A 3% weight error on a 50-tonne marine angle steel order is 1.5 tonnes of freight nobody budgeted for. That is one container slot, or one rejected loading plan. This is how we build the number.
To calculate the total weight of a marine angle steel order, take the theoretical mass per metre — (leg A + leg B − thickness) × thickness × 0.00785 — multiply it by length and piece count for every size on the list, then add 2% to 5% for rolling tolerance and export packing.
Weight is the one number that appears on every document in a marine steel deal. It sits on the quotation, the purchase order, the mill test certificate, the packing list, the bill of lading and the customs entry. When those documents disagree, the shipment stops. I have watched a bundle sit on the quay in Qingdao for four days because the invoice said 24.6 tonnes and the forwarder’s manifest said 25.9 tonnes. Nobody was dishonest. Two people used two different methods and never compared them. So let us compare them here, properly, size by size.
What Is the Formula for the Weight of Marine Angle Steel per Metre?
Most weight disputes start with a number copied off a website calculator that was never checked. The formula behind that number is simple, and worth understanding once.
The mass of a steel angle in kilograms per metre equals the cross-sectional area in square millimetres multiplied by 0.00785. For an equal or unequal angle that area is (A + B − t) × t, where A and B are the leg lengths and t is the thickness, all in millimetres.
The Shortcut Formula and Where It Comes From
Steel weighs about 7,850 kilograms per cubic metre. That is 7.85 grams per cubic centimetre. If you measure legs and thickness in millimetres, one square millimetre of section one metre long holds 0.00785 kilograms. So the whole job reduces to finding the area of the L shape and multiplying.
The L shape is two rectangles that overlap at the corner. Leg A gives you A × t. Leg B gives you B × t. The corner is counted twice, so you subtract t × t. That leaves (A + B − t) × t. Multiply by 0.00785 and you have kilograms per metre.
For a 75 × 75 × 6 angle the arithmetic is: 75 + 75 − 6 = 144. Then 144 × 6 = 864. Then 864 × 0.00785 = 6.78 kg/m. A six-metre piece lands at 40.7 kg. A twelve-metre piece lands at 81.4 kg. Those are the numbers I use on the phone when a buyer asks what a bundle will weigh.
Where the Shortcut Falls Short: The Root Fillet
The shortcut treats the corner as a sharp inside angle. Real hot-rolled angles are not sharp. There is a fillet radius at the root and rounded toes on both leg ends, and that added metal is not in the formula. The published mass tables in GB/T 706 and EN 10056-2 include it. So the table figure sits slightly above your hand calculation, and the gap grows with section size up to a point, then flattens.
| Angle size (mm) | Shortcut formula (kg/m) | Standard table (kg/m) | Gap | 12 m piece (kg) |
|---|---|---|---|---|
| 50 × 50 × 5 | 3.73 | 3.77 | +1.1% | 44.7 |
| 63 × 63 × 6 | 5.65 | 5.72 | +1.2% | 67.8 |
| 75 × 75 × 6 | 6.78 | 6.85 | +1.0% | 81.4 |
| 80 × 80 × 8 | 9.55 | 9.66 | +1.2% | 114.6 |
| 100 × 100 × 10 | 14.92 | 15.10 | +1.2% | 179.0 |
| 125 × 125 × 12 | 22.42 | 22.70 | +1.3% | 269.0 |
| 200 × 200 × 20 | 59.66 | 59.70 | +0.1% | 716.0 |
Read that table carefully, because it decides which number you put on the purchase order. If you quote a client from the shortcut formula, you are quoting about 1% light. On a 50-tonne order that is half a tonne. Your client’s freight forwarder will not care that your calculator was convenient.
My rule is blunt. Use the shortcut to check a supplier. Use the standard table to commit to a contract. When the two disagree by more than about 1.5%, somebody is using the wrong table, or quoting a nominal size that is not the size being rolled.
Why Grade Does Not Change the Number
Buyers sometimes assume AH36 angle is heavier than A-grade angle because it is stronger. It is not. Density is a property of steel, not of yield strength. A 100 × 100 × 10 angle weighs the same whether the mill rolled it to A, AH36 or DH36, because the section is the same and the density is the same.
