Calculate paper roll weight, density, outer radius, core radius, or width from the other four values in cm, in, kg, lb, or g/cm³ as needed.
Paper Roll Weight Formula
The calculator estimates roll weight from the roll geometry, paper thickness, roll width, and basis weight. It first calculates the length of paper wound on the roll, then multiplies that length by width to get area, then multiplies area by basis weight.
L = pi*(OD^2 - CD^2)/(4*T)
A = L*W
Weight_kg = A*GSM/1000
- L = roll length in meters
- OD = outer diameter of the roll in meters
- CD = core diameter in meters
- T = paper caliper or thickness in meters
- A = paper area in square meters
- W = roll width in meters
- GSM = basis weight in grams per square meter
- Weight_kg = estimated paper roll weight in kilograms
The calculator converts all length inputs to meters before applying the formulas. It converts caliper values from microns, millimeters, mils, or inches to meters. It also converts common paper basis weights, such as text, cover, and index, to gsm before calculating weight.
The result section shows the estimated roll weight, roll length, paper area, and the gsm value used in the calculation.
Basis Weight Conversion Reference
These are the approximate basis weight conversions used for non-gsm inputs.
| Input Type | Conversion to GSM | Example |
|---|---|---|
| gsm | same value | 80 gsm = 80 gsm |
| lb text | lb text × 1.4802 | 50 lb text ≈ 74.01 gsm |
| lb cover | lb cover × 2.708 | 80 lb cover ≈ 216.64 gsm |
| lb index | lb index × 1.807 | 90 lb index ≈ 162.63 gsm |
Common Paper Thickness Values
| Paper Type | Typical Caliper | Notes |
|---|---|---|
| Light office or copy paper | 90 to 110 microns | Common around 75 to 90 gsm |
| Book or text paper | 70 to 130 microns | Depends on finish and bulk |
| Cover stock | 180 to 350 microns | Heavier and stiffer than text paper |
| Label or specialty paper | Varies widely | Use the supplier caliper when available |
Example Calculations
Example 1: Metric roll
You have a roll that is 1000 mm wide, with a 1000 mm outer diameter, a 76 mm core, 100 micron caliper, and 80 gsm paper.
- Roll length ≈ 7,808.6 m
- Paper area ≈ 7,808.6 m²
- Paper roll weight ≈ 624.7 kg
Example 2: Inch inputs with text weight
You have a roll that is 30 in wide, with a 40 in outer diameter, a 3 in core, 4 mil caliper, and 50 lb text basis weight.
- 50 lb text ≈ 74.01 gsm
- Roll length ≈ 7,934.4 m
- Paper area ≈ 6,046.0 m²
- Paper roll weight ≈ 447.5 kg, or about 986.6 lb
FAQ
Does the paper roll weight include the core?
No. The formula estimates the weight of the paper only. It subtracts the core diameter from the roll geometry, but it does not add the physical weight of the cardboard, plastic, or metal core.
Why does caliper matter so much?
Caliper controls how much paper length fits into the roll diameter. A thinner sheet produces more length in the same roll size. More length means more area, which increases the estimated roll weight when the basis weight stays the same.
Why is this an estimate?
Real roll weight can vary because of winding tightness, moisture content, coating, density changes, and measurement tolerance. For best results, use the actual measured outer diameter, actual core diameter, supplier caliper, and supplier basis weight.
