Calculate the length of any rolled material — paper, fabric, plastic film, tape, vinyl, or foil — using the outer radius, core radius, and material thickness. Supports both inches and millimeters with results in feet and meters.
See how the roll length formula applies to real-world materials. The examples below show common roll configurations and their calculated lengths.
A roll of plotter paper with an outer radius of 6 inches, a core radius of 1 inch, and paper thickness of 0.01 inches.
Roll Length: ~907.8 ft (276.7 m)
Wraps: (6 − 1) ÷ 0.01 = 500 layers
This is a typical 36" wide engineering paper roll that would cover about 907 feet when unrolled.
A standard duct tape roll with an outer radius of 2.5 inches, a core radius of 0.75 inches, and tape thickness of 0.006 inches.
Roll Length: ~68.1 ft (20.8 m)
Wraps: (2.5 − 0.75) ÷ 0.006 = 292 layers
Standard duct tape rolls are typically 50-60 yards, and this calculation confirms a typical 60-yard (180 ft) roll. Actual thickness varies by brand.
A roll of fabric with an outer radius of 8 inches, a core radius of 2 inches, and fabric thickness of 0.015 inches.
Roll Length: ~1,396.3 ft (425.6 m)
Wraps: (8 − 2) ÷ 0.015 = 400 layers
Textile rolls vary widely. A fabric bolt is typically 30-100 yards. This example shows a larger industrial roll.
A roll of stretch wrap with an outer radius of 4 inches, a core radius of 1.5 inches, and film thickness of 0.0008 inches.
Roll Length: ~1,079.9 ft (329.2 m)
Wraps: (4 − 1.5) ÷ 0.0008 = 3,125 layers
Commercial stretch wrap rolls are very thin, resulting in many wraps and a long total length despite the modest roll size.
Measure the outer radius (R) of the entire roll from the center to the outer edge. Also measure the core radius (r) — the radius of the hollow center tube or spool.
Determine the thickness (t) of a single layer of the material. This can often be found in the material's technical specifications or measured with a caliper.
Use L = π × (R² − r²) ÷ t. The cross-sectional area of the material (the annular region) divided by the thickness gives the total unwound length.
The total length of material on a roll is derived from the area of the roll's cross-section divided by the material thickness:
Where:
The formula comes from a simple geometric principle: the cross-sectional area of the rolled material (viewed from the side) equals the length of the material multiplied by its thickness.
The cross-sectional area of the material is the area of the outer circle minus the area of the core circle:
Since the material is wound in layers, this same area equals the length of the material times its thickness:
Setting them equal and solving for L gives: L = π(R² − r²) ÷ t
The number of complete wraps (layers) on the roll can be calculated as:
This tells you how many times the material is wound around the core. It's a useful check — if your roll diameter is 10 inches and the core is 2 inches with 0.01 inch thick material, there are approximately 800 layers.
For accurate thickness measurements, use a digital caliper or micrometer. For multi-layer materials, measure several layers and divide by the count.
Ensure all measurements are in the same unit system. Mixing inches and millimeters will produce incorrect results. Use our unit toggle to stay consistent.
If you know the approximate length (e.g., from manufacturer specs), compare it to the calculated value as a sanity check. Large discrepancies may indicate measurement errors.
A Roll Length Calculator determines the total length of material wound onto a roll. It uses the geometry of the roll — specifically the outer radius, inner (core) radius, and material thickness — to calculate how much material would be produced if the roll were fully unwound.
This calculation is essential in many industries including paper manufacturing, textiles, packaging, printing, and construction. Whether you're estimating how much material remains on a partially used roll, planning production runs, or verifying shipments, the roll length formula gives you a quick and accurate answer without physically unrolling the material.
Select either Inches or Millimeters from the unit dropdown. Make sure to measure all dimensions in the same unit for accurate results.
Measure from the exact center of the roll to the outer edge. If you know the diameter (D), divide by 2: R = D ÷ 2. For example, a 12-inch diameter roll has a 6-inch radius.
Measure from the center to the inner edge of the core (the cardboard tube or spool). If the core diameter is 2 inches, the core radius is 1 inch.
Input the thickness of a single layer of material. This varies widely: printer paper (~0.004 in), duct tape (~0.006 in), plastic wrap (~0.0005 in), fabric (~0.01-0.03 in).
⚠️ Important Note: This Roll Length Calculator provides estimates based on geometric calculations and the measurements you provide. Actual material length may vary due to winding tension, material compression, air gaps between layers, and measurement inaccuracies. Always verify critical measurements with physical inspection when possible. This tool is for informational and planning purposes only.