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.
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.
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.
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 move it. Weigh a few reels whose diameter you know, work backwards, and you'll have a figure worth more than any published table.
Measure the Reel Properly
Because the diameter gets squared, how you measure matters more than which formula you pick.
Run the tape around, not across
Measure the circumference and divide by 3.1416. A stub that's been lying on its side goes out of round, and a single reading across one axis can be three-eighths of an inch out — more than a kilo on a small reel.
Measure the core outside, not the hole
The formula needs the diameter at which paper actually starts winding. A 4 inch bore with a 9 mm wall measures 120 mm outside. Use the bore instead and you'll inflate every stub in the register, permanently.
If it fits on a scale, weigh it
No calculation beats a platform scale. Keep the formula for reels still mounted on the corrugator, or stacked where a forklift trip isn't worth the trouble.
What the Shortcut Takes Out of You
Take a unit holding forty stub reels averaging 80 kg each, kraft at ₹42 a kilo. The no-core version at those diameters overstates each one by roughly six percent.
of paper sitting in the register and not in the godown — every month, quietly, until a physical count forces it out as one adjustment entry nobody can explain.
The same arithmetic runs underneath your costing. Consumption per box comes off sheet weight, and sheet weight comes off reels whose balances you either know or guess at. Our corrugated box price calculator works from GSM and ply for exactly that reason — the paper is the cost, and everything after it is conversion.
Talk to Someone Who Runs the Line
If your reel stock and your physical count never quite agree, it's one of three things: the core, the tape, or a register mixing gross and net. Any of them is fixable in an afternoon.
We run corrugation and conversion at NS-66, Adityapur Industrial Area, Jamshedpur, supplying corrugated boxes across Jharkhand — Ranchi, Bokaro, Dhanbad, Hazaribagh, Ramgarh — and into Bengal and Bihar. The numbers above aren't from a textbook. They came out of building reel tracking into our own stock system and arguing with the weighbridge until the two agreed.
Frequently Asked Questions
What is the formula to calculate the weight of a partly used paper reel?
W₂ = W₁ × (D₂² − Dc²) ÷ (D₁² − Dc²), where W₁ is the original net paper weight, D₁ the original diameter, D₂ the present diameter and Dc the outside diameter of the core. All three diameters must be in the same unit, and both weights must exclude the core.
Why does the simple (D₂ ÷ D₁)² formula give a higher answer?
It assumes paper runs all the way to the axis and ignores the hollow core. Because the core takes up a fixed area that never contains paper, leaving it out inflates the result. The error stays under one percent on a nearly full reel but crosses sixteen percent once the reel is down to a 200 mm stub.
Does the deckle change the calculation?
Not when you're comparing a reel against its own original weight — the width is identical on both sides of the ratio and cancels out completely. Deckle only enters when you calculate from density with no reference weight, or when comparing two different reels, where it scales linearly.
What is the core diameter of a kraft paper reel?
Indian mills commonly supply 3 inch (76 mm) and 4 inch (102 mm) bore cores, but the outside diameter is what the formula needs and it runs 15 to 25 mm larger depending on wall thickness. Confirm it per supplier rather than assuming a standard, and record it against the reel.
What is the density of kraft paper in a wound reel?
Roughly 650 to 780 kg per cubic metre for the grades used in corrugation, rising with both GSM and BF. It is lower than the density of the sheet itself, because a wound roll holds air between its layers.
How accurate is calculating reel weight compared with weighing it?
Within two to three percent on working reels, provided you measure the circumference and use the correct core diameter. Accuracy drops on very small stubs, where the inner wraps are denser than the reel average and the formula reads low. Weigh anything you reasonably can.