Two questions, two different formulas

Roll calculations come in two directions, and mixing them up is the usual source of errors in a pressroom.

Length from weight

If you know the roll weight, the web width and the paper’s gsm, the length follows from the definition of gsm — grams per square metre:

area (m²) = weight (kg) × 1000 ÷ gsm
length (m) = area (m²) ÷ width (m)

Weight from length

Reverse the same two steps: multiply width by length to get area, then multiply by gsm and divide by 1000.

weight (kg) = width (m) × length (m) × gsm ÷ 1000

A worked example

A label stock roll weighs 25 kg, the web is 330 mm wide, and the material is 80 gsm. How much is on the roll?

1. Width in metres: 330 ÷ 1000 = 0.33 m.
2. Area = 25 × 1000 ÷ 80 = 312.5 m².
3. Length = 312.5 ÷ 0.33 = 947 metres.

Check it in reverse: 0.33 × 947 × 80 ÷ 1000 = 25.0 kg. Good.

Length from roll diameter, when there is no scale

In a pressroom you often have the physical roll and no weight reading. If you know the outer diameter, the core diameter and the material caliper, the length can be estimated from the cross-sectional area of the wound material — a spiral, which unwinds to a long thin rectangle:

length ≈ π × (D² − d²) ÷ (4 × caliper)

where D is the outer diameter, d is the core diameter, and all three are in the same unit. Treat this as an estimate: winding tension compresses the layers, so the real length is usually a little longer than the calculation suggests, and the gap widens as the roll gets softer towards the core.

Things that shift the answer

• Core weight. A quoted roll weight may or may not include the core and the pallet. A board core is typically 1–3 kg; on a 25 kg roll that is a 4–12% error, which is the difference between a job finishing and running short.
• Moisture. Paper is hygroscopic. A roll conditioned in a damp warehouse genuinely weighs more than the same roll in a dry one, and gsm figures are quoted at a standard relative humidity.
• Coating and liner. For label stock, the gsm quilted into the calculation should be the total for the face, adhesive and liner, or you will overestimate the length substantially.
• Web width tolerance. Slitting is not exact. A millimetre of width error on a narrow web is a larger relative error than on a wide one.

Common questions

Why does my calculated length not match the supplier’s figure?

Usually the core, the moisture content, or which gsm figure was quoted. Ask whether the supplier’s weight includes the core, and whether the gsm is nominal or actual.

Can I use this for film or foil?

Yes, if you use the material’s grammage. For films, density and thickness are often quoted instead, in which case convert to grammage first: gsm = thickness (mm) × density (g/cm³) × 1000.

How much waste should I order?

Add for make-ready and tail waste. A useful default is 3–5% on a straightforward run, plus the length lost to each splice if the job runs across multiple rolls.