Roll Length Calculator — Film, Tape & Sheet on a Reel
Find how many metres of film, tape, paper, foil or sheet is on a roll. Enter the outer diameter of the wound roll, the core (cardboard) diameter, and the material thickness — the calculator uses the cross-sectional area formula to give total length and number of turns.
mm
mm
mm
L = π(D² − d²) / (4t)
661.5 m
roll lengthCore cross-section
6.4%
Material cross-section
93.6%
- 1
Annulus area (D² − d²)
300² − 76² = 84,224 - 2
Length in mm
π × 84,224 ÷ (4 × 0.1) = 661,494 - 3
Roll length in metres
661,494 ÷ 1,000 = 661.5
How does this calculator work?
Length of material on a roll: L = π(D² − d²) / (4t), where D is outer diameter, d is core diameter, and t is material thickness (all in the same unit). For example, a 300 mm roll on a 76 mm core of 0.1 mm film holds about 520 m of material in roughly 1 120 turns.
Formula
How this is calculated
A wound roll is an annulus (ring) in cross-section. The total cross-sectional area of material is π/4 × (D² − d²), where D is the outer diameter and d is the core diameter. If the material has thickness t, dividing the area by t gives the total length: L = π(D² − d²) / (4t). This derivation assumes the material is wound tightly with no air gaps — a reasonable assumption for film, adhesive tape, paper and thin metal foil.
The number of turns follows directly: each additional layer adds one thickness t to the radius on each side, so the radial build-up (D − d)/2 divided by t gives the turn count. Multiply by π × average diameter and you recover the same length formula, confirming the derivation.
The main source of error is air entrapment between layers, which effectively increases the layer thickness. For loosely wound rolls — thick cardboard, foam, bubble wrap — the actual length will be somewhat less than calculated. For tightly wound precision rolls (capacitor film, photographic film, precision tape), the formula is accurate to within 1–2%.
Frequently asked questions
Yes — measure the outer diameter and the inner cardboard core diameter with a ruler or caliper, and estimate the paper thickness (standard household tissue is roughly 0.10–0.12 mm per ply; kitchen paper 0.2–0.3 mm). Results will be approximate because these rolls are lightly compressed and layer thickness is variable.
The formula L = π(D²−d²)/(4t) works in any consistent unit system. If D, d, and t are all in inches, L is in inches. Convert the result to metres by dividing by 39.37. Enter thickness in thousandths of an inch (mil) only if D and d are also in thousandths.
Wrap a piece of string around the roll and measure the circumference; divide by π. A digital caliper gives a direct outer-diameter reading. For very large rolls (paper reels), laser distance meters or ultrasonic sensors are used industrially.
Also known as
TG we-Calculate Editorial Team. (2026). Roll Length Calculator — Film, Tape & Sheet on a Reel [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/roll-length-calculator
TG we-Calculate Editorial Team. "Roll Length Calculator — Film, Tape & Sheet on a Reel." TG we-Calculate. 2026. https://we-calculate.com/calculator/roll-length-calculator.
TG we-Calculate Editorial Team, "Roll Length Calculator — Film, Tape & Sheet on a Reel," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/roll-length-calculator
@misc{wecalculate_roll_length_calculator, title = {Roll Length Calculator — Film, Tape & Sheet on a Reel}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/roll-length-calculator}}, year = {2026}, note = {TG we-Calculate} }
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