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.

Formula to Calculate Roll Diameter

The accurate formula for calculating roll diameter is:

$\text{Roll Diameter} = \sqrt{\text{Core Diameter}^2 + \frac{4 \times \text{Thickness} \times \text{Length}}{\pi}}$

Where all measurements should be in the same units (inches or millimeters).

How the Formula Works

1. Core Area Calculation: The formula begins with $CD^2$, which represents the area of the core.
2. Material Volume Calculation: $4 \times T \times L$ calculates the cross-sectional area of the material when unrolled.
3. Adjustment for Rolled Form: Dividing by $π$ converts this area into an equivalent circular form.
4. Combining Components: The square root combines the core area with the material's effective area to give the total diameter.

Example Calculation

Let's walk through an example:

Given:

• Core Diameter ($CD$) = 3 inches
• Material Thickness ($T$) = 0.005 inches
• Roll Length ($L$ ) = 1000 feet = 12,000 inches

Calculation:

$RD = \sqrt{3^2 + \frac{4 \times 0.005 \times 12000}{3.1416}} \\ RD = \sqrt{9 + \frac{240}{3.1416}} \\ RD = \sqrt{9 + 76.394} \\ RD = \sqrt{85.394} \\ RD \approx 9.24 \text{ inches}$

Practical Applications

This calculation is vital for:

• Estimating remaining material on a partial roll
• Planning storage space requirements
• Determining machine compatibility
• Calculating shipping costs based on roll size

Try our Roll Diameter Calculator today to simplify your material planning and logistics!

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.