kraft paper reel weight calculation formula
What Is That Half-Used Kraft Paper Reel Actually Worth? Every corrugated unit has the same corner — reels pulled off the machine before they finished, stood against a wall waiting for a job small enough to use them. Ask what’s in that corner and you get a shrug and a number that sounds confident and isn’t. It matters more than it looks. That corner is stock. It sits on your balance sheet at month end, it’s what you draw against when a mill delivery runs late, and it’s what you’re pricing when a neighbouring unit calls asking to buy your odd sizes. Get it wrong by ten percent and you’re carrying paper in the register that isn’t in the godown. The arithmetic that fixes it takes thirty seconds and a measuring tape. Most people already know half of it. The half they’re missing is the half that goes wrong on small reels. W₂ = W₁ × (D₂² − Dc²) ÷ (D₁² − Dc²) W₁ original net paper weight · D₁ original diameter · D₂ present diameter · Dc core outside diameter. Any unit, so long as all three diameters match. Paper Sits in a Ring, Not a Disc Paper occupies the annulus — the reel’s full circle minus the hollow core. Its area, and so its weight, goes with the square of the diameter. Every wrap runs the full width of the reel at the same substance, so weight simply tracks the area of that ring. Which is why doubling a reel’s diameter does considerably more than double its weight. It’s also why careless measurement hurts twice over. A one percent error on the tape becomes a two percent error on the weight. Nothing else in this calculation punishes sloppiness that hard. The Version Doing the Rounds Is Missing the Core Most people use W₂ = W₁ × (D₂ ÷ D₁)². That treats the reel as solid paper right down to the axle. It isn’t — there’s a 3 or 4 inch core in there holding no paper at all. Drop the core term and you always overstate stock, never understate it. Worse, the error grows exactly where your counting is already weakest. On a 1200 mm reel over a 76 mm core: Diameter remaining Overstated by 1000 mm 0.2% 800 mm 0.5% 600 mm 1.2% 400 mm 3.3% 300 mm 6.4% 200 mm 16.4% Half a percent on a working reel is noise — ignore it. Sixteen percent on a stub, multiplied across forty stubs at closing, is a number your auditor eventually puts a finger on. Two conditions on the correct formula, and neither is optional. Both weights must be net of the core, and you must compare a reel against itself. Scale one reel from a different reel’s weight and the density and width stop matching, so the cancellation collapses. A Reel From Our Own Floor This one came through our Adityapur unit. A 48 inch reel landed at 785 kg on the weighbridge, standing 41¾ inches across. After a run it came off at 13¾ inches, over a core measuring 4.72 inches outside. Step Figure Weighbridge, at receipt 785.00 kg Less core − 5.24 kg Net paper at receipt 779.76 kg Factor, (13.75² − 4.72²) ÷ (41.75² − 4.72²) 0.0969 Net paper remaining 75.58 kg Reads on the scale, core in 80.82 kg The platform scale said 80.82 kg. That agreement is the whole point of showing the working — when the formula and the weighbridge argue, it’s almost never the physics. It’s the core convention, or a diameter someone eyeballed. The gross-versus-net trap. A 48 inch core weighs a shade over 5 kg. If your stock register mixes gross mill weights with net calculated balances, that error rides on every single stub, and the sign flips depending on which way you were careless. Subtract the core once, at the receipt entry, and let everything downstream run on paper weight alone. Reel Weight Calculator Enter your reel’s figures. Use From mill weight whenever you have the original weight — it assumes nothing about the paper. From mill weightFrom densityDiameter unitInchesMillimetresOriginal diameter (D₁)Original weight (kg)Present diameter (D₂)Core outside diameterCore weight (kg)Mill weight includes core?Yes — grossNo — net paperRate (₹/kg, optional)Diameter unitInchesMillimetresPresent diameter (D₂)Deckle (inches)Core outside diameterWound density (kg/m³)Core weight (kg, optional)paper left vs full reel—kg net paperReads on the scale, core in—Share of the full reel—Paper already consumed—Value at the rate entered—Fill in the fields above to see the weight. Load the worked example Step-down chartCopy for Excel Diameter Net paper With core % of reel When There’s No Mill Slip Opening stock. A reel bought second-hand from another unit. A stub whose label came off months ago. Sometimes there’s no original weight to work from, and then you need the paper’s density instead. W = 0.0000000007854 × (D² − Dc²) × w × ρ D, Dc and deckle w in millimetres · ρ wound density in kg/m³ · result in kg That ρ is wound density, not the density of the sheet — and this is where most reel calculators go wrong. A roll traps air between its wraps, and kraft is rough enough that layers never lie perfectly flat, so a reel works out lighter per unit of volume than the paper itself. Plug in a sheet density near 1200 kg/m³, as several online tools do, and you’ll overstate a reel by more than half. Radial pressure also means the innermost wraps pack harder than the outer ones. That’s the reason the first formula quietly reads low on a very small stub. Where to start on wound density GSM 12–14 BF 16–18 BF 20–22 BF 100 655 675 700 120 670 695 720 140 685 710 740 160 695 725 755 180 705 735 765 200 715 745 775 Treat these as seeds, not gospel. The spread between two mills supplying the same nominal grade is wider than the gap between any two rows above — refining, wet pressing and winder tension all
