Calculate the length of material on a roll from diameter, core and thickness
| Outer diameter | Roll length | Number of wraps | vs current |
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Faiq Ur Rahman is a web designer, digital product developer, and founder of Toolraxy, a growing platform of web-based calculators and utility tools. He specializes in building structured, user-friendly tools focused on health, finance, productivity, and everyday problem-solving.
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A roll of tape, film, paper, or fabric is a spiral. Every wrap sits slightly outside the one before it, and the total length depends on how much space the material takes up between the core and the outer edge. This calculator uses the standard spiral formula to convert those dimensions into a length. It’s useful in manufacturing, packaging, printing, and warehouse work where you need to know how much material is left on a roll without unwinding it. Enter the outer diameter, core size, and thickness. The tool returns the length in feet or metres, the number of wraps, and the average circumference. Switch to reverse mode if you know the length and need the diameter.
Pick US or Metric from the setup dropdown.
Choose your mode: find roll length or find outer diameter.
Enter the outer diameter (or roll length, depending on mode).
Add the inner core diameter.
Enter the material thickness and pick its unit.
Optionally add material width and density for surface area and weight.
Read the roll length or outer diameter in the hero panel.
Check the table for lengths at other diameters.
The calculation models the roll as a tight spiral with no air gaps.
Formula: Roll length L = π (D² − d²) ÷ (4 t)
Formula: Outer diameter D = √(d² + 4 L t ÷ π)
Formula: Number of wraps N = (D − d) ÷ (2 t)
Formula: Average circumference = π (D + d) ÷ 2
Formula: Surface area A = L × width
Formula: Weight W = L × width × t × density
Where D = outer diameter, d = core diameter, t = material thickness, L = roll length
The core formula comes from the difference in area between the outer circle and the inner circle. That area, divided by the thickness of the material, gives the length of the strip. It works because every wrap adds a layer of constant thickness, so the total cross-sectional area of the material equals the area of the annulus between the two diameters.
The reverse formula solves the same equation for D instead of L. Given a target length, it returns the diameter the roll will reach. That’s useful when planning packaging or storage: you know how much material needs to fit and you need to size the roll.
Validation requires a positive outer diameter and thickness, and the outer diameter must be larger than the core. If the material thickness is zero or the input is invalid, the tool returns an error instead of a number.
A roll of LDPE stretch film has an outer diameter of 12 inches, a 3-inch core, and a thickness of 1 mil (0.001 inches). Width is 24 inches and density is 0.0332 lb/in³ (typical for LDPE).
Outer diameter: 12 in
Inner core: 3 in
Thickness: 1 mil = 0.001 in
Roll length: π × (144 − 9) ÷ (4 × 0.001) = π × 135 ÷ 0.004 = 106,029 inches
That’s 106,029 ÷ 12 = 8,836 feet.
Number of wraps: (12 − 3) ÷ (2 × 0.001) = 4,500 wraps
Average circumference: π × (12 + 3) ÷ 2 = 23.56 in
Surface area: 106,029 × 24 = 2,544,696 in² = 17,671 ft²
Weight: 106,029 × 24 × 0.001 × 0.0332 = 84.5 lbs
The badge reads “Very large roll” because 4,500 wraps crosses the 1,500-wrap threshold. A thicker film would produce fewer wraps and a shorter total length. Doubling the thickness to 2 mils would halve the length to about 4,418 feet.
Use the formula L = π × (D² − d²) ÷ (4t), where D is the outer diameter, d is the core diameter, and t is the material thickness. All measurements must be in the same unit. A 10-inch roll with a 3-inch core and 10-mil material gives about 596 feet.
D = √(d² + 4Lt ÷ π). For 5,000 feet of 1-mil material on a 3-inch core, convert to inches first (60,000 inches), then apply the formula. The result is about 9.24 inches outer diameter.
Divide the diameter difference by twice the thickness: N = (D − d) ÷ (2t). A roll from a 3-inch core to a 10-inch outer with 5-mil material has about 700 wraps.
Film and tape use mils or microns. Paper uses points. Cardboard uses millimetres. Pick the unit that matches your spec sheet, and make sure the calculator uses the same unit for all inputs.
Multiply mils by 25.4. A 2-mil film is 50.8 microns thick. To go the other way, divide microns by 25.4.
Multiply length × width × thickness × density. Use consistent units across all four values. The calculator handles the conversions automatically and returns the weight in pounds, ounces, grams, or kilograms.
Thicker material fills the space between the core and the outer edge faster, so fewer wraps fit. Halving the thickness roughly doubles the roll length for the same diameter range.
It’s π × (D + d) ÷ 2, the circumference at the midpoint between the core and outer diameter. Multiplying it by the number of wraps gives a sanity check on the roll length.
Measure across the roll with a caliper or tape, through the centre. Take two or three readings at different angles and average them. Measure the core the same way. For soft rolls, press gently so you don’t deform the material.
Mixing units is the top error. Mils with inches or microns with millimetres produces wildly wrong results. Using the core’s outer diameter instead of its inner diameter is second. Ignoring air gaps in loosely wound rolls is third.
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