing distance larger letters are necessary, to the reference pixel is in fact an angle, not a distance:

(1 inch / 96) / (28 inch * 2π) * 360 degrees = 0.0213°

In other words, a right angle (90°) contains about 4222.3 logical pixels.

A program

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

void Usage (void)
{
   fprintf(stderr, "Usage: logpix screen res1 res2\n");
   fprintf(stderr, "screen is the screen diagonal, in decimal inches\n");
   fprintf(stderr,
      "res1 and res2 are the number of physical pixels, in any order\n");
}

int main (int argc, char **argv)
{
   double diagon, bigres, smlres;
   double diagpix;
   double ratio;

   if (argc != 4)
   {
      Usage();
      exit(1);
   }
   diagon = atof(argv[1]);
   bigres = atof(argv[2]); smlres = atof(argv[3]);
   if (smlres > bigres)
   {
      double swap = bigres;
      bigres = smlres;
      smlres = swap;
   }
   /* Pythagoras */
   diagpix = sqrt(bigres*bigres + smlres*smlres);

   /* 72 points (pt) in an inch.
      12 pt = 16 logical pixels.
      96 logical pixels in an inch. */

   printf(
      "Screen is %4.1f inch, %4.0f x %4.0f = %4.0f physical pixels\n",
      diagon, bigres, smlres, diagpix);
   /* printf("Diagonal is %5.0f physical pixels\n", diagpix); */
   ratio = diagpix / (diagon * 96);
   printf("Screen is %4.0f px,   %4.0f x %4.0f logical pixels\n",
      diagon * 96, bigres / ratio, smlres / ratio);
   printf("One logical pixel is %5.3f physical pixel\n", ratio);
   printf("Pixel density is %5.1f logical pixels per inch\n",
   	diagpix / diagon);

   return 0;
}

Compiling it

cc logpix.c -lm -o yourbinpath/logpix

Sample output

user@machine:curdir$ logpix 6.3 2424 1080

Screen is  6.3 inch, 2424 x 1080 = 2654 physical pixels
Screen is  605 px,    552 x  246 logical pixels
One logical pixel is 4.388 physical pixel
Pixel density is 421.2 logical pixels per inch