What changes with grade is how much section you need. AH36 gives you 355 MPa minimum yield against 235 MPa for A-grade, so a designer can specify a lighter angle and carry the same load. That is where weight savings actually come from in a ship structure. Not from the density, but from the substitution of a smaller section. If your naval architect has done that work, the weight drops. If nobody has, you pay for mild steel section sizes at high-strength steel prices, and the vessel gains tonnage it does not need.
Running the Formula in Your Head
I keep one anchor number in my head: 100 × 100 × 10 is 15.1 kg/m. Everything nearby scales from it. Halve the legs and you land near 3.77 for 50 × 50 × 5. Drop to 75 × 75 × 6 and you get 6.85. This is not precise enough for a purchase order, but it is fast enough to catch a supplier who quotes 100 × 100 × 10 at 13 kg/m because he mistyped a cell in his spreadsheet.
How Do You Turn a Piece List into a Total Order Weight?
A single kg/m figure is not an order weight. An order is a list of sizes, lengths and quantities, and the total only appears when every line is extended and added.
Build the total line by line: for each size, multiply mass per metre by cut length by piece count to get kilograms, divide by 1,000 for tonnes, then sum the lines. Never multiply one average kg/m by the total metre count when the order has more than one section size.
Work from the Marked Drawing, Not the Tonnage
The worst way to price a marine angle steel order is to start from the tonnage in the enquiry. That number was usually produced by someone else, for a different purpose, at an earlier stage of the design. It may include cutting allowance, it may include wastage, and it may include sections that were later deleted.
Start from the material takeoff. Every line should carry four fields: section, grade, length and quantity. If the takeoff only gives you total metres of 75 × 75 × 6, you can still work, but ask whether those metres are 6 m stock lengths or 12 m bars cut down. That single question changes the piece count and the offcut.
A Worked Order
Here is a real shape of order, the kind of mixed list that comes out of a deckhouse and hull outfitting package. I have rounded the masses to the table values, because that is what the mill will invoice against.
| Section (mm) | Mass (kg/m) | Length (m) | Pieces | Line weight (kg) | Line weight (t) |
|---|---|---|---|---|---|
| 50 × 50 × 5 | 3.77 | 12 | 120 | 5,428.8 | 5.43 |
| 75 × 75 × 6 | 6.85 | 12 | 200 | 16,440.0 | 16.44 |
| 100 × 100 × 10 | 15.10 | 12 | 80 | 14,496.0 | 14.50 |
| 150 × 90 × 12 | 21.48 | 12 | 40 | 10,310.4 | 10.31 |
| 200 × 200 × 20 | 59.70 | 6 | 12 | 4,298.4 | 4.30 |
| Total | 452 | 50,973.6 | 50.97 |
Fifty-one tonnes, 452 pieces, 5,352 metres. That is the theoretical weight. It is also the number you send to a freight forwarder, with a clear label saying it is theoretical, not weighed.
Add the Two Things Buyers Forget
The first is rolling tolerance. Hot rolling cannot hold a section to the millimetre of mass, and every standard allows a band. EN 10056-2 permits roughly ±3% to ±5% on the mass of a single angle, tighter on thin sections and wider on heavy ones. On our 50.97 t order, ±3% is 49.4 t to 52.5 t. That band is legal material either way.
The second is packing. Export bundles are strapped with steel band, separated with timber, and sometimes cradled. That adds roughly 1% to 3% of the steel weight to the gross shipped weight. It is not steel, so it never appears in your kg/m calculation, but it absolutely appears on the weighbridge.
Add 3% for tolerance and 2% for packing and the same order leaves the yard at about 53.5 t gross. If your loading plan assumed 51 t, you have a problem at the gate.
Round Up, Never Down, at the Container
A 20-foot general purpose container takes about 27 to 28 tonnes of payload, and the exact figure depends on the box, the carrier and the road limits at both ends. Our 51 t order does not fit in two boxes at 25.5 t each without care. Add tolerance and packing and two boxes at 26.7 t each is right at the edge.
