Film Roll Length Formula & Methodology

The math behind the Film Roll Length Calculator. Every formula is shown with derivation, units, and worked example.

1. Total film length

When film is wound onto a cylindrical core, the cross-section is an annular ring — the area between the outer roll diameter (D) and the inner core diameter (d). The ring's area equals the film's length × thickness, so:

Ring area = π × (D² − d²) / 4
Length × thickness = ring area
L_mm = π × (D² − d²) / (4 × t_mm)
L_m  = L_mm / 1000

Since thickness is entered in micrometers (μm) and 1 μm = 0.001 mm, the /1000 cancels with the μm-to-mm conversion, giving the final compact form:

L_m = π × (D² − d²) / (4 × t_μm)

Worked example: D=300 mm, d=76 mm, t=50 μm → L = π × 84,224 / 200 = 1,322.99 m.

2. Total film weight

Weight = volume × density. Volume = ring cross-section area × film width.

V_mm³ = π × (D² − d²) / 4 × w_mm
V_cm³ = V_mm³ × 1e-3
W_g   = V_cm³ × ρ (g/cm³)
W_kg  = W_g × 1e-3 = π × (D² − d²) × w_mm × ρ × 1e-6 / 4

Worked example: same roll, w=400 mm, ρ=0.922 g/cm³ (LDPE) → W = 24.40 kg.

Cross-check: W = L × w × t × ρ = 1322.99 m × 400 mm × 0.05 mm × 0.922 g/cm³ → same 24.40 kg.

3. Bags per roll

Two bag styles are supported, with lanes derived from film width vs bag width:

• Flat pouch / single-web: each bag uses bagWidth of film across the web. lanes = floor(filmWidth / bagWidth)
• VFFS back-seal (center-folded): each bag uses 2 × bagWidth of film across the web because the film is folded in half. lanes = floor(filmWidth / (2 × bagWidth))

bagsPerLane = floor(L_m × 1000 / (bagLength_mm + sealAllowance_mm))
totalBags   = lanes × bagsPerLane

Worked example: L=1322.99 m, w=400 mm, bw=100 mm, bl=200 mm, seal=8 mm, flat pouch → lanes=4, bagsPerLane=6360, totalBags=25,440.

Real-world caveat: this is an idealized count. Expect ±5–10% deviation from startup waste, splice loss, and forming-tube efficiency.

4. Cost, runtime & inventory extras

These outputs appear only if you enter the corresponding input:

Film price ($/kg):
  costPerRoll  = W_kg × pricePerKg
  costPerBag   = costPerRoll / totalBags
  costPer1000  = costPerBag × 1000   (industry "K-cost")

Machine speed (bags/min):
  minutesPerRoll = totalBags / speedBpm
  hoursPerRoll   = minutesPerRoll / 60
  shiftsPerRoll  = hoursPerRoll / 8   (8-hour shift convention)

Daily target (bags/day):
  rollsPerDay  = ceil(dailyTargetBags / totalBags)
  rollsPerWeek = rollsPerDay × 7

5. Density values

Material densities are publicly published industry averages (matweb.com, manufacturer datasheets). Individual film lots vary ±2–5%. Use the density field override if you have a precise value from your supplier.

Questions about the math? Email our team or try the calculator.