Precise mathematical conversion between typographic units requires distinguishing between fixed absolute units and context-dependent relative units:
Absolute Point to Pixel Transformation:
$$text{Pixels (px)} = text{Points (pt)} times frac{96}{72} = text{Points (pt)} times frac{4}{3} approx text{Points (pt)} times 1.333333$$
Pixel to Point Inverse Transformation:
$$text{Points (pt)} = text{Pixels (px)} times frac{72}{96} = text{Pixels (px)} times 0.75$$
Relative Root-Em (rem) Conversion:
$$text{Pixels (px)} = text{Value (rem)} times text{BaseFontSize}_{text{root}}quad (text{Default } text{BaseFontSize}_{text{root}} = 16text{ px})$$
Harmonic Modular Typographic Scale:
$$f_n = f_0 times r^nquad (f_0 = text{base font size, } r = text{scale ratio, } n = text{scale step})$$
A UX design technologist is constructing a responsive design token architecture for an enterprise web application. The design specification calls for a base body copy of $16text{ px}$ ($1text{ rem}$), with headings scaling on a Major Third ratio ($r = 1.250$). Let us compute the exact values in pixels, rems, points, and picas for the Heading 1 ($n = 4$):