Calculate the length of material on a roll from its outer diameter, core diameter, and material thickness. Works for paper, film, tape, fabric, and wire.
How much material is left on a partially-used roll? You can't unwind it to measure, but you CAN calculate the length from three measurements: the roll's outer diameter, the core (inner) diameter, and the material thickness. This roll length calculator uses the exact mathematical relationship between these measurements to determine total length.
The formula models the roll as an Archimedean spiral — each wrap adds one material thickness to the radius. The length equals the total cross-sectional area of material divided by the material thickness: L = π × (R² − r²) / t, where R is the outer radius, r is the core radius, and t is the material thickness. This works for any rolled material: paper, plastic film, tape, fabric, wire, carpet, vinyl, foil, and more.
The calculator supports multiple units (inches, mm, feet), converts results to both linear feet and meters, and includes presets for common materials. It also estimates the number of wraps (turns) on the roll, which is useful for quality control and inventory management.
It turns three quick measurements into a usable length estimate without unwinding or damaging the roll. That is useful for inventory checks, purchasing, and production planning. It also gives you a faster answer when the roll is too heavy or awkward to measure by hand in a shop or warehouse.
Length = π × (Outer Radius² − Core Radius²) ÷ Material Thickness. Wraps = (Outer Radius − Core Radius) ÷ Material Thickness. Cross-sectional area = π × (R² − r²). For imperial: measure diameters in inches, thickness in mils (1 mil = 0.001"). Convert length to feet by dividing inches by 12.
Result: 1,985 feet (605 meters), 1,167 wraps
R = 5", r = 1.5", t = 0.003". Length = π × (25 − 2.25) ÷ 0.003 = 23,825 inches = 1,985 feet. Wraps = (5 − 1.5) ÷ 0.003 = 1,167 turns.
Each wrap around the core adds one material thickness to the radius, so the roll can be modeled as a spiral with a known cross-sectional area. Once you know the outer radius, core radius, and thickness, you can back out the total length without unwinding anything.
The formula assumes a consistent thickness and relatively firm winding. That is a good approximation for paper, film, foil, and many tapes, but soft materials can compress near the core and make the true length slightly shorter than the ideal calculation. The thinner the material, the more important an accurate thickness measurement becomes.
This kind of estimate is useful when you need to know whether a remaining roll will finish a job, whether a shipment is short, or how much stock is left on the shelf. Measuring the current outer diameter and comparing it with the full-roll spec is usually faster than trying to track every cut or unwind sample lengths.
Use a micrometer or caliper. Measure the material (not the roll gap). For paper, thickness is called "caliper" and measured in mils (thousandths of an inch) or microns. Standard copy paper is about 4 mils (0.004").
The formula assumes uniform thickness. Tightly-wound rolls may compress inner layers slightly, making the actual length 1-3% shorter than calculated. For soft materials like foam or bubble wrap, the error is larger.
Include the total tape thickness (backing + adhesive layer). A standard roll of packing tape is about 2 mils (0.002") total thickness. The adhesive doesn't add to diameter because it fills the gaps between wraps.
Measure the inside diameter of the cardboard tube/core. Common cores: 1" (tape), 1.5" (small rolls), 3" (industrial standard), 6" (large industrial). If no core, use 0 for coreless rolls.
Yes! Measure the current outer diameter and enter it instead of the full roll outer diameter. Compare the resulting length to the original full roll length to get the percentage remaining.
The material occupies a ring-shaped cross-section (annulus) between the core and the outer edge. This area equals the material's length × thickness when "unwound." So length = area ÷ thickness. It's equivalent to counting wraps but mathematically exact.