Roll Length Calculator
Enter outer diameter, core diameter, and thickness to get unwound length, turns, and surface area instantly.
Worked examples
Vinyl flooring roll off a showroom rack
A flooring retailer wants to know how much vinyl sheet is left on a display roll without unrolling it across the store.
- OD
- 12 in
- ID
- 3 in
- t
- 60 mil
≈ 147.3 ft remaining, about 75 turns
Jumbo newsprint roll at a paper mill
A mill technician logs how much paper is wound onto a freshly finished jumbo reel before it ships to a printer.
- OD
- 1.5 m
- ID
- 0.3 m
- t
- 0.15 mm
≈ 11,309.7 m of paper, 4,000 turns
Packing tape roll fresh off the shelf
A shipping desk wants to know how many meters of packing tape are on a new roll before it goes into the dispenser, straight from the box dimensions.
- OD
- 100 mm
- ID
- 38 mm
- t
- 0.05 mm
≈ 134.4 m of tape, 620 turns
Toilet paper roll, core to full wrap
A curious shopper wants to compare how much paper a "jumbo" bath tissue roll actually holds versus a standard one, using nothing but a tape measure.
- OD
- 4.5 in
- ID
- 1.6 in
- t
- 0.13 mm
≈ 226.2 ft of paper, about 283 turns
Aluminum foil roll checked before a production run
A converting operator measures a part-used foil roll's outer diameter and core so the line knows whether it'll finish the current job without a mid-run splice.
- OD
- 180 mm
- ID
- 38 mm
- t
- 16 µm
≈ 1,519.5 m of foil remaining, about 4,438 turns
How the formula works
Slice the roll straight across and you see a ring, or annulus: an outer circle (OD) with a smaller core circle (ID) cut out — peel that ring apart and stretch it flat, and it becomes a long, thin rectangle whose sides are the unwound length L and the thickness t. Peeling doesn't change the amount of material, so the ring's cross-sectional area must equal the rectangle's area: π/4 · (OD² − ID²) = L · t. Rearranging for L gives the formula below, and dividing the radial buildup by the thickness gives the turn count N.
This area-conservation argument is exact for the same reason a flattened tin can and a rolled-up one contain the same amount of metal — nothing is approximated in the geometry, only in the physical assumption (very close to true for a tightly wound roll) that every layer packs against the next with no air gap. There's a second, purely mathematical way to arrive at a roll's length: model the wound material as a continuous Archimedean spiral, r(θ) = r₀ + (t/2π)θ, and integrate its arc length one turn at a time. Worked all the way through, that integral collapses back down to this exact same L = π(OD² − ID²)/(4t) formula for any roll with more than a handful of turns — the annular-area method and the spiral-arc-length method aren't two competing approximations, they're the same geometry seen two ways.
The spiral integral only pulls away from the annular-area formula in a regime real winding essentially never reaches: a core so small, or material so thick, that only one or two turns fit before you hit the outer diameter. Push that to an extreme — a 2 mm-thick strap wound barely one full turn around a 2 mm core — and the true spiral length comes out about 1% longer than the area formula gives. Any roll with a realistic turn count (tens of turns and up, which covers essentially everything this calculator is built for) sees that gap shrink toward zero, which is why the area method is what's used here: it's exact for real rolls without needing an arc-length integral to get there.
Estimating remaining length from OD alone
The usual shop-floor question isn't "solve the formula," it's "I have a part-used roll and a tape measure." Outer diameter is the one dimension you can read straight off a roll sitting in a rack; core diameter is fixed per core type and only needs measuring once; thickness comes from the material's spec sheet or, more reliably, from measuring a stack of several layers with calipers and dividing by the count — a single-layer reading on anything under a few mils is mostly measurement noise. Feed those three into the calculator above and length and turn count come out together. Working the other direction — predicting a roll's finished OD before you wind it — is the job of the roll diameter calculator.
