Calculate roll length from outside diameter, core diameter and material thickness, or find the roll diameter from length, for paper, film, foil and tape.

Measure the core outside surface where material starts. Zero models a coreless roll.

1 mil = 0.001 in. Include any liner in the total wound layer thickness.

Optional settings

Roll Length Formula

The following formula is used to calculate the length of a roll of material.

L = pi × (OD² / 4 - ID² / 4) / t
  • Where L is the roll length
  • OD is the outer diameter
  • ID is the diameter of the core outside winding surface, not the hollow core bore; use zero for an ideal coreless roll
  • t is the uniform effective wound thickness, including any liner; use the same length unit for all three dimensions

The wound annular area equals material length times effective thickness. The formula assumes tightly wound material of uniform caliper. Gaps, compression, winding tension and stretch can change the actual dimensions. The calculator also rearranges this relationship to solve for outside diameter, core winding diameter or material thickness.

Roll Length Definition

A roll length is defined as the length of a material that has been rolled into a cylindrical form with a given material thickness.

Example Problem

How to calculate roll length?

First, determine the outer diameter. For this problem, we are looking at a roll of duct tape that has an outer diameter of 5 inches.

Next, measure the core outside winding diameter. In this illustrative example, material starts winding at a diameter of 2 inches.

For this example, assume an effective tape thickness of 0.011 inches, or 11 mil. Use the measured thickness for the actual product; this value is an example, not a universal duct-tape specification.

Finally, use the formula to calculate the roll length:

L = pi * (OD^2/4 – ID^2/4) / t

= 3.14159 *(5^2/4 – 2^2/4)/.011

Using full precision for pi gives approximately 1499.40 inches, or 124.95 feet.