A worked example: a 175cm man with a 17.5cm wrist at 20% body fat
Feeding this person's height and wrist circumference into the body type formula gives a ratio of exactly 10 (175 divided by 17.5), which falls inside the 9.6-10.4 band, so the result is "Mesomorph." Feeding his sex and current body fat percentage into the ideal body fat formula separately returns "Acceptable," since 20% falls inside the men's 18-24% acceptable band. Both results describe the same person, but neither formula uses the other's input or output to get there.
The formulas: two independent calculations, not a pipeline
The body type formula only takes height and wrist circumference and never looks at body fat percentage. The ideal body fat formula only takes sex and current body fat percentage and never looks at height or wrist circumference. Running both on the same person produces two separate, non-overlapping pieces of information — a frame estimate from skeletal proportions, and a body-composition category from a directly measured or estimated body fat percentage — rather than one feeding into the other.
A second worked example: a 160cm woman with a 15cm wrist at 28% body fat
This person's height and wrist circumference give a ratio of 10.67 (160 divided by 15), which is above the 10.4 cutoff, so the body type formula returns "Ectomorph" — the calculator's label for a narrower frame. Her sex and body fat percentage put her in "Acceptable" on the ideal body fat formula, since 28% falls inside the women's 25-31% acceptable band — the same category label as the first example's man, even though her frame classification (Ectomorph) is different from his (Mesomorph).
Why frame and composition are separate signals
The body type calculator's own documentation notes that a skeletal frame estimate stays relatively fixed over time, while body composition — muscle and fat levels — can change significantly with training and diet regardless of the underlying frame. The second worked example above shows this directly: an "Ectomorph" frame reading doesn't by itself say anything about which body-fat band a person falls into, because the two calculators are measuring different things from different inputs.