Calculate total length or required diameter for paper, film, and foil rolls.
Find Total Length
(100 microns = 0.1 mm)
Find Outer Diameter
How to Use the Paper Roll Calculator
Managing inventory in the printing, packaging, and paper manufacturing industries requires precise measurements. This calculator helps you determine the total length of material on a roll or estimate how large a roll will be once a specific length of paper is wound onto a core.
The Physics Behind the Math
The calculation is based on the cross-sectional area of the paper roll. By calculating the area of the ring formed by the paper (the total area minus the core area) and dividing it by the thickness (caliper) of the paper, we get the linear length.
The Formula: Length (L) = π × (D² - d²) / (4 × t)
Where:
– D = Outer Diameter
– d = Inner Core Diameter
– t = Thickness of the material
Practical Examples
Example 1: Finding Length
Suppose you have a roll of bond paper with an outer diameter of 400mm, a core of 76mm, and a thickness of 0.1mm (100 microns).
Using the calculator, the total length would be approximately 1,213 meters.
Example 2: Finding Diameter
You need to wind 2,000 meters of film (0.05mm thick) onto a 76mm core. What will the final roll size be?
The calculator determines the outer diameter will be approximately 444.1mm.
Tips for Accuracy
Consistent Units: Ensure you use the same units (usually millimeters) for all diameter and thickness inputs. The length result is automatically converted to meters for convenience.
Measure Thickness Carefully: A small error in thickness (e.g., 0.01mm) can result in a massive difference in the total length for large rolls. Use a micrometer for best results.
Winding Tension: Note that "soft" winding can increase the outer diameter without increasing the length. This calculator assumes a solid, standard wind density.
function calculateLength() {
var outerD = parseFloat(document.getElementById('outerD').value);
var coreD = parseFloat(document.getElementById('coreD').value);
var thickness = parseFloat(document.getElementById('thickness').value);
var resultDiv = document.getElementById('lengthResult');
if (isNaN(outerD) || isNaN(coreD) || isNaN(thickness) || outerD <= coreD || thickness <= 0) {
resultDiv.style.display = 'block';
resultDiv.style.background = '#fdeaea';
resultDiv.innerHTML = 'Error: Please enter valid dimensions. Outer diameter must be larger than core diameter.';
return;
}
// Formula: L = pi * (D^2 – d^2) / (4 * t)
var lengthMM = (Math.PI * (Math.pow(outerD, 2) – Math.pow(coreD, 2))) / (4 * thickness);
var lengthMeters = lengthMM / 1000;
resultDiv.style.display = 'block';
resultDiv.style.background = '#e8f4fd';
resultDiv.innerHTML = '