Roll Paper Length Calculator – Remaining Length from Roll and Core Diameters

Use the free tool below: your data never leaves your browser — all work happens on your device, and nothing is uploaded to any server.

What this tool does

A roll of paper looks the same whether it holds five metres or fifty, and unrolling it to find out ruins the point of keeping it rolled. This roll paper length calculator works out how much paper is left from three measurements you can take without unrolling anything: the outer diameter of the roll, the diameter of the cardboard core, and the thickness of one sheet of the paper. From those three numbers it gives the remaining length in metres and millimetres, plus a rough count of how many wraps are still on the roll.

The tool is useful for receipt rolls, plotter paper, wrapping paper, baking paper, and any workshop roll where running out mid-job is embarrassing. It runs in your browser and needs no account, no upload, and no connection to the roll itself: just a ruler or calipers and thirty seconds.

The formula, in plain words

Think of the roll from the side, as a ring. The paper is the ring between the core and the outside. The area of that ring, divided by the thickness of one layer, is the total length of paper wound into it. In symbols, the length is pi times the outer radius squared minus the core radius squared, all divided by the thickness. Every wrap adds one thickness to the radius, so a roll with many thin wraps holds far more paper than a roll of the same size wound from thick card.

That last point is the one people get wrong. Two rolls can share the same outer diameter and hold wildly different lengths if their papers differ in thickness. A 0.05 mm receipt paper holds twice the length of a 0.10 mm paper on the same core. Guessing from the size of the roll alone is guesswork; measuring the thickness turns it into a number you can plan around.

A worked example

Take a roll with an outer diameter of 100 mm, a core of 50 mm, and paper 0.10 mm thick. The ring area is pi times 2,500 minus 625 square millimetres, which is about 5,890 square millimetres. Divide by the 0.10 mm thickness and you get about 58,900 mm of paper, or 58.9 metres. The same roll wound from 0.05 mm paper would hold about 117.8 metres, which is why the thickness measurement matters more than any other input.

The wraps count follows from the same numbers: the roll grew from a 50 mm core to a 100 mm outside, a gain of 25 mm of radius, and each wrap adds 0.10 mm, so there are about 250 wraps left. That number is approximate, because real rolls are never wound perfectly tight, but it is a good sanity check. If the calculator says 250 wraps and you count something wildly different by eye, one of your measurements is probably off.

How to measure well

Measure the outer diameter across the widest point of the roll, not across a squashed side, and measure the core through the centre hole, not the cardboard wall. A roll that has been stored on its side often goes slightly oval, so take two diameters at right angles and use the average. For thickness, do not trust the packet: measure ten sheets stacked together with calipers and divide by ten. A single sheet is too thin to measure reliably with a ruler, and a 0.02 mm error on a big roll swings the answer by metres.

Also remember that the first and last wraps behave badly. The outermost wrap is often loose or creased, and the innermost wraps are glued to the core and cannot be used. If the job needs every metre, subtract a small safety margin from the result, especially on rolls that have been handled roughly. A five percent margin is cheap insurance against running out with one page left to print.

What this calculator cannot do

The formula assumes the paper is wound evenly, with no air gaps and no change of thickness along the roll. Real rolls break that assumption in small ways: a roll wound loosely in the middle reads longer than it is, and a roll with a crushed section reads shorter. The result is an estimate, and a good one, but it is not a substitute for weighing the roll when money depends on the answer. For stock control across many rolls, weigh a full roll and an empty core once, and use weight as your routine check, with this calculator as the cross-check.

One more limit: the calculator tells you length, not area. If you need square metres, multiply the length by the roll width, which you must measure separately. And if the roll is not paper at all, for example film or foil, the same formula still works, provided you measure the true thickness of that material.

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