Fabric Handling
Diameter grows as the square root of length. Mass grows linearly. That is why rolls get heavy before they get big.
— mm
Outside diameter at this wound length
The spiral model assumes uniform thickness through the build, which winding tension violates - the inner wraps are compressed by everything above them, so a real roll is slightly denser at the core and this reads marginally large on diameter. Thickness must be the effective wound thickness rather than a flat measurement, particularly for napped, pile or lofty fabric where the difference is substantial. The wrap count is a geometric average and does not correspond to a countable number on a real roll. Mass excludes the core, which on a heavy cardboard or steel tube is not negligible when checking against a lifting limit. Handling limits are entered as inputs because they depend on local regulation, on the equipment available and on whether the lift is manual or mechanical.
Fabric Roll Diameter, Mass & Handling Limit Calculator — free, with the formula and a worked example, at Textile School.