Outside Diameter of a Roll Calculator

Formula

To calculate the Outside Diameter (OD):

\[ OD = \sqrt{\left(\frac{L \cdot t}{\pi} + \frac{ID^2}{4}\right)} \times 2 \]

Where:

\(OD\) is the Outside Diameter of the roll in inches
\(L\) is the Length of the roll in inches
\(t\) is the Thickness of the roll in inches
\(ID\) is the Inside Diameter (core diameter) in inches

What is Roll Diameter?

Roll diameter is a measure of the diameter of the circle created when a material of a certain thickness is rolled into a cylindrical shape. The thicker and longer the material, the greater the roll diameter will be.

Example Calculation 1

Let's assume the following values:

Length of the Roll (\(L\)) = 100 inches
Thickness of the Roll (\(t\)) = 0.1 inches
Inside Diameter (\(ID\)) = 2 inches

Using the formula:

\[ OD = \sqrt{\left(\frac{100 \cdot 0.1}{\pi} + \frac{2^2}{4}\right)} \times 2 = \sqrt{\left(\frac{10}{3.1416} + 1\right)} \times 2 \approx \sqrt{4.183} \times 2 \approx 4.09 \text{ inches} \]

The Outside Diameter is approximately 4.09 inches.

Example Calculation 2

Let's assume the following values:

Length of the Roll (\(L\)) = 200 inches
Thickness of the Roll (\(t\)) = 0.2 inches
Inside Diameter (\(ID\)) = 3 inches

Using the formula:

\[ OD = \sqrt{\left(\frac{200 \cdot 0.2}{\pi} + \frac{3^2}{4}\right)} \times 2 = \sqrt{\left(\frac{40}{3.1416} + 2.25\right)} \times 2 \approx \sqrt{14.99} \times 2 \approx 7.75 \text{ inches} \]

The Outside Diameter is approximately 7.75 inches.