Discrete ManufacturingFree calculatorPDF, Excel, Word exportPackaging and Printing

Paper Roll Length, Weight and Run Time Calculator

Rolls are bought by weight, scheduled by length and run by time. This calculator links all three from the geometry of the roll, so you can check a mill tag, plan a changeover or estimate how long a roll will last on press.

Your numbers

Roll outer diameter

1,000 mm

Core outer diameter

Roll width

Basis weight

g/m2

Caliper (thickness)

microns

Air entrainment in wound roll

Winding adds air between layers, which makes the effective layer thicker.

Press speed

m/min

Your results

Roll length

7,581.18

Metres. Spiral formula: area of the annulus divided by layer thickness.

Roll net weight

606.4945

Kilograms of paper, excluding core.

Effective layer thickness

103

Microns, including air.

Roll area

7,581.18

Square metres.

Run time at press speed

50.5 min

Results assume uniform caliper and tension. Real rolls vary. Confirm with scale weights or the mill roll tag.

Save results:

Roll weight vs outer diameter

Sweeps Roll outer diameter from 300 to 1500, holding your other inputs fixed.

Roll inventory in your ERP

Optional review of how to track remaining roll length and weight against work orders.

Optional. The tool and every export work without this. No spam.

How to use it

Enter outer diameter, core diameter, width, basis weight and caliper. Add an air entrainment allowance if you know it, then the press speed. Roll length comes from the annulus area divided by the effective thickness of one layer. Area is length times width, weight is area times basis weight, and run time is length divided by speed. Use the slider to see how weight grows with diameter.

The formulas

The wound layers form a ring between the core and the outer diameter. Its area is pi x (OD squared minus core squared) / 4. Divide that by the effective layer thickness to get length. Because weight scales with the square of diameter, a roll that is 10 percent larger in diameter holds roughly 20 percent more material. Basis weight in grams per square metre multiplied by area in square metres gives grams.

Length = pi x (OD^2 - core^2) / (4 x thickness)
Area = length x width
Weight = area x basis weight
Run time = length / speed

Common mistakes

Mixing millimetres and metres is the usual problem, followed by using the core inner diameter instead of the outer. Calipers also vary by grade and calender setting. For films the same formula works with thickness in microns; basis weight is then thickness times density. Always allow for splices, leaders and waste when scheduling a roll to a specific job quantity.

Use core outer diameter
Measure caliper on the actual grade
Subtract leader, splice and start-up waste from usable length
Compare to the mill tag and update the air factor

Frequently Asked Questions

Does weight include the core?

No. The result is net paper or film weight. Add the core weight and any wrapping to get gross weight for shipping or receiving checks.

How do I find caliper?

Take it from the mill certificate, a micrometer reading on a sample, or compute it as basis weight divided by apparent density. Use the thickness measured at roll winding conditions.

Why include air entrainment?

Air is dragged between layers as the web winds, so a wound roll is slightly bulkier than the sum of the layer thicknesses. A small percentage keeps the length estimate closer to reality.

Can I use this for plastic film?

Yes. Enter thickness in microns and set basis weight as thickness times density, for example 20 microns of polyethylene at 0.92 g/cm3 is about 18.4 g/m2.

We can connect roll geometry and remaining footage to your ERP inventory and work orders, so planners see accurate run times.

Talk to an Expert Explore More Free Tools

Related Tools

Costing & Finance

More Discrete Manufacturing tools

See all

Back to All Tools