Coil Weight and Length: Formula, Example and Free Calculator

Knowing the weight of a coil and the length of strip inside it drives two decisions directly: what decoiler capacity you need and how many hours one coil will run. Neither can be handled by guesswork. Fortunately both follow from a single geometric fact and can be worked out by hand.

If you want the answer right away, use the coil calculator on our calculators page; below we explain the reasoning behind it.

Coil geometry: it all comes down to an annulus#

Seen from the side, a wound coil is an annulus: the band between the outer diameter (OD) and the inner diameter (ID). Its area is:

A = π/4 × (OD² − ID²)

Here is the key point: when the coil is unwound, that area is conserved. The steel is no longer a ring but a long rectangle — yet the cross-section is the same. One side of that rectangle is the sheet thickness (t) and the other is the strip length (L), so:

A = L × t   →   L = A / t

Length is nothing more than area divided by thickness.

The weight formula#

For weight, multiply the annulus area by the coil width (W) to get volume, then multiply by density (ρ):

Weight (kg) = π/4 × (OD² − ID²) × W × ρ / 1,000,000

OD, ID and W are in millimetres and ρ is in g/cm³. That division by one million is the unit factor converting a mix of mm³ and g/cm³ into kilograms — it is the detail most often skipped.

Common densities#

Material	ρ (g/cm³)
Steel	7.85
Stainless	7.90
Aluminium	2.70
Copper	8.96

Note that aluminium is roughly one third the weight of steel: a coil with identical geometry comes out at 34% of the steel figure. Choosing decoiler capacity without looking at the material is therefore misleading.

Worked example#

Suppose we have this coil:

• Outer diameter: 1,400 mm
• Inner diameter (core): 508 mm
• Width: 1,250 mm
• Thickness: 2 mm
• Material: steel (7.85 g/cm³)

1. Annulus area

A = π/4 × (1400² − 508²)
A = π/4 × (1,960,000 − 258,064)
A = π/4 × 1,701,936 ≈ 1,336,697 mm²

2. Weight

1,336,697 × 1,250 × 7.85 / 1,000,000 ≈ 13,116 kg

About 13.1 tonnes. This coil calls for a 15-tonne decoiler; the 12-tonne series will not do.

3. Strip length

L = 1,336,697 / 2 ≈ 668,349 mm ≈ 668 m

How the result drives line selection#

Once you know the length, you also know how long the coil will last. Consider a press line running a 250 mm pitch at 40 strokes per minute:

Per minute: 250 × 40 = 10,000 mm = 10 m
Per hour:   10 × 60 = 600 m

A 668 m coil lasts roughly 1.1 hours on that line. That means about 7 coil changes per shift — and every change is downtime. At this point two options appear: heavier coils (a bigger decoiler) or faster coil changes (a loading car). Without the calculation, that discussion cannot even start.

Three common mistakes#

Ignoring the core. Treating the coil as a solid cylinder instead of subtracting the inner diameter inflates the weight badly. A 508 mm core is about 13% of the cross-section on a 1,400 mm coil.

Trusting the nominal thickness. Sheet tolerance can reach ±5%. Because length is inversely proportional to thickness, material that measures 2.1 mm instead of 2 mm yields 5% less length — 636 m instead of 668 m.

Mixing units. Every length in the formula must be in millimetres. Entering the width in metres makes the result a thousand times too small; this mistake shows up regularly at the quotation stage.

Working backwards: from weight to length#

If the supplier gives you the coil weight but not the diameters, you can get the length directly:

L (m) = Weight (kg) / (W (m) × t (m) × ρ (kg/m³))

For steel, ρ = 7,850 kg/m³. Let us test it against the example above:

13,116 / (1.25 × 0.002 × 7,850) ≈ 668 m

The same answer — proof that the calculation is consistent. Arriving at the same number by two routes is the most practical way to validate your inputs.

Summary#

Coil calculation is not intuition, it is two lines of geometry. Weight is annulus area × width × density; length is annulus area ÷ thickness. With those two numbers in hand, decoiler capacity, coil change frequency and shift planning all become discussable.

Try it with your own figures using the coil calculator, and get in touch if you would like to talk line sizing.

Frequently asked questions

Why does the coil weight formula divide by 1,000,000?

With diameters and width in millimetres and density in g/cm³, that unit factor converts the result into kilograms. It is the detail most often skipped; entering the width in metres instead makes the result a thousand times too small.

How much does an aluminium coil of the same size weigh?

Aluminium's density is 2.70 g/cm³ against 7.85 for steel, so a coil with identical geometry comes out at about 34% of the steel figure. Choosing decoiler capacity without looking at the material is therefore misleading.

How do I get strip length if I only know the coil weight?

Use L (m) = Weight (kg) / (W (m) × t (m) × ρ (kg/m³)), with ρ = 7,850 kg/m³ for steel. For 13,116 kg, 1.25 m width and 2 mm thickness, the result is again about 668 m.

What are the most common coil calculation mistakes?

Ignoring the core, trusting the nominal thickness and mixing units. Thickness tolerance can reach ±5%; material measuring 2.1 mm instead of 2 mm yields 5% less length.