What this calculator does
The length on a roll is the cross-sectional area of the material divided by its thickness. The area is the outer circle less the core, so length is π times the outer radius squared minus the core radius squared, all over the thickness.
The relationship is not proportional to diameter, which is why a roll that looks half used usually has far less than half its material left. A 12 cm roll on a 4 cm core holds 100.5 m; at 9 cm outer diameter it holds 51.1 m, so losing a quarter of the diameter has cost almost half the material.
The formula
The cross-sectional area of the wound material is π multiplied by the outer radius squared less the core radius squared. Dividing by the material thickness gives the length, since the material is effectively a long thin rectangle wound up. The calculation assumes the material is wound tightly with no air gaps and that the thickness is uniform.
| Term | Meaning |
|---|---|
| Outer diameter | Across the full roll including the material. |
| Core diameter | Across the cardboard or plastic tube at the centre, which holds no material. |
| Thickness | Of a single layer of the material, which is the divisor. |
| Spiral approximation | Treating the winding as concentric circles rather than a true spiral, which is accurate to well within measurement error. |
The inputs explained
| Field | What to enter |
|---|---|
| Outer diameter (cm) | Outer diameter of the roll in centimetres. |
| Core (inner) diameter (cm) | Core diameter in centimetres. |
| Material thickness (mm) | Material thickness in millimetres. Thin films may need a specification sheet, since measuring a single layer is difficult. |
When to use it
Estimating remaining stock
Knowing how much is left on a part-used roll without unwinding it is the ordinary use, whether for film, paper, fabric or cable.
Checking a supplier claim
A roll sold as a stated length can be checked by measuring the diameters and the thickness, which occasionally reveals a shortfall.
Planning a job
Whether the material on hand covers the job is answered by this calculation rather than by looking at the roll.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much material is left at each diameter?
A range of outer diameters on the same core with the same material.
| Outer diameter | Length remaining | In feet | Cross-section area |
|---|---|---|---|
| 6 cm | 15.7 m | 51.5 ft | 15.71 cm² |
| 9 cm | 51.1 m | 167.5 ft | 51.05 cm² |
| 12 cm | 100.5 m | 329.8 ft | 100.53 cm² |
Questions
Why does a half-diameter roll have so little left?
Because length depends on the area of the material band, which goes with the square of the radius, and the core takes a fixed bite out of the middle. A roll at half its original outer diameter typically has well under a quarter of its material remaining.
How do I measure material thickness?
For thicker materials, a caliper on a single layer works. For thin films, measure a known number of layers and divide, or take the figure from the specification sheet. Thickness is the divisor, so an error in it translates directly into an error in the length.
Does winding tension affect the result?
Yes, slightly. A loosely wound roll has air between layers, so the effective thickness is greater than the material thickness and the real length is less than calculated. For tightly wound commercial rolls the effect is small.
Does this work for cable and wire?
Reasonably, using the cable diameter as the thickness. It is less accurate than for flat material because round cable does not pack into perfectly concentric layers, and the packing arrangement varies. Expect a figure within about 10%.
For paper counted in sheets rather than length, see the paper quantity converter. For how long a roll of toilet paper lasts, see the toilet paper calculator.