Core ID vs core OD
Core ID is the diameter of the hole. Core OD is the outside diameter of the core material. Roll geometry uses the outside surface where the label stock begins winding.
Why core OD belongs in the formula
The roll-length equation subtracts the core's cross-sectional area from the finished roll's cross-sectional area. Because no label material occupies the core wall, the boundary must be the outside of the core.
Equipment specifications often use ID
Printers and unwinders frequently specify core ID because the core must fit a spindle or holder. That specification is important for compatibility, but it is not automatically the number to place in a roll-length formula.
When only ID is known
If the core wall thickness is known, outside diameter can be estimated as core ID plus twice the wall thickness. Direct measurement is preferable when the calculation is production-critical.