Estimating Paper Left on a Roll from Its Diameter

A partly used paper roll does not contain half its original length merely because half of its radial paper thickness remains. The outer turns are longer than the inner turns. When a suitable full-roll reference is available, the area of the wound paper in a cross-section provides a more useful estimate for replenishment planning.

Measure the outside of the core, not its bore

Record three diameters: the current outside roll diameter D, the full reference roll diameter F, and the outside diameter of the core C. The core's central hole is a different measurement. Using the bore would incorrectly count some core material as paper.

The model assumes the same core size, paper thickness and winding density as the reference. It also assumes a round roll with paper wound uniformly across the same width. Loose winding, a crushed core or a different material can invalidate the comparison. This is an inventory estimate, not a way to establish dispenser compatibility.

Use the paper area in the cross-section

The circular ring occupied by paper has an area proportional to outside diameter squared minus core diameter squared. Under the stated assumptions, the remaining fraction is (D² − C²) ÷ (F² − C²). Multiply that fraction by the known reference length. Use the same units for every diameter.

The radial paper thickness has fallen from 4 inches to 2 inches, but the modeled remaining length is one third, not one half. A linear thickness estimate would report 450 feet and overstate this example by 150 feet.

Keep the product specification separate from the model inputs

KP2440V virgin kraft paper is listed as a 24-inch by 900-foot roll with 40# basis weight, supplied as one roll. The 10-, 6- and 2-inch diameters above are hypothetical; they are not specifications for KP2440V. Its basis weight does not provide its caliper, core diameter or outside roll diameter.

For a real estimate, use an appropriate reference for the actual stock and document how its length was established. Retain the measured diameters and the assumptions with the estimate. A nominal listing alone does not verify the winding conditions of a partly used roll.

Use the estimate to trigger a stock decision

Compare the estimate with the upcoming requirement while keeping setup waste, damaged material and inaccessible tail length separate. If a run requires nearly all of the estimated length, obtain a more reliable usable-length check or plan additional supply before committing the job. An area model cannot guarantee that every estimated foot is available as an acceptable continuous cut.