What is Roll Length?
Roll length is the total linear length of material wound on a cylindrical core. Whether you are working with paper, film, foil, tape, or fabric, knowing the roll length helps with inventory management, cost estimation, and ensuring you have enough material to complete a job.
How to Calculate Roll Length
Here is the formula:
[\text{L} = \pi \times \frac{\text{OD}^{2} / 4 - \text{ID}^{2} / 4}{T}]
Where:
- L is the roll length.
- OD is the outer diameter of the roll.
- ID is the inner diameter of the core.
- T is the material thickness.
All measurements must use the same unit. The result will be in that same unit.
Calculation Example
A roll of aluminum foil has an outer diameter of 7 inches, an inner core diameter of 1.5 inches, and a material thickness of 0.002 inches.
Calculate the area terms:
[\frac{\text{OD}^{2}}{4} - \frac{\text{ID}^{2}}{4} = \frac{49}{4} - \frac{2.25}{4} = 12.25 - 0.5625 = 11.6875]
Multiply by π:
[\pi \times 11.6875 = 36.70]
Divide by the thickness:
[\text{L} = \frac{36.70}{0.002} = 18{,}351.9 \text{ inches}]
The roll length is approximately 18,352 inches.