Enter the density, roll width, core radius, and outer radius into the calculator to determine the weight of a paper roll. This calculator helps in estimating the weight for logistics and material handling purposes.
Paper Roll Weight Formula
The following formula is used to calculate the weight of a paper roll:
W = ρ * π * (R² - r²) * w / 1000
Variables:
- W is the weight of the paper roll (kg)
- ρ is the (bulk) density of the paper/roll material (g/cm³)
- R is the outer radius of the roll (cm)
- r is the radius of the core (cm)
- w is the width of the roll (cm)
- The term π(R² − r²)w is the volume of paper in the roll (cm³).
To calculate the weight of a paper roll, multiply the density by the volume of paper material on the roll and divide by 1000 to convert grams to kilograms.
What is Paper Roll Weight?
Paper roll weight is the weight of the paper material wound around a core. It is an important metric for manufacturers, printers, and shippers to determine the amount of material and the weight for transportation. The weight depends on the density of the paper (or bulk density of the wound roll), the roll dimensions, and the size of the core.
How to Calculate Paper Roll Weight?
The following steps outline how to calculate the Paper Roll Weight.
- First, determine the density (ρ) in grams per cubic centimeter (g/cm³).
- Next, determine the width of the roll (w) in centimeters (cm).
- Next, determine the outer radius of the roll (R) in centimeters (cm).
- Next, determine the core radius (r) in centimeters (cm).
- Next, gather the formula from above = W = ρ * π * (R² – r²) * w / 1000.
- Finally, calculate the Paper Roll Weight (W) in kilograms.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge.
Density of the paper (ρ) = 0.8 g/cm³
Width of the roll (w) = 100 cm
Core radius (r) = 5 cm
Outer radius (R) = 50 cm
Weight of the roll (W) = 0.8 × π × (50² − 5²) × 100 / 1000 ≈ 622.0 kg