Roll Length Calculator (length of paper, film, tape or fabric on a roll)

Understanding the roll length calculator — concept and principle

This calculator estimates how much material is left on a roll of paper, film, tape, fabric or foil from its outer diameter, core diameter and material thickness. Print shops, warehouses and crafters use it to check stock without unrolling.

Ring area ÷ thickness: with the default inputs the result is 99.2 m (≈ 390 wraps).

How it is calculated

Length = π × (D² − d²) ÷ (4 × t), with outer diameter D, core diameter d and thickness t in mm; ÷ 1,000 for metres.
Wraps = (D − d) ÷ (2 × t).
Average wrap length = π × (D + d) ÷ 2.
Wound thickness on each side = (D − d) ÷ 2.
Feet = metres ÷ 0.3048.

The principle

Seen end-on, the wound material fills a ring between the core and the outer edge. The area of that ring, π(D² − d²) ÷ 4, is the same as the material laid out flat seen edge-on, length × thickness. Setting the two equal gives the length. The same result comes from counting wraps: each layer adds two thicknesses to the diameter, and the average wrap is the circumference at the middle diameter. The method assumes tight winding with no air between layers.

Worked example

Default inputs: outer diameter 120 mm, core 42 mm, thickness 0.1 mm.

Ring area = π × (120² − 42²) ÷ 4 = π × 12,636 ÷ 4 = 9,924 mm².
Length = 9,924 ÷ 0.1 = 99,244 mm = 99.2 m (325.6 ft).
Wraps = (120 − 42) ÷ 0.2 = 390; average wrap = π × 162 ÷ 2 = 25.4 cm.
Wound thickness each side = (120 − 42) ÷ 2 = 39 mm.

Each point is the calculator re-run with only “Thickness of the material (mm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Thickness of the material (mm)	Length on the roll (m)
0.025	397
0.05	198.5
0.075	132.3
0.1	99.2
0.125	79.4
0.15	66.2
0.2	49.6

How to read the result

Compare with the length printed on a new roll to check the thickness you used. Loosely wound or compressible materials, such as tissue, foam or fleece, hold less than calculated because of air gaps. For very thin films, measure thickness with a micrometer; small errors in t change the result a lot.

Common mistakes

Using the radius instead of the diameter.
Mixing mm for thickness with cm for diameters.
Guessing the thickness of thin films.
Forgetting the core.

Keep in mind: The result assumes tight, even winding. Use it as an estimate for stock checks.

Frequently asked questions

How do I calculate the length of material on a roll?

Length = π × (outer² − core²) ÷ (4 × thickness).

How many wraps are on the roll?

(outer − core) ÷ (2 × thickness): 390 in the example.

Why is my roll shorter than calculated?

Loose winding or compressible material leaves air between layers.

Sources: Elementary geometry: area of an annulus π(D² − d²)/4 equated with length × thickness

Checked 9 Nov 2026. Cross-section area of an annulus equated with length × thickness (standard geometry); 1 ft = 0.3048 m (exact).

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