The formulas are KDP's, and visible
Spine width is page count times the paper's per-page thickness: 0.002252 inches for white and standard color, 0.0025 for cream, 0.002347 for premium color. Spine text is only placed above KDP's 79-page threshold, with clearance kept on both sides. The numbers appear on screen so you can audit them, not inside a black box.
Preflight before upload, not after rejection
The most common KDP rejections, wrong sheet size, missing bleed, spine text on a thin book, content in the barcode zone, are checked live while you design. If the page count changes after formatting, re-enter it and the wrap recalculates; the design layers never need rebuilding.
Beyond KDP, honestly
The Print package also renders IngramSpark, Lulu, and Barnes & Noble Press paperback wraps, built from the exact spine width shown on each platform's official title-specific template, which you supply. The official template remains the authority for those platforms; Coverfairy's sheet is built to match it, and you verify before upload.
Honest boundary. Always compare the exported PDF against the printer's freshly generated template before uploading, KDP's generator is the final authority for KDP, and the title-specific templates are the authority for IngramSpark, Lulu, and Barnes & Noble Press.

