Nonwovens
Length grows with the square of diameter. Splices cost the same whatever the roll holds, so short rolls pay the toll more often.
— m
From the annulus between core and finished diameter
Caliper is the input that decides everything and it is the one most often taken from the wrong measurement: what matters is the compressed thickness of the web as wound under tension, not the free-state caliper from a thickness gauge, and for a lofty nonwoven the two can differ by a factor of two. Back-calculate it from a roll of known length rather than measuring a sample, and the geometry becomes reliable. The model treats caliper as constant through the build, while a real roll is wound harder at the core and softer toward the outside, so the true length sits a little above this figure on a soft-wound roll and a little below on a hard one. Splice count uses a uniform parent-roll interval and assumes every splice falls inside the roll being wound; in practice a splice landing near a set change is often trimmed out at no additional cost, so the waste figure is a mild overstatement and the downtime figure is not. The availability loss is the number worth arguing with a supplier over: at these settings the stops cost several times what the wasted web does, and a converter comparing parent-roll offers on price per kilogram alone is comparing the smaller of the two effects.
Roll Build, Splice Count & Converting Yield — free, with the formula and a worked example, at Textile School.