Roll Length Calculator: Length of Paper, Tape, Film or Fabric on a Roll
Find the length of material on a roll from its outer diameter, core diameter and thickness, or solve for the roll diameter or material thickness, with wraps and a remaining-length table.
How it works
Length L = π × (D² − d²) ÷ (4 × t) · Outer diameter D = √(4 × L × t ÷ π + d²) · Thickness t = π × (D² − d²) ÷ (4 × L) · Wraps N = (D − d) ÷ (2 × t), where D = roll outer diameter, d = core diameter, t = material thickness (all in the same unit).
Seen from the end, a roll is a ring: the area between the outer circle and the core circle. Unrolled, the same material is a long thin strip whose edge area is length × thickness. Because the material does not change volume when you wind it, the two areas are equal, so length = ring area ÷ thickness. The same relation solved the other way gives the diameter a given length will wind up to, or the thickness of material on a roll whose length is printed on the label. The number of wraps is the wound depth divided by one thickness, and wraps × the average wrap length gives the same answer as the area method. The result assumes tight winding with no air gaps. Real rolls of compressible material (foam, fabric, bubble wrap) hold less, so measure a sample if accuracy matters, or use Find thickness with a roll of known length to get the effective thickness of your material. The remaining-length table shows how much is left as a roll is used up, which is handy for printing, label and converting jobs. Unlike the wallpaper roll calculator, which counts how many rolls cover a wall, this works out what is on one roll.
Worked example
A roll is 12 in across on a 3 in core, and the material is 0.005 in (5 mil) thick. Ring area = π × (12² − 3²) ÷ 4 = π × 135 ÷ 4 = 106.03 sq in. Length = 106.03 ÷ 0.005 = 21,205.8 in = 1,767.1 ft (538.6 m or 589.0 yd). The material is wound (12 − 3) ÷ (2 × 0.005) = 900 times, the wound depth is 4.5 in, and an average wrap is π × 7.5 = 23.56 in long; 900 × 23.56 in gives the same 1,767 ft.
Sources: Omni Calculator: Roll length (ring area ÷ thickness) · Math Central (University of Regina): A reel of paper, 7,750 m on a 1,240 mm roll · Math Central: The diameter of a roll of plastic (765 m, 0.8 mm, 400 mm core) · Math Central: A roll of paper (60 in roll, 10.75 in core, 0.014 in paper)
Frequently asked questions
How do I calculate the length of material on a roll?
Measure the outer diameter (D), the core diameter (d) and the material thickness (t) in the same unit. Length = π × (D² − d²) ÷ (4 × t). For a 12 in roll on a 3 in core with 0.005 in material, that is π × 135 ÷ 0.02 = 21,206 in, or about 1,767 ft.
How do I measure the thickness of paper or film?
Use a micrometer or caliper on a stack of layers and divide by the number of layers, or check the spec sheet (often given in mil, microns or caliper points). If you know the length of one full roll, choose Find thickness and the calculator works it out from the roll size.
How much material is left on a partly used roll?
Measure the roll as it is now and use that as the outer diameter. The table under the results also shows the length left at each diameter down to the core, so you can mark a roll or set a reorder point.
How big will a roll be for a given length?
Choose Find roll diameter and enter the length, thickness and core size. The outer diameter is √(4 × L × t ÷ π + d²). For example, 765 m of 0.8 mm plastic on a 400 mm core winds to about 969 mm across.
Why does my real roll hold less than the calculator says?
The formula assumes the layers are packed with no air between them. Loose winding, soft or textured material, and wrinkles all take up extra space, so actual length is often a few percent lower. Working out the thickness from a roll of known length gives an effective thickness that already includes this.
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This calculator is for educational purposes. Double-check important results before acting on them.