This is where a calculation error becomes a commercial event. You cannot load 26.7 t into a box rated for 26.0 t. You split into three boxes and pay for a third box that is a third full. Or you ship breakbulk, which is fine for 12 m bars and often cheaper per tonne, but needs a berth window you may not have.
I always advise buyers to plan the container count on the gross weight with tolerance and packing included, then work backwards to how much steel fits. Not the other way round.
Why Does the Delivered Weight Rarely Match Your Calculation?
Your calculation is a model. The delivered weight is a measurement. They differ for reasons that are all legal, and a buyer who knows the reasons can tell a normal deviation from a real quality problem.
Delivered weight differs from calculated weight because of three things: dimensional tolerance in leg length and thickness, the difference between table mass and scale mass, and the packing included in the gross figure. A deviation inside ±5% is normal; a consistent one-direction deviation is a signal to inspect.
Three Sources of Deviation
The first is thickness. EN 10056 allows about ±0.4 mm on a 10 mm leg, and similar bands exist in GB/T 706 and ASTM A6. Thickness enters the formula linearly, so a 10 mm angle rolled at 9.7 mm is 3% light before you look at anything else. That is still compliant. A 10 mm angle rolled at 9.2 mm is not.
The second is leg length. Leg tolerance moves the number too, but less, because each leg contributes one thickness of area. A 100 mm leg at 99 mm costs you about 0.5% on mass.
The third is the measurement method itself. Mills in our region usually invoice sections on theoretical weight, using the standard table. Plate is more often invoiced on actual weighed weight. If your supplier quotes theoretical and your forwarder weighs actual, the two numbers will never be identical, and neither party has done anything wrong. The mistake is leaving the basis unstated.
The Weight Check That Catches Thin Material
You do not need a laboratory to test a shipment. You need a scale, a tape and twenty minutes.
Take ten random pieces from different bundles. Measure the actual length of each. Weigh them. Divide total weight by total length to get actual kg/m. Compare that with the table value for the size.
| Actual vs table | What it usually means | What to do |
|---|---|---|
| Within ±2% | Normal rolling, material is on size | Accept, file the record |
| +2% to +5% | Mill rolled heavy, legs or thickness over nominal | Accept, but check deadweight impact on the vessel |
| −2% to −5% | Mill rolled light, at the edge of tolerance | Accept with a note, check section modulus in critical members |
| Beyond −5% | Under-thickness or under-length, likely non-compliant | Hold the bundle, call for third-party verification |
| Wide spread within one bundle | Mixed heats or mixed sources | Hold, check heat numbers against the certificate |
I ran this check myself on a stack of 100 × 100 × 10 in our yard last month, and the average came out at 15.4 kg/m against a table value of 15.10. That is 2% heavy, which is inside the band, but it told me the mill was running the pass slightly open. I mentioned it to the mill and the next batch came in at 15.2. Nothing was wrong with either shipment. It is just useful to know what your supplier’s rolling practice looks like before it becomes a shipyard argument.
What Tolerance Actually Says
Tolerance is not a licence to ship less steel. It is a recognition that rolling is a hot process. But the direction of deviation matters to a shipyard in a way it does not matter to a warehouse.
A hull that gains 2% of steel weight in its stiffeners gains tonnage high in the vessel. That reduces deadweight and can shift stability margins the naval architect did not plan for. A hull that loses 2% of steel in its stiffener section can lose section modulus in exactly the members designed to resist buckling. Both are legal. Neither is free.
This is why I ask buyers for the design assumption, not just the section list. If the structure was designed with the table mass, you want material at or slightly above the table mass. If it was designed with a conservative allowance, a light shipment is harmless. The calculation should serve the design, not the invoice.
Certificate Weight vs Scale Weight
The mill test certificate to EN 10204 3.1 or 3.2 carries the heat number, the chemistry and the mechanical results. It may also carry a theoretical mass and, on some mill formats, a weighed mass for the test piece. Those are not the same thing. The certificate mass is usually calculated from nominal dimensions. The scale mass is measured.
