How to properly size door frame headers
The fetched OmniCalculator page treats door headers as simply supported beams, but then gives a quick field rule for standard openings: multiply the lumber depth in inches by 12 to get the maximum rough opening in inches.
L = d x 12
Door header size chart from Omni
The fetched chart maps rough openings to nominal sizes: 48 in to 4 x 4, 72 in to 4 x 6, 96 in to 4 x 8, 120 in to 4 x 10, and 144 in to 4 x 12.
Recommended size workflow
Omni's FAQ example takes a 50-inch rough opening, divides by 12, then rounds up to the next even header depth, giving a 4 x 6 recommendation. This rebuild supports both directions: choosing a header from the opening or checking the maximum span from a selected header.