How to use the roll length calculator
- Choose what to find: the length on the roll, the thickness of the material, or the outer diameter a given length will make.
- Pick millimeters (lengths in meters) or inches (lengths in feet), then enter the core diameter and the other measurements the page asks for.
- Open the advanced options if you also know the width of the material and its density, and the page adds the weight of what is on the roll.
- Read the length, the number of wraps and the other sizes, and use the steps to see how they were found.
Formula
Length = pi x (outer diameter squared - core diameter squared) / (4 x thickness)
Thickness = pi x (outer diameter squared - core diameter squared) / (4 x length)
Outer diameter = square root of (core diameter squared + 4 x length x thickness / pi)
Wraps = (outer diameter - core diameter) / (2 x thickness)
A roll seen from the end is a ring, and the material is a thin strip that fills the ring. The ring area divided by the thickness of one layer is the length of the strip. All three sizes must use the same unit.
A film roll and a paper roll
A roll 100 mm across on a 40 mm core, wound with film 0.1 mm thick, holds pi x (10,000 - 1,600) / 0.4 = 65,973 mm, or 65.9734 m. It has (100 - 40) / 0.2 = 300 wraps. Summing 300 separate rings, one per layer, gives the same length.
A paper roll 120 mm across on a 45 mm core with 0.1 mm paper holds 97.193 m. If the paper is 210 mm wide and has a density of 0.8 g/cm3, the paper weighs about 1.6328 kg. If the same 100 mm roll held 50 m instead, each layer would be 0.131947 mm thick.
Where the estimate comes from
The formula treats the material as a perfect spiral with no gaps. Winding tension, a soft core, air between layers and a liner that is not counted in the thickness all change the real length. Measure a short sample with a caliper and enter the thickness of one layer including the liner for the best result.
To turn a length of filament into a weight use the filament length to weight calculator. For the size of a circle from its diameter, see the circle calculator.
Getting the measurements
Measure the outer diameter across the widest point of the roll, not across a flange. Measure the core where the first layer sits. For thickness, stack ten layers and divide by ten, which is more accurate than measuring one layer. The same math works for tape, film, paper, fabric, wire, cable, foil, rope and sheet metal coil.
Assumptions and limits
- The material forms a tight, even spiral, so the roll is a ring with no gaps between layers.
- The thickness is the same all the way along, and it includes any liner wound with the material.
- All the diameters and the thickness use the same unit. Lengths come out in meters for millimeters and in feet for inches.
- Weight is the length times the width times the thickness times the density, and it ignores the core.
Frequently asked questions
How do I calculate the length of material on a roll?
Take the outer diameter squared minus the core diameter squared, multiply by pi, and divide by four times the thickness of one layer. A 100 mm roll on a 40 mm core with 0.1 mm film holds 65.97 m.
How do I find the thickness of the material from a roll?
Choose the thickness mode and enter the diameters and the known length. The page divides the ring area by the length, which is the thickness of one layer.
Why is my real length different from the result?
The result assumes a perfect spiral. Loose winding, compressible material, a liner or a wrong thickness all change the answer, so measure a sample and treat the result as an estimate.
Can I use this for tape or cable?
Yes, for anything wound in layers. For cable or wire use the diameter of the cable as the thickness, since each turn sits beside the next in the same layer and the layers stack by about one diameter.