Roll Length Calculator
Enter the outer diameter, inner diameter, and material thickness of any roll to find the total length of material wound on it. Works for tape, paper, film, foil, fabric, wire, hose, and any other uniformly wound material. Switch to reverse mode to calculate what outer diameter a roll must reach to hold a target length. Toggle between metric and imperial units at any time.
Formula
Worked example
A roll of adhesive tape has an outer diameter of 200 mm, a core (inner) diameter of 76 mm, and the tape is 0.10 mm thick. Number of turns: N = (200 - 76) / (2 x 0.10) = 124 / 0.20 = 620 turns. Roll length: L = pi x 620 x (200 + 76) / 2 = pi x 620 x 138 = 268,606 mm ≈ 268.6 m.
How the roll length formula works
A wound roll is a close approximation of an Archimedean spiral, where each successive layer sits one material-thickness further out from the centre than the previous one. The number of turns is simply the total radial build-up divided by twice the material thickness: N = (D - d) / (2t), where D is the outer diameter, d is the inner (core) diameter, and t is the material thickness. Each turn has a circumference of roughly pi times its own diameter, so the total length is the average circumference multiplied by the number of turns: L = pi x N x (D + d) / 2. Combining the two expressions gives the compact single-formula form: L = pi x (D^2 - d^2) / (4t). The error compared with an exact spiral-integral calculation is typically below 0.1% when the thickness is small relative to the inner diameter, which is true for almost all practical materials.
Forward mode: find how much material is on a roll
Measure the outer diameter of the full roll, the inner diameter of the hollow core or spool, and the nominal or measured thickness of the material. Enter those three values and the calculator returns the total length immediately. Metric inputs are in millimetres; the result is returned in metres. Imperial inputs are in inches; the result is in feet. Use a pair of calipers for the most accurate diameter readings, and a micrometer for thickness, because even a 5-10% error in thickness directly causes a 5-10% error in the computed length.
Reverse mode: plan how large a roll you need
Switch to reverse mode when you want to know how large a roll must be to hold a specific length of material. Supply the target length, the core diameter, and the material thickness, and the calculator solves for the required outer diameter. This is useful when winding wire, hose, cable, or film onto a spool and you need to know whether your target length will fit on the available bobbin or if you need a wider spool.
Common applications and typical dimensions
Roll-length calculations appear across packaging (tape, cling film, foil), manufacturing (label stock, release liners, non-woven fabric), electrical (cable, wire, flat flex), printing (paper and film rolls), plumbing (hose, tubing), and agriculture (irrigation drip tape, mulch film). Standard office tape cores are typically 25-76 mm in diameter. Industrial paper rolls can have cores of 76-152 mm. Film and foil thicknesses range from 0.01 mm (thin food wrap) to 0.5 mm (thick foam tape), so entering an accurate thickness value has a large effect on the result.
Typical material thickness by type
| Material | Typical thickness | Notes |
|---|---|---|
| Cling film / food wrap | 0.008-0.015 mm | Very thin; measure with micrometer |
| Aluminium kitchen foil | 0.015-0.025 mm | Standard household grade |
| Office / stationery tape | 0.05-0.10 mm | Includes adhesive layer |
| Packaging tape (OPP) | 0.05-0.08 mm | Clear polypropylene |
| Standard printer paper (80 g) | 0.10-0.11 mm | 80 gsm bond paper |
| Label stock (self-adhesive) | 0.12-0.20 mm | Includes liner and adhesive |
| Garden hose (12 mm bore) | 2.0-3.0 mm | Wall thickness only |
| Electrical wire (insulated) | 0.5-3.0 mm | Overall diameter varies widely |
Representative thickness values for common wound materials. Always measure your specific material for best accuracy.
Frequently asked questions
What inputs do I need for the roll length calculator?
You need three measurements: the outer diameter of the full roll (from one side to the other at the widest point), the inner diameter of the hollow core or spool at the centre, and the thickness of a single layer of material. All three must be in the same units. Use a caliper or ruler for diameters and a micrometer for thickness.
How accurate is the Archimedean spiral approximation?
For most practical materials the approximation error is below 0.1%. The formula is exact when the thickness is infinitesimally small relative to the inner diameter. For thick or stiff materials wound on small cores the error can rise slightly, but even at an outer-to-inner diameter ratio of 2:1 with a thickness equal to 5% of the inner diameter the error remains under 0.5%.
Can I use this calculator for wire, cable, or hose?
Yes. The same Archimedean spiral formula applies to any uniformly wound material. For cable or hose, the "thickness" to enter is the outer diameter of the cable or hose (not the wall thickness), because each wrap takes up that much radial space on the spool.
What is reverse mode and when do I use it?
Reverse mode solves the formula for outer diameter instead of length. You enter the length you want to store, the core diameter, and the material thickness, and the calculator tells you the outer diameter the roll must reach. Use it when choosing spool sizes or planning production: if your roll diameter at the target length exceeds the available spool capacity, you need a larger spool or must split the material into shorter lengths.
Why does small thickness make such a big difference?
The roll length is inversely proportional to thickness: halving the thickness doubles the number of turns and therefore doubles the length for the same roll geometry. This means a 10% error in measured thickness translates directly into a 10% error in computed length. Always measure the actual material with a micrometer rather than relying on the printed nominal value, especially for thin films and foils.
How do I measure the inner and outer diameter of a roll?
For outer diameter, place the roll flat and use a ruler or caliper across the widest point. For inner diameter, measure the hollow core at the centre of the roll from one inner wall to the other. A digital caliper gives the most accurate reading. For small cores, insert the caliper jaws into the hole and spread them to the inner walls.