OD is also the dimension that costs the most when it's wrong, because it enters the formula squared. On a comfortably full roll — 500 mm OD over a 100 mm core, say — a 1% OD reading error moves the length estimate by only about 2%, because OD² still dominates the OD² − ID² difference. On a nearly-spent roll that same 1% OD error is far more expensive: at 150 mm OD over a 140 mm core (a thin 5 mm wall of material left), a 1% OD error swings the length estimate by roughly 15–16%, because OD² and ID² are now close in size and a small absolute change in OD is a large share of their difference. The practical rule: the emptier the roll, the more that last diameter reading matters — take two or three OD readings at different angles and average them rather than trusting one pass with a rule across a roll that may already be slightly out of round.
When you can put the roll on a scale, weight sidesteps that squared-OD sensitivity entirely: length = (roll weight − core weight) ÷ (basis weight × material width), with every mass in the same unit and basis weight in mass per unit area. A roll that weighs 18.4 kg on an empty-core weight of 1.2 kg, wound from 80 g/m² stock 1.05 m wide, works out to (18.4 − 1.2) ÷ (0.080 × 1.05) = 17.2 ÷ 0.084 ≈ 204.8 m — a figure that doesn't care whether the wind was tight, loose, or slightly out of round, which is exactly where the diameter method above is weakest. If instead you need the material's physical volume rather than its length — estimating resin, adhesive, or ink coverage, say — that same annulus shape extruded across the roll's width is a cylinder with a smaller cylinder removed from its center, which the cylinder volume calculator handles directly. Measuring roll length without unwinding it works through all three practical methods — diameters, weight, and counting wraps — with the accuracy you can expect from each.
Getting the inputs right: core, units, and thickness
Core OD, not core ID. The calculator's "Core diameter (ID)" field wants the diameter the wound material actually sits against — the outside of the cardboard tube or chuck, which is the inner boundary of the roll. That's easy to confuse with the core's own inner bore (the hole a spindle or chuck arbor passes through), a smaller, unrelated number further in. If a supplier's spec sheet lists both a "core OD" and a "core ID," the core OD is almost always what belongs in this field.
Mixing thickness units. Film and foil thickness shows up in mil, micron (µm), and — for US polyethylene film specifically — "gauge," a unit where 1 mil = 100 gauge = 25.4 µm exactly; treat it as a straight unit conversion, not an approximation, and don't confuse it with sheet-metal gauge, a completely different, non-linear numbering system for a different material class. Paper and board are more often specified by basis weight (grams per square meter, "gsm") than by caliper directly; convert with thickness [µm] = basis weight [g/m²] ÷ bulk density [g/cm³] — a stock rated at 80 g/m² with an illustrative bulk density of 0.8 g/cm³, for instance, works out to 80 ÷ 0.8 = 100 µm.
Caliper on a spec sheet isn't caliper on the roll. A material's published thickness is normally measured flat, under a light, evenly distributed load — that's what standards like TAPPI T411 (paper and paperboard, North America) and ISO 534 (the international equivalent, at a lighter load than T411) define; plastic film and sheeting has its own family of thickness standards, chiefly ASTM D374 and ISO 4593. A roll wound under tension compresses that same material somewhat, while a loosely wound roll traps air between layers and reads thicker than the flat caliper would predict. None of that changes which formula to use — it changes what number belongs in the thickness field — and the fix, per the guide above, is to back-calculate an effective thickness from one roll run to completion rather than trusting the spec sheet indefinitely.
Thickness drifts across a roll. Real material isn't perfectly uniform — caliper can vary a few percent across a jumbo roll's width or from batch to batch. Small, random variation mostly averages out over hundreds or thousands of turns and barely moves the length estimate; a systematic bias (a spec-sheet number that's simply wrong for the batch on hand) does not average out, and passes straight through into the length result. That's the failure mode weight cross-checking, above, is built to catch.
Sources: Caliper/thickness measurement conventions referenced above — TAPPI T411 (paper and paperboard caliper, North America), ISO 534 (paper and board thickness, international, lighter measuring load than T411), and ASTM D374 / ISO 4593 (plastic film and sheeting thickness) — describe how a material's published thickness is measured, not a specific numeric value used in this calculator's math. Unit relationships stated above (1 mil = 25.4 µm = 100 gauge for US polyethylene film) are exact unit-conversion definitions, not measured data.
