The Three Core Formulas
Film roll math comes down to three formulas that everyone in packaging should know cold. They convert between weight, length, area, and cost — the four dimensions along which film moves through a factory.
The first formula: length from weight. You have a roll of known weight, width, and thickness. How long is it?
Length (m) = Weight (g) / (Width (mm) × Thickness (µm) × Density (g/cm³) × 0.001)
The 0.001 converts the cross-sectional area from mm × µm to cm², which matches density in g/cm³.
The second formula: weight from length. You know how many meters of film you need for a production run. How much does it weigh, and how much does it cost?
Weight (g) = Length (m) × Width (mm) × Thickness (µm) × Density (g/cm³) × 0.001
The third formula: cost per square meter. You want to compare two films on a level playing field.
Cost ($/m²) = Price ($/kg) × Thickness (µm) × Density (g/cm³) / 1,000
All three formulas hinge on density. Get density wrong and everything else follows. The next sections walk through each formula with worked examples.
Length from Weight
This is the formula you use when receiving film. The supplier invoice says 180 kg. The line supervisor wants to know if that roll will last the shift.
Formula: Length (m) = Weight (g) / (Width (mm) × Thickness (µm) × Density (g/cm³) × 0.001)
Worked example: 180 kg roll of 500 mm wide, 50 micron PE film. Density of LLDPE is 0.92 g/cm³.
Step 1 — convert units to grams: 180 kg = 180,000 g
Step 2 — calculate cross-section: 500 mm × 50 µm = 25,000 mm·µm. Converting to cm²: 25,000 × 0.0001 cm/mm × 0.0001 cm/µm = 0.0025 cm² per linear cm of film. Per linear meter: 0.025 cm² × 100 = 0.25 cm²/m.
Actually, let us work through the simplified version directly:
Length (m) = 180,000 / (500 × 50 × 0.92 × 0.001) = 180,000 / 23 = 7,826 m
That roll is 7,826 meters long. At a line speed of 60 m/min (typical for a VFFS snack line), the roll will last about 130 minutes of run time, or roughly 2 hours plus changeover.
Subtract the core weight. The 180 kg includes a 76 mm cardboard core weighing about 3.5 kg. Actual film weight: 176.5 kg. Actual length: 176,500 / 23 = 7,674 m. The 152-meter difference is real — about two minutes of run time — and matters when planning changeovers.
For a quick estimate without a calculator, memorize the PE constant: 1 kg of PE film = 1,087,000 / (width mm × thickness microns) meters. For 500 mm × 50 micron: 1,087,000 / 25,000 = 43.5 m/kg. So 176.5 kg × 43.5 = 7,678 m. Matches.
Weight from Length
You need to know how much film a production run will consume. This formula answers that.
Formula: Weight (g) = Length (m) × Width (mm) × Thickness (µm) × Density (g/cm³) × 0.001
Worked example: A run of 80,000 stand-up pouches. Each pouch body uses 0.18 m of film at 300 mm wide. The film structure is PET/PE laminate, total thickness 110 microns, blended density 1.05 g/cm³ (PET 1.40 and PE 0.92 weighted by layer thickness).
Total film length: 80,000 × 0.18 = 14,400 m
Weight: 14,400 × 300 × 110 × 1.05 × 0.001 / 1,000 = 498 kg
At $2.80/kg for that laminate, the run consumes $1,394 of film in raw material alone, before scrap, before ink, before the zipper. This is why roll math matters: without it, you cannot quote a job accurately.
Add scrap: typical flexible packaging scrap runs 3-8%. At 5% scrap, you actually consume 523 kg of film ($1,464). The scrap rate is a function of line setup, changeover frequency, and run length — short runs scrap more per unit.
For different polymers, the same length and width give different weights. A 14,400 m run of 300mm × 110µm film at density 0.92 (all PE) weighs 437 kg. At density 1.40 (all PET) it weighs 665 kg. That is a 52% weight difference for the same dimensional film — and a 52% cost difference if priced by weight.
Cost Per Bag
Cost per bag is the number that ultimately matters for product economics. It combines film area per bag, cost per area, and scrap rate.
Formula: Cost per bag = Bag area (m²) × Cost per m² × (1 + Scrap rate)
Cost per m² = Price ($/kg) × Thickness (µm) × Density (g/cm³) / 1,000
Worked example: A snack bag uses 0.045 m² of film. The film is 80 micron total thickness, blended density 1.02 g/cm³, priced at $2.40/kg. Scrap runs 5%.
