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Rolled Material Length, Core and Thickness

Estimate tightly packed roll length from outer diameter, core diameter and uniform material thickness, or solve a missing measurement with compatible units.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A roll 10 cm across around a 4 cm core, with material 10 thousandths of an inch thick (0.254 mm), has an ideal modeled length of about 25.97 meters.

L = π(D²−d²)/(4t); thickness t is a single material layer

Worked example

Enter these known values and leave the other values blank.

Roll outer diameter D
10 cm
Core diameter d
4 cm
Single-layer thickness t
10 mil
Estimated material length L
2597.4 cm

Assumptions and limitations

  • The model divides ideal annular area by uniform layer thickness. It assumes tight packing, constant thickness and circular inner/outer boundaries. Compression, air gaps, stretching and winding details can change actual usable length.
  • A nonnegative core is allowed; outer diameter, length and thickness are positive. The roll must accommodate at least one layer: core diameter plus twice thickness cannot exceed outer diameter.
  • The initial thickness unit is thou: one thousandth of an international inch, exactly 0.0254 mm. Diameter and length defaults differ under imperial preferences, so check each selected unit.
  • A missing core uses the nonnegative square root. Known length times thickness cannot exceed the full outer disk area. Clear unknown measurements before solving backward; incompatible measurements must be corrected.
  • Use the actual wound layer thickness, including a backing where present. Width is not an input because the same uniform width cancels in the ideal volume relationship.
  • Near a zero-core or one-layer boundary, independently rounded measurements can be incompatible even when the unrounded relationship is valid. Keep adequate measurement precision and check the physical bounds; display rounding is not a tolerance or accuracy estimate.

Common questions

What is a thou in the thickness control?

One thou is 0.001 international inch, exactly 0.0254 mm. Ten thou is 0.254 mm. It is not one millimeter.

Does this predict an exact usable length for every roll?

It is an ideal annular-area estimate. Packing gaps, compression, thickness variation and material stretching can change the length available from a real roll.

Can the core diameter be zero?

Yes, the source model permits a zero core. The roll must still have positive thickness and enough outer diameter to contain at least one layer.

References

Require length times layer thickness to fit within the outer disk area for a real nonnegative core inverse.

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