Paper Roll Length & Remaining Calculator
Enter the roll diameter, core diameter, paper caliper, and print run details to estimate how much paper is left and whether the roll can finish the job.
Estimated paper remaining661.25
- Usable length after setup waste
- 641.25
- Maximum complete impressions
- 1,282
- Required job length
- 500
- Enough paper for the run?
- Yes
- Length surplus
- 141.25
- Estimated net paper weight
- 40.34
- Estimated diameter after the job
- 154.25
Uses the annular reel-length formula with a single wound caliper and no allowance for air gaps or compression changes.
How to use this calculator
- Measure the current outside diameter across the roll and enter the core outside diameter.
- Enter the wound paper caliper, roll width, and grammage from the paper specification when available.
- Enter the web advance per impression, the required impressions, and setup waste.
- Read the usable length, complete impressions, surplus or shortfall, estimated weight, and after-run diameter.
How the roll length is calculated
This calculator treats the paper on the roll as an annulus: the area between the outside of the roll and the outside of the core. Dividing that area by the thickness of one wound layer gives the paper length. It is the same reel geometry used in paper reel measurement references, with the caliper converted from micrometres to millimetres.
The length formula is:
L = pi x (D^2 - d^2) / (4 x t_mm x 1000)
- L is the estimated paper length in metres.
- D is the current outside diameter in millimetres.
- d is the core outside diameter in millimetres.
- t_mm is the wound paper caliper in millimetres.
After the total length is estimated, setup and changeover waste are subtracted to produce the usable length. The maximum complete impressions are the floor of usable length divided by the web advance per impression, so a partial repeat is not counted. Required job length is impressions multiplied by repeat length. The surplus or shortfall is usable length minus required job length.
What moves the answer most
Diameter changes are squared, so a small measuring error on the outside diameter can move the result more than expected. The core diameter also matters more near the end of the roll because a larger share of the cross-section is core rather than paper. Caliper is equally important: using an unloaded sheet caliper when the wound roll has compressed, or using nominal caliper for a bulky grade, can overstate or understate length.
The weight estimate uses the full estimated length, roll width, and grammage:
weight kg = L x width_m x gsm / 1000
When the roll can complete the job, the remaining post-run length is converted back to a diameter with:
D_after = sqrt(d^2 + 4 x 1000 x remaining_length x t_mm / pi)
What this leaves out
The calculation assumes a uniformly wound roll with no air gaps, wrinkles, telescoping, crushed edges, moisture change, or caliper variation through the roll. It also excludes core weight, wrapping, plugs, and damaged material beyond the setup waste you enter. For production planning, leave a margin instead of planning to run to the final calculated metre.
Worked example
Suppose a roll measures 300 mm outside diameter on a 76.2 mm outside core. The wound paper caliper is 100 micrometres, the roll is 610 mm wide, and the paper is 100 g/m2. The calculator estimates 661.25 m of paper on the roll.
If setup waste is 20 m and each impression uses 500 mm of web, the usable length is 641.25 m and the roll can make 1,282 complete impressions. A job needing 1,000 impressions requires 500.00 m, leaving a surplus of 141.25 m. The estimated net paper weight is 40.34 kg, and the expected diameter after the job is 154.25 mm.
Common questions
How do I calculate paper length from roll diameter?
Use the outside roll diameter, subtract the core area, and divide the remaining annular area by the wound caliper. In metres, the formula is pi times outside diameter squared minus core diameter squared, divided by four times caliper in millimetres times 1000.
Should I use the core's inside or outside diameter?
Use the core outside diameter because the paper is wrapped around the outside of the core. The inside opening is smaller and would make the calculator count space that cannot hold paper.
Where can I find paper caliper or thickness?
Start with the paper specification sheet or ask the mill, merchant, or converter for the grade caliper. A micrometer reading on a sample can help, but wound caliper may differ from an unloaded sheet because paper compresses on the roll.
Why is half the roll diameter not half the paper length?
Roll length follows cross-sectional area, not diameter. The outer wraps contain more paper per layer than the wraps near the core, so length falls faster than diameter near the outside and slower near the core.
Can I estimate the weight of paper left on the roll?
Yes. Multiply estimated length by roll width in metres and grammage in grams per square metre, then divide by 1000 to get kilograms. This is net paper weight only, so it excludes the core and packaging.