Cost per m² = 2.40 × 80 × 1.02 / 1,000 = $0.196/m²
Cost per bag (film only) = 0.045 × 0.196 × 1.05 = $0.00926, call it $0.0093
That is 0.93 cents of film per snack bag. Add ink ($0.001-0.003), zipper if applicable ($0.005-0.015), and the film package climbs to 1.5-2.5 cents per bag. At 1 million bags per week, every 0.1 cent of film cost equals $52,000 per year.
This is why lightweighting matters. Drop the structure from 80 to 70 microns (assuming barrier allows) and cost per m² falls to $0.171 — a 12.5% reduction. On the 1 million bags per week line, that is $65,000 per year saved.
Worked Example: Full Run Calculation
Putting it all together. A coffee roaster running 50,000 250g stand-up pouches per month wants to know the film budget.
Inputs:
- Pouch uses 0.20 m of roll stock per unit
- Roll stock is 320 mm wide
- Structure: PET12 / AL7 / LLDPE70, total 89 microns
- Blended density: 1.08 g/cm³ (weighted by layer)
- Price: $3.40/kg
- Scrap rate: 6%
- Production: 50,000 pouches/month
Step 1 — total film length: 50,000 × 0.20 = 10,000 m
Step 2 — net film weight: 10,000 × 320 × 89 × 1.08 × 0.001 / 1,000 = 308 kg
Step 3 — including scrap: 308 × 1.06 = 326 kg
Step 4 — film cost: 326 × $3.40 = $1,108 per month, or $0.0222 per pouch in film
Step 5 — adding one-way degassing valve ($0.010 each) and zipper ($0.012 each): total packaging cost per pouch = $0.0222 + $0.010 + $0.012 = $0.0442
At 50,000 pouches per month, the film and accessories budget is $2,210. Add labor, depreciation, energy, and overhead per the five-component model and you have fully-loaded cost per pouch. See the Complete Guide to Packaging Film for the full framework.
Layer-weighted density deserves a quick note. For the coffee structure above (PET 12, AL 7, LLDPE 70), the weighted density is not the simple average of 1.40, 2.70, and 0.92 — it is weighted by layer thickness. Calculation: (12 × 1.40 + 7 × 2.70 + 70 × 0.92) / 89 = (16.8 + 18.9 + 64.4) / 89 = 100.1 / 89 = 1.12 g/cm³. The difference between 1.08 and 1.12 is small but real, and it compounds across long runs. Always calculate weighted density rather than guessing.
Common Mistakes
We see the same errors repeatedly in factory audits. Most are preventable with a checklist.
Wrong density. Using 0.95 for LLDPE (actually 0.915-0.922) inflates weight by 3-4%. Using 1.0 for PE because it is round inflates by 8-9%. Always confirm density with the supplier's data sheet for the specific grade.
Ignoring core weight. The cardboard core is 2-5 kg depending on length. On a 50 kg roll, that is 4-10% of the billed weight. Either subtract the known core weight or weigh the empty core after the roll is used.
Mixing gauge systems. "50 gauge PE" is 12.7 microns, not 50 microns. Mixing gauge and micron produces results off by 4x. Pick one system per spec and use it consistently. See Film Thickness Explained for full conversions.
Using list price instead of actual. The $2.80/kg list price becomes $2.55/kg after volume discount and $2.42/kg after rebate. Use actual paid price for cost calculations.
Forgetting slip and antiblock additives. These add 1-3% to density and slightly to cost. Minor but adds up across millions of bags.
Assuming wound density equals solid density. Wound rolls have air between layers, but the math uses solid polymer density. This is correct for length-weight conversion — the formulas give you solid-film length, not wound roll dimensions. The confusion arises when measuring roll diameter (see next).
Using the Calculator
The Film Roll Calculator automates all of the above. Enter three of the four variables (width, thickness, density, weight or length) and it computes the fourth, plus cost per linear meter, cost per square meter, and projected run time at any line speed.
The calculator handles the four most common tasks:
- "How long is this roll?" — Enter weight, width, thickness, density. Get length and area.
- "How much film do I need?" — Enter production volume, area per unit, scrap rate. Get weight and cost.
- "What does this film cost per bag?" — Enter price, thickness, density, bag area. Get cost per bag.
- "Compare two films" — Enter specs for both. Get side-by-side cost per m² and per bag.
The calculator uses the formulas above with no shortcuts. Density values for common polymers are pre-loaded. Results are accurate to within 2-5% of actual, which matches the inherent variability of film gauge and density.
For complex multi-layer structures, enter total thickness and use a weighted-average density. The calculator has a layer-weighted density helper that walks you through it.
Run the numbers before every job quote. Run them again at month-end with actual scrap rates. Run them whenever a supplier proposes a new film structure. The five minutes of math saves tens of thousands of dollars in mispriced product or mis-budgeted material per year.