How the roll length is calculated
The total length of material wound on a roll follows from the cross-sectional area of the wound material divided by its thickness. The formula is:
L = π × (D² − d²) / (4 × t)
Where D is the outer diameter, d is the core (inner) diameter, and t is the material thickness — all in the same units. The result L is in those same units.
Working in microns (μm)
Thin films, foils, paper grades and label stock are commonly specified in microns. One micron (μm) is one-thousandth of a millimetre (1 μm = 0.001 mm). This calculator lets you enter thickness directly in microns without having to convert by hand — just type the value (e.g. 50 for a 50 μm film) and the unit conversion is handled automatically.
Mixed units
You can mix and match measurement systems: enter the diameters in millimetres and the thickness in microns, or diameters in inches and thickness in microns. The calculator converts everything to millimetres internally, computes the length, then converts the result to your chosen output unit.
When is this useful?
- Printing & packaging — estimate how many metres of film or label stock are on a roll before buying or running a job.
- Foils & metals — work out the length of aluminium or copper foil on a core, where thickness is usually in microns.
- Paper & board — convert between GSM, caliper and roll length when planning print runs.
- Textiles & tape — estimate how much material remains on a partial roll given the current diameter.
Tips
The formula assumes the material is wound uniformly with no air gaps. Real-world rolls typically run 2–5% shorter than the theoretical value due to tension winding (the material stretches slightly under tension, taking up more length per layer) and air entrapment (which makes the roll appear thicker than the net material). For critical production work, subtract ~3% as a starting tension allowance and verify against a measured sample. The thickness you enter should be the caliper of the material under light pressure — using GSM (grammage) directly will give the wrong result.