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
≈ 226.3 ft of paper, about 283 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.
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.