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Roll Diameter From Length Calculator

Work out roll diameter from length instantly with clear inputs, formula shown and shareable results.

About Roll Diameter From Length Calculator

Winding length onto a core builds diameter according to D_outer = sqrt(D_core^2 + 4 x thickness x length / pi). Rearranged, it gives the maximum length that fits within a machine's diameter limit, which is the constraint that sets roll changes on a converting line.

Formulas

Roll diameter

D_outer = sqrt(D_core^2 + 4 x t x L / pi)

Maximum length

L_max = pi x (D_max^2 - D_core^2) / (4 x t)

Worked example

With the default values below, Roll Diameter From Length Calculator returns Finished Roll Diameter of 729.66. Change any input above and every figure here is recalculated in your browser.

Inputs used

Material Lengthminimum 0.01 m
5,000 m
Material Thicknessminimum 0.01 micron
80 micron
Core Diameterminimum 1 mm
152 mm
Maximum Roll Diameterminimum 1 mm
1,000 mm

Results

Finished Roll Diameter
729.66
Number Of Wraps
3,610
Radial Build-Up
288.83
Maximum Length At Diameter Limit
9,590.7

Step by step

  1. 1Values used
  2. 2Roll diameter
  3. 3Maximum length
  4. 4Finished Roll Diameter= 729.66
  5. 5Number Of Wraps= 3,610
  6. 6Radial Build-Up= 288.83
  7. 7Maximum Length At Diameter Limit= 9,590.7

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why is my measured diameter larger than calculated?

Air entrainment and low winding tension leave gaps between layers, so effective thickness exceeds nominal. Films and papers typically build 2-5% more than theory.

Does core size matter much?

Yes for capacity. A larger core wastes diameter capacity, but too small a core buckles under winding stress and makes unwinding at speed unstable.

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