Work out roll diameter from length instantly with clear inputs, formula shown and shareable results.
Winding length onto a core builds diameter according to D_outer = sqrt(D_core^2 + 4 x thickness x length / pi). Rearranged, it gives the maximum length that fits within a machine's diameter limit, which is the constraint that sets roll changes on a converting line.
Roll diameter
D_outer = sqrt(D_core^2 + 4 x t x L / pi)
Maximum length
L_max = pi x (D_max^2 - D_core^2) / (4 x t)
Air entrainment and low winding tension leave gaps between layers, so effective thickness exceeds nominal. Films and papers typically build 2-5% more than theory.
Yes for capacity. A larger core wastes diameter capacity, but too small a core buckles under winding stress and makes unwinding at speed unstable.