Accurate calculator for logistics, printing, and inventory management
The width of the paper roll.Please enter a valid width.
Total diameter including the core.Must be larger than core diameter.
Standard cores are 76mm (3″) or 152mm (6″).Please enter a valid core size.
Grams per Square Meter (g/m²).Please enter a valid GSM.
Caliper in microns (µm).Please enter a valid thickness.
Estimated Roll Weight
0 kg
Total Length
0 m
Total Surface Area
0 m²
Paper Volume
0 m³
Formula Used: Weight = Length × Width × (GSM / 1000).
Length is derived from the volume of the annulus (Outer Area – Core Area) divided by paper thickness.
Figure 1: Weight progression as roll diameter increases
Diameter (mm)
Estimated Weight (kg)
Length (m)
Table 1: Weight milestones at different diameters based on current inputs.
What is "How to Calculate Weight of Paper Roll"?
Understanding how to calculate weight of paper roll is a fundamental skill in the printing, packaging, and logistics industries. It refers to the mathematical process of determining the total mass of a wound roll of paper based on its physical dimensions—specifically width, outer diameter, core diameter—and its material properties like Basis Weight (GSM) and Caliper (thickness).
This calculation is critical for warehouse managers planning floor load capacities, logistics coordinators estimating shipping costs, and printers determining how many linear meters of material are available for a production run. A common misconception is that you can simply weigh a roll on a scale; while true for single items, planning and purchasing often happen theoretically before the physical stock arrives. Therefore, knowing how to calculate weight of paper roll mathematically is essential for accurate forecasting.
Paper Roll Weight Formula and Mathematical Explanation
To accurately calculate the weight, we must first determine the volume of paper on the roll and then apply the density factor. The most reliable method involves deriving the length of the paper from the roll's geometry.
Step 1: Calculate the Cross-Sectional Area
The paper forms an annulus (a ring shape) around the core. The area of this ring is:
Area = π × (R² – r²)
Where R is the outer radius and r is the core radius.
Step 2: Calculate Linear Length
Once we have the cross-sectional area, we divide it by the paper's thickness (caliper) to find the total length:
Length (m) = (Area in m²) / (Thickness in m)
Step 3: Calculate Weight
Finally, we use the GSM (Grams per Square Meter) to find the weight:
Table 2: Key variables used in paper weight calculations.
Practical Examples (Real-World Use Cases)
Example 1: Standard Newsprint Roll
A printing press needs to know the weight of a standard newsprint roll to ensure the forklift capacity is sufficient.
Width: 840 mm
Outer Diameter: 1000 mm
Core Diameter: 76 mm
GSM: 45 gsm
Thickness: 70 microns
Using the calculator, the total length is approximately 11,140 meters. The calculated weight would be roughly 421 kg. This confirms a standard 1-ton forklift can easily handle the roll.
Example 2: Heavy Cardboard Stock
A packaging company is ordering Kraft linerboard.
Width: 1200 mm
Outer Diameter: 1250 mm
Core Diameter: 100 mm
GSM: 200 gsm
Thickness: 280 microns
Due to the thickness, the length is shorter (approx 4,200 meters), but the weight is significant. The calculation yields approximately 1,008 kg. This exceeds the limit for some light-duty pallet jacks, requiring heavy-duty equipment.
How to Use This Paper Roll Weight Calculator
Enter Dimensions: Input the roll width, outer diameter, and core diameter in millimeters. These are standard metric units in the industry.
Input Material Properties: Enter the GSM (weight) and Thickness (microns). If you don't know the exact thickness, check the paper specification sheet, as this drastically affects the length calculation.
Review Results: The tool instantly updates the estimated weight, total length, and surface area.
Analyze the Chart: Use the dynamic chart to see how weight increases as the roll diameter grows. This helps in determining when a roll will reach a specific weight limit.
Copy Data: Use the "Copy Results" button to paste the data into your inventory spreadsheets or shipping manifests.
Key Factors That Affect Paper Roll Weight Results
When learning how to calculate weight of paper roll, consider these six factors that influence the final number:
Paper Density (Bulk): Two papers can have the same GSM but different thicknesses. A "bulky" paper is thicker, resulting in less length on a roll of the same diameter, and thus a lighter total roll weight.
Winding Tension: If a roll is wound tightly, it contains more paper (length) than a loosely wound roll of the same diameter. This calculator assumes a solid, consistent wind.
Core Weight: The formula calculates the net weight of the paper. The fiber or plastic core itself adds 2-5 kg depending on wall thickness, which must be added for Gross Weight.
Moisture Content: Paper is hygroscopic. High humidity can increase the weight of a roll by 5-8% as it absorbs moisture from the air, affecting shipping costs.
Manufacturing Tolerances: Paper mills have tolerances for GSM (±5%). A 1000kg roll could actually weigh 950kg or 1050kg, affecting truck loading plans.
Wrapper & Packaging: The calculated weight is "Net Weight". For shipping (Gross Weight), you must add the weight of the header, wrapper, and pallet.
Frequently Asked Questions (FAQ)
1. Why do I need the thickness (caliper) to calculate weight?
Thickness determines how many layers of paper fit into the roll's diameter. Without knowing thickness, you cannot calculate the total length of paper, and without length, you cannot calculate the total weight accurately from GSM.
2. Can I calculate weight with just GSM and Diameter?
Not accurately. You would have to guess the paper density. Standard bond paper has a density of roughly 800 kg/m³, but this varies wildly between tissue, cardboard, and coated papers.
3. How do I convert inches to millimeters for this calculator?
Multiply inches by 25.4. For example, a 40-inch roll is 1016 mm. A 3-inch core is 76.2 mm.
4. Does this calculator include the weight of the core?
No, this tool calculates the Net Weight of the paper material only. You should add the core weight (typically 1-3 kg) manually for Gross Weight.
5. What is the difference between GSM and Basis Weight?
GSM (Grams per Square Meter) is the metric standard. Basis Weight is the Imperial standard (lbs per ream). They measure the same property but in different units.
6. How accurate is this calculation?
It is theoretically exact, but real-world results vary due to winding tension and moisture. Expect a variance of ±5%.
7. Why does the weight increase exponentially with diameter?
As the roll grows, each new layer of paper has a larger circumference than the previous one. Therefore, the outer inches of a roll contain significantly more paper volume than the inner inches.
8. Is this useful for freight classification?
Yes. Freight carriers often charge by weight or dimensional weight. Knowing the exact weight helps in selecting the correct freight class and avoiding overweight fees.