Frequently asked questions
Why does the calculator need a core diameter instead of assuming a solid roll?
Almost every wound roll is hollow at the center — a cardboard core, a chuck, or an empty spindle hole. Treating the roll as a full disk would count that empty core as material and overstate the length. Subtracting the core's area (ID) from the outer area (OD) before dividing by the thickness is what makes the formula accurate for real cores.
Will the result be exact if the roll isn't wound perfectly tight?
The formula assumes the material is packed uniformly with no air gaps between wraps, which is a very close approximation for most tightly wound rolls. Loosely wound or telescoping rolls compress slightly once measured, so treat the output as a close estimate rather than a lab-grade measurement in those cases.
Can I use this for cloth, foil, or plastic film, not just paper?
Yes. The math only depends on geometry — outer diameter, core diameter, and thickness — so it works for any flexible material wound into a spiral roll: textiles, foil, film, tape, wire insulation, and more. Just make sure the thickness you enter is the material's true caliper, not a padded or laminated estimate.
Why isn't the number of turns a whole number?
The turn count comes from dividing the total radial buildup by the material thickness, which treats winding as a smooth, continuous spiral rather than counting discrete wraps. In practice the last partial wrap accounts for the fractional part, so a result like 74.6 turns simply means the roll ends partway through its final revolution.
What if I don't know my material's exact thickness?
Check the manufacturer's spec sheet first — thickness (or "caliper" / "gauge") is usually listed alongside width and weight. If it isn't available, measure a stack of a known number of sheets with calipers and divide, or wind a short known length onto a spare core and back-solve thickness from the diameter change — precision here matters most for thin films, where a small error compounds over hundreds of turns.
How do I find how much tape is left on a roll?
Measure the outer diameter of the roll as it sits, the diameter of the empty cardboard core, and the tape's thickness (most packing and masking tape runs 0.045–0.07 mm, often listed on the packaging as "mil" gauge). Plug those into the calculator as OD, ID, and t, and the unwound length is how much tape is left. This works the same way for masking tape, duct tape, and ribbon — any thin material spiral-wound onto a core.
Can I use this for a wallpaper roll or a roll of toilet paper?
Yes — the geometry doesn't care what the material is, only its outer diameter, core diameter, and thickness. For a toilet paper roll, treat the cardboard tube as the core (ID) and the outer edge of the wound paper as the OD; for wallpaper, do the same with its center tube. Consumer paper products are thin enough that small thickness errors matter, so if you can, measure a stack of a known number of sheets and divide rather than guessing a single-sheet caliper.
Why does a 1% error in outer diameter matter so much more on an almost-empty roll?
Because outer diameter enters the length formula squared, and on a full roll that squared term dwarfs the core's squared term, so a small OD error is a small share of the difference that actually drives the result. As the roll empties, OD and ID converge toward each other, so the same absolute reading error becomes a much larger share of the shrinking OD² − ID² gap. A 1% OD error on a comfortably full roll (500 mm OD over a 100 mm core) moves the length estimate by roughly 2%; the identical 1% error on a nearly-spent roll (150 mm OD over a 140 mm core) can move it by 15% or more. Measure OD more carefully as the roll gets smaller, not less.
How do mil, micron, gauge, and gsm relate to each other?
Mil and micron (µm) are both units of linear thickness — 1 mil = 25.4 µm exactly, the same inch-to-metric conversion this calculator uses. "Gauge," when applied to plastic film in the US, is a different-looking but directly proportional unit: 1 mil = 100 gauge, so 2 mil film is 200 gauge — don't confuse it with sheet-metal gauge, an unrelated non-linear scale. Grams per square meter (gsm, or basis weight) isn't a thickness at all — it's mass per area — so converting it needs the material's bulk density too: thickness [µm] = basis weight [g/m²] ÷ density [g/cm³]. Once you have a thickness figure in any of these units, this calculator's unit selector converts it for you.