A quotation arrives with a tonnage figure, and you have no way to tell if it is honest. A wrong number means you overpay by hundreds of dollars or the steel arrives short and your hull schedule slips. Here is how to check it.

Theoretical weight is calculated from nominal section dimensions using the formula kg/m = t × (a + b − t) × 0.00785. To check a marine angle steel quotation, recalculate the tonnage from the quoted sizes and lengths, then question any supplier figure that drifts more than 2–3% from your own arithmetic.

I have reviewed quotations from steel mills and trading companies for more years than I want to admit, and the tonnage line is where I look first. Most suppliers are honest, but the quotation is also the one document where a small arithmetic choice — a different section table, a rounded kg/m, a wrong length basis — quietly changes your landed cost. The check takes twenty minutes with a calculator and a weight table. This article walks through the method I use on every marine angle steel order, from the formula itself to the moment you decide whether a gap is normal rolling practice or a reason to hold the shipment.

What Does Theoretical Weight Actually Mean on a Supplier Quotation?

The quotation says 18.4 tonnes, your own estimate says 17.9 tonnes, and nobody can explain the difference. That gap is not always a trick, but it is always worth understanding before you sign. Theoretical weight is not a guess — it is a definition, and once you know the definition you can rebuild the number yourself.

Theoretical weight is the mass calculated from nominal dimensions and steel density of 7.85 g/cm³, before any rolling tolerance is applied. It is the invoicing basis on most angle steel quotations, and it differs from actual weighed weight because hot rolling never lands exactly on nominal size.

The Formula Behind Every Angle Weight Table

Every weight table you have ever used comes from one formula. For an unequal angle with legs a and b and thickness t:

kg/m = t × (a + b − t) × 0.00785

For an equal angle it simplifies to:

kg/m = t × (2a − t) × 0.00785

The 0.00785 constant converts square millimetres of cross-section into kilograms per metre, because steel density is 7.85 g/cm³. Let me verify one size so you can see the arithmetic. For L100 × 100 × 10: cross-section = 10 × (100 + 100 − 10) = 1,900 mm². Multiply by 0.00785 and you get 14.9 kg/m; the standard tables list 15.1 kg/m because the real section has rounded toes and fillets that the sharp-corner formula ignores. That small difference is why I always check against the standard table value, not just the raw formula. A few more common ship angles, computed the same way:

Where the Quotation Number Comes From

When a supplier quotes in tonnes, the figure is almost always theoretical weight: the table kg/m multiplied by the total metres on the order. That is the convention in Chinese mills and most Asian export supply, and it is how we quote at Yichen Steel. Actual (weighed) weight is what the truck scale or the vessel draft survey reads, and it moves with rolling tolerance. Some suppliers — and some European buyers — invoice on actual weight instead. Both systems are legitimate. What breaks deals is a quotation that does not say which basis it uses. I saw a buyer in Qatar nearly reject a clean shipment because his forwarder’s draft survey read 2% below the theoretical tonnage on the proforma invoice. Nothing was wrong. The quotation was theoretical, the survey was actual, and nobody had written the basis on the purchase order. So step one of the check is not arithmetic at all — it is reading the quotation’s weight basis line. If the basis is missing, ask before you compare anything.

Rebuilding the Number Yourself

Here is the exact procedure I run for every quotation, and it takes about fifteen minutes for a typical ten-line angle order. Take the section list from your purchase order — not from the quotation, from your own material list. For each line, look up the standard table kg/m for that section. Multiply kg/m by the total metres you ordered. Sum the lines. Compare your total against the quotation tonnage. The comparison should land within 2–3%. If it does, the quotation is arithmetically honest and you can move on to price per tonne. If the gap is bigger, the causes are almost always one of three things, and the next section shows you how to tell them apart. One practical tip from our yard: keep your section table printed and pinned above the desk. I recalculate by hand even though we sell this steel, because the discipline of doing the arithmetic myself is what lets me spot a wrong section schedule in someone else’s document.

How Do You Recalculate the Quotation Tonnage Step by Step?

So you have the quotation in front of you and a calculator on the desk. What exactly do you multiply, in what order, and what counts as an acceptable gap? This is the mechanical part of the check, and it is worth doing the same way every time so your numbers stay comparable across orders and suppliers.

Multiply the standard table kg/m for each quoted section by the ordered metres, sum the lines, and compare against the quotation tonnage. A gap within 2–3% is normal rounding and tolerance. A larger gap usually means a different section schedule, a wrong length basis, or an outright error.

A Worked Example on a Real Order Shape

Let me run a realistic mixed order the way I would at my desk. Say your material list calls for: 120 pieces of L100 × 100 × 10 at 12 m, 80 pieces of L75 × 75 × 8 at 9 m, and 60 pieces of L150 × 90 × 10 at 12 m. Line one: table kg/m is 15.1, metres are 120 × 12 = 1,440 m, so 21.74 tonnes. Line two: table kg/m is 9.03, metres are 80 × 9 = 720 m, so 6.50 tonnes. Line three: table kg/m for L150 × 90 × 10 is about 18.7, metres are 60 × 12 = 720 m, so 13.46 tonnes. Total: 41.7 tonnes. If the quotation says 42.0 tonnes, that is a 0.7% gap — clean rounding, sign it. If it says 44.5 tonnes, that is 6.7% high, and before you argue with the supplier you should check one specific thing: did they quote a heavier schedule, for example L150 × 150 instead of L150 × 90, or 11 mm instead of 10 mm thickness? Nine times out of ten, a big gap is a schedule mismatch, not greed. The last time in ten that it is actual money, you want to have caught it before the deposit, not after the vessel sails.