When you receive the documents, put the certificate mass beside your own calculation and beside the packing list gross. Three numbers, three purposes: certificate for compliance, calculation for planning, packing list for freight. If they are within 2% of each other and the tolerance story explains the rest, the shipment is clean. If the packing list is 8% above the certificate and nobody can explain the packing, ask for the bundle weights.
What Should the Purchase Order Say About Weight?
Most weight disputes I see are not calculation mistakes. They are contract gaps. The buyer and supplier each used a reasonable method, and the purchase order never said which one governed.
Your purchase order should state four things about weight: the basis for pricing and invoicing (theoretical or actual), the mass tolerance allowed, whether packing weight is included in the invoiced quantity, and the method of verification at loading.
Nail the Basis
Theoretical weight is calculated from nominal dimensions using the standard table. Actual weight is what the scale reads. Both are legitimate. They are not interchangeable, and the gap between them can reach several percent on a large mixed order.
A supplier who quotes on theoretical weight and ships at the low end of tolerance is not cheating, but the buyer pays for steel that was never delivered. A supplier who quotes on actual weight and ships heavy is also not cheating, but the buyer pays more than the quotation suggested. The only defence is a sentence in the purchase order.
| Point to specify | Theoretical basis | Actual basis |
|---|---|---|
| Quantity in the contract | Nominal mass × length × pieces | Weighed mass at mill or at loading port |
| Typical gap to scale | −3% to +3% depending on rolling | Near zero by definition |
| Who carries the risk of a light shipment | Buyer, within tolerance | Supplier |
| Who carries the risk of a heavy shipment | Buyer, within tolerance | Buyer, at the higher invoice |
| Freight planning accuracy | Good, if tolerance is added | Best, but only known late |
| Practical for mixed-size orders | Yes, one table serves every line | Harder, needs bundle-by-bundle weights |
| Common in our region for sections | Yes | Less common, requested by larger buyers |
My own preference, and what we write into most contracts, is a hybrid. Price on theoretical weight from the standard table, allow a stated mass tolerance, and require the supplier to declare the weighed gross weight of each bundle on the packing list before the vessel sails. The buyer gets a predictable invoice and an accurate freight number.
Put the Numbers in the PO
Do not write “about 50 tonnes”. Write the section list, the length, the piece count and the calculated mass per line, and let the total fall out. Then add the tolerance. Then add a quantity tolerance clause, typically ±5% on the total order, so a mill that rolls a little long does not create a documentary problem at customs.
I learned this the hard way with a buyer in Dammam. Gulf Metal Solutions placed a mixed plate and angle order with us, and their first version of the purchase order gave only a total tonnage. We built the weight from their drawing and came out 4% above their figure, because their number had been carried forward from an early budget estimate. We sent the line-by-line breakdown with the table mass for every section, they checked it against the drawing, and the order moved. Since then they send the section list with quantities and we return the calculation with the quotation. Their words to me were that we were the first supplier to answer within two hours and keep answering at that speed. The weight sheet was part of that. It showed we had actually read the drawing.
The Bundles and the Bill of Lading
The bill of lading carries a gross weight. That figure includes steel, strapping, timber and any cradle. If your commercial invoice is on theoretical steel weight and the bill of lading is on gross, the two will differ, and a customs broker in some markets will flag it.
The fix is documentary, not technical. Show both numbers and label them. State theoretical steel weight, state packing weight, state gross. Every document then agrees on the steel and accounts for the rest openly. I have seen a 6% gap between invoice and manifest hold a container for a week in a port where the authority wanted a written explanation. The explanation took ten minutes to write and would have taken zero minutes if the packing list had separated the two figures.
What We Do on Our Side
Every quotation we issue for marine angle steel carries a weight column, not just a price per tonne. For each line we show the standard table mass, the length, the piece count and the line total. We show the theoretical total. We show the tolerance band. And before loading we send bundle weights against the packing list.
That is not generosity. It is the cheapest way to avoid an argument three weeks later, when the steel is on the water and nobody can reweigh it.
Conclusion
Weight is not an admin detail. Calculate per line, use the table not the shortcut, add tolerance and packing, and write the basis into the purchase order.