Calculate the width, height limits for a given dpi threshold

hidpi_limits.py

#!/usr/bin/env python3

import sys
import numpy as np

def limit(ts, r):
    return (r / ts) * 25.4

def ds(w, h):
    return np.sqrt(w**2 + h**2) / 25.4

res = [(3840, 2048)]

def main():
    ts = [192, 182, 181, 180] if len(sys.argv) < 2 else [int(sys.argv[1])]

    for t in ts:
        for r in res:
            x, y = r[0], r[1]
            w, h = limit(t, x), limit(t, y)
            d = ds(w, h)
            print("%d  %d×%d => %5.2f×%5.2f [%2.2f]" % (t, x, y, w, h, d))


if __name__ == '__main__':
    main()

192  3840×2048 => 508.00×270.93 [22.67]
182  3840×2048 => 535.91×285.82 [23.91]
181  3840×2048 => 538.87×287.40 [24.04]
180  3840×2048 => 541.87×289.00 [24.18]