What the Tolerances Allow Before You Complain

Rolling is a hot process, so no bar lands exactly on nominal size. The standards recognise this with tolerances, and knowing them tells you how big a weight gap can be explained by tolerance alone. The two standards our buyers reference most are EN 10056-2 and ASTM A6:

Do the sensitivity math on thickness, because thickness enters the weight formula twice. On an L100 × 100 × 10 rolled 0.7 mm light at the negative end of tolerance, the kg/m drops by roughly 1.4%. Add a leg slightly under and a length at the short end of the ±50 mm cut tolerance, and a theoretical-vs-actual gap of 2–3% is fully explained by legal tolerance. That is why I do not get excited below 3%. Above 5%, tolerance cannot explain it, and you should ask the supplier to reconcile the number line by line.

The Three Numbers That Must Agree

A marine angle steel shipment carries three weight figures, and each has a different job. The theoretical tonnage on the quotation and purchase order is the invoicing basis. The mill test certificate, issued to EN 10204 3.1 or 3.2, carries the heat number, chemistry, mechanical results, and usually a theoretical mass computed from nominal dimensions. The packing list carries gross and net weights for freight and customs. When I review documents, I put the three numbers side by side. They should sit within about 2% of each other, and any residue should be explained by the tolerance story. If the packing list runs 8% above the certificate with no explanation, ask for bundle-level weights before the container is released. If the certificate mass is far below your own calculation, check whether the certificate describes the same section schedule you ordered. Mixed heats and mixed schedules cause more document confusion than fraud ever does in our market, but the check costs you five minutes either way.

When Does a Weight Gap Mean a Real Problem?

Your check shows a gap. Is it normal, or is it the start of a claim? This is the judgment call, and after enough shipments you develop a feel for it — but the feel can be written down as decision bands, and that is what I use when I train new sales staff on our side.

A gap within ±2% is normal rolling practice, 2–5% in either direction deserves a note and a scale check on arrival, and beyond 5% — or a wide spread inside one bundle — should hold the shipment until the supplier reconciles the figures or a third-party survey verifies the load.

The Decision Bands I Use on Every Discrepancy

These bands assume the quotation basis is theoretical and the arrival check compares actual weighed weight per metre against the table value. I measure ten random pieces from different bundles, weigh them, divide total weight by total length, and get an actual kg/m:

The direction matters as much as the size. Heavy steel is a cost problem; light steel is a structural problem. A hull that loses steel weight in its stiffeners can lose section modulus in exactly the members designed to resist buckling, and no classification surveyor will accept “but we paid less” as an excuse. Light gaps deserve the more careful look even though the invoice impact is smaller.

Make the Purchase Order Say Which Weight Governs

Most weight disputes I have handled were not calculation mistakes. They were contract gaps. Two reasonable parties each used a legitimate method, and the purchase order never said which one governed. Fix it with one sentence. State the invoicing basis — theoretical per the standard table, or actual weighed — and state the tolerance band you will accept, for example ±3% between invoice tonnage and surveyed weight. State whether packing and bundling weight is included in the invoiced quantity, because banding steel is heavy and it adds up on a full container. And state the verification method at loading: draft survey, weighbridge, or a sampled piece-count check with the surveyor’s report attached. I have watched a buyer and a supplier spend three weeks arguing over a 1.8-tonne difference that neither of them had priced into the deal, all because the PO was silent. The sentence costs nothing to write and saves that argument. If your supplier resists writing the basis down, that resistance is itself information.

The Two-Minute Arrival Check That Catches Thin Material

You do not need a laboratory to police a shipment — you need a tape, a scale, and twenty minutes at the warehouse door. Pick ten pieces from different bundles. Measure each actual length. Weigh them. Divide total weight by total length to get actual kg/m, and compare it with the table value for the section. If the average lands within 2%, accept and move on. If it does not, you now hold objective numbers, not an opinion, and the conversation with your supplier becomes arithmetic instead of argument. We had a Gulf Metal Solutions shipment to Dammam where their inspector ran exactly this check on an angle line while our SGS surveyor watched; the sample averaged a hair over the table value, well inside tolerance, and the paperwork closed the same afternoon. That is what a good weight culture looks like — both sides doing the same simple math and trusting the result. I would rather my customers check our steel and find it honest than take it on faith, because a buyer who verifies once becomes a buyer who stops worrying.

Conclusion

Recalculate the tonnage from the standard table, check the basis on the quotation, and hold anything beyond 5%. Twenty minutes of arithmetic protects both your budget and your hull.

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