The Roll Diameter Calculator helps determine the overall diameter of a roll based on the core diameter, material thickness, and length of the material wound around it.

Key Components of the Roll Diameter Calculation

To calculate the roll diameter, you need:

1. Core Diameter: The diameter of the hollow core at the center of the roll.
2. Material Thickness: The thickness of the material being wound.
3. Material Length: The total length of the material wound around the core.

Formulas to Calculate Roll Diameter

1. Calculate the Radius of the Core

The radius of the core is half of its diameter:

$\text{Core Radius} = \frac{\text{Core Diameter}}{2}$

Where:

• Core Diameter: The total diameter of the roll's core.

2. Calculate the Total Area of the Material

The area of the material is determined by multiplying the material thickness and length:

$\text{Material Area} = \frac{\text{Material Length}}{\text{Thickness}}$

Where:

• Material Length: Total length of the material wound on the roll.
• Thickness: Thickness of the material.

3. Calculate the Roll Radius

The roll radius is calculated by adding the core radius and the area of the material wound in circular layers:

$\text{Roll Radius} = \sqrt{\frac{4 \times \text{Material Area}}{\pi} + \text{Core Radius}^2}$

Where:

• Material Area: Total area of the material calculated in the previous step.
• Core Radius: Radius of the roll’s core.

4. Calculate the Roll Diameter

The roll diameter is simply twice the roll radius:

$\text{Roll Diameter} = 2 \times \text{Roll Radius}$

Example Calculation

Inputs:

• Core Diameter (CD): 3 inches
• Material Thickness (T): 0.01 inches
• Material Length (L): 500 feet

Step 1: Calculate the Core Radius

Using the formula:

$\text{Core Radius} = \frac{\text{Core Diameter}}{2}$

Substitute the values:

$\text{Core Radius} = \frac{3}{2} = 1.5 \, \text{inches}$

Step 2: Calculate the Material Area

Using the formula:

$\text{Material Area} = \frac{\text{Material Length}}{\text{Thickness}}$

Substitute the values (convert length to inches since thickness is in inches):

$\text{Material Area} = \frac{500 \times 12}{0.01} = 600000 \, \text{square inches}$

Step 3: Calculate the Roll Radius

Using the formula:

$\text{Roll Radius} = \sqrt{\frac{4 \times \text{Material Area}}{\pi} + \text{Core Radius}^2}$

Substitute the values:

$\text{Roll Radius} = \sqrt{\frac{4 \times 600000}{\pi} + 1.5^2}$

$\text{Roll Radius} = \sqrt{\frac{2400000}{3.1416} + 2.25}$

$\text{Roll Radius} = \sqrt{764543.23} = 874.33 \, \text{inches}$

Step 4: Calculate the Roll Diameter

Using the formula:

$\text{Roll Diameter} = 2 \times \text{Roll Radius}$

Substitute the values:

$\text{Roll Diameter} = 2 \times 874.33 = 1748.66 \, \text{inches}$

Conclusion

The Roll Diameter Calculator is a valuable tool for calculating the diameter of material rolls used in various industries. By using inputs like core diameter, material thickness, and length, the calculator simplifies complex geometry into an easy-to-understand process, ensuring precise measurements and efficient operations.