Working out the weight of steel from its shape
How to find the weight of TMT bars, plates, pipes and angles from their size, why the D²/162 rule works, how many bars make a tonne, and where theoretical weight differs from the scale.
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In short
- Weight = volume × density. Mild steel is 7,850 kg/m³, so a plate 1 m by 2 m and 10 mm thick weighs 157 kg.
- For round bars, D² ÷ 162 gives kg per metre with D in mm. A 12 mm bar is 0.889 kg/m and a 16 mm bar is 1.58 kg/m.
- A standard 12 m length of 12 mm TMT is 10.67 kg, so a tonne holds about 93 bars.
- For a pipe or tube, weigh only the metal, the area between the outer and inner shapes.
- Actual weight differs from theoretical weight by rolling tolerance, so a bill by weight and a bill by theoretical length may not agree exactly.
Steel is sold by weight and used by length, so every builder, fabricator and purchaser spends time turning one into the other. The sum is simple once you see it: the cross-section of the piece, multiplied by its length, multiplied by the density of the metal. This page shows that sum for each common shape, explains the D²/162 shortcut that site engineers use for reinforcement, and notes where the theoretical number differs from what a weighbridge shows.
The formula
weight = cross-section area × length × density
Take care with the units. If the area is in mm² and the length in metres, then:
kg = area (mm²) ÷ 1,000,000 × length (m) × 7,850
The 7,850 is the density of mild steel in kg/m³. Stainless steel is about 8,000, aluminium about 2,700, copper about 8,960 and brass about 8,500, all of which the calculator offers.
Every shape then comes down to finding its cross-section:
| Shape | Cross-section in mm² | Example | kg per metre |
|---|---|---|---|
| Round bar | π ÷ 4 × D² | 12 mm | 0.888 |
| Square bar | side² | 20 mm | 3.14 |
| Flat or plate | width × thickness | 50 × 5 mm | 1.96 |
| Round pipe | π ÷ 4 × (D² − d²) | 50 mm, 3 mm wall | 3.48 |
| Square tube | A × B − (A − 2t) × (B − 2t) | 50 × 50 × 3 mm | 4.43 |
| Angle | (A + B − t) × t | 50 × 50 × 5 mm | 3.73 |
For a pipe, d is the inner diameter, which is the outer diameter less twice the wall. For an angle, the sum counts the two legs and removes the small square where they overlap at the corner.
Real angle sections have rounded corners, so published tables can differ from this figure slightly. Where the exact weight of a rolled section matters, use the manufacturer's table.
The D²/162 rule
Site engineers do not reach for π every time. For a round mild steel bar, they use:
kg per metre = D² ÷ 162
where D is the diameter in mm. The rule is the same sum with the numbers folded together. π ÷ 4 × 7,850 ÷ 1,000,000 comes to 0.006165, which is almost exactly 1 ÷ 162. So a 12 mm bar is 144 ÷ 162 = 0.889 kg/m, and the exact sum gives 0.888. The difference is about a tenth of a percent, far smaller than the rolling tolerance on any real bar.
| Diameter | kg per metre | 12 m bar | Bars in a tonne |
|---|---|---|---|
| 6 mm | 0.222 | 2.67 kg | 375 |
| 8 mm | 0.395 | 4.74 kg | 210 |
| 10 mm | 0.617 | 7.41 kg | 135 |
| 12 mm | 0.889 | 10.67 kg | 93 |
| 16 mm | 1.580 | 18.96 kg | 52 |
| 20 mm | 2.469 | 29.63 kg | 33 |
| 25 mm | 3.858 | 46.30 kg | 21 |
| 32 mm | 6.321 | 75.85 kg | 13 |
Notice how quickly weight climbs with size, because it grows with the square of the diameter. A 16 mm bar has only a third more diameter than a 12 mm bar, but it weighs nearly 80 percent more. That is why a change of bar size on a drawing has such a large effect on the steel bill.
Worked examples
A pile of rebar. A site needs 20 lengths of 16 mm TMT, each 12 m. One metre weighs 1.578 kg, one bar 18.94 kg, and the lot 378.8 kg, or 0.379 tonnes. At a rate per kg, the cost follows directly.
An MS sheet. A sheet 1,250 mm wide, 2,500 mm long and 6 mm thick has a section of 7,500 mm². Over 2.5 m that is 147.19 kg. Sheet of this size is a common cut size, and a quick check like this confirms a supplier's figure.
A square tube for a frame. A 50 × 50 × 3 mm tube has a section of 564 mm², which is 4.43 kg/m. A 6 m length weighs 26.56 kg. For a gate or shed, multiply by the total running metres of tube.
A pipe. A pipe with a 50 mm outer diameter and a 3 mm wall has an inner diameter of 44 mm. The metal's section is π ÷ 4 × (2,500 − 1,936), which is 443 mm², or 3.48 kg/m.
Why the scale disagrees
The figures here are theoretical weights. Real steel is rolled to a tolerance, so a bar described as 12 mm can be slightly under or over. Standards allow a percentage either side of nominal weight, and the allowance is larger for smaller bars.
That matters when steel is billed. Some dealers bill by actual weight on a scale. Others bill by theoretical weight from the number of bars. If bars are running light, you pay less by actual weight but also receive less steel. An honest check is to weigh a sample bundle and compare it with the table above. A large shortfall from the theoretical figure, beyond the tolerance in the standard, is worth raising with the supplier, because a bar that is under-weight is also under-section.
Rust is a smaller matter. Light surface rust adds very little, but heavy flaking scale means lost section, and such steel should not be used without an engineer's approval.
Estimating steel for a slab or column
The steel in a structure comes from the bar schedule on the drawings, not from a rule of thumb. For a rough budget before drawings exist, builders use a figure in kg per square foot of built-up area. That figure varies with the number of storeys, the spans, the soil and the seismic zone, so it is only a planning number.
Once you have a schedule, add up the running metres of each diameter, multiply by the kg/m above, and allow a few percent for lap lengths, bends and offcuts. Bars come in 12 m lengths, so laps and cutting waste are inevitable. Buying by the bundle can also leave you with lengths to store until they are used.
For the concrete that surrounds the bars, the cement calculator works out cement, sand and aggregate by grade, and the brick calculator handles the walls. The volume calculator is useful for odd shapes.
Going from weight back to length
Purchasing often runs the other way. You have a budget or a quantity in kilograms and want to know how much bar it buys. Divide the weight by the kg per metre. An order of 500 kg of 10 mm bar is 500 ÷ 0.617 = 810 m, which is about 67.5 lengths of 12 m. At ₹65 per kg, a rate used here only as an example, the steel costs ₹32,500 before GST and carriage.
Rates are quoted per kg by small dealers and per tonne by larger ones, so check which you are looking at before comparing them. A rate of ₹62,000 per tonne is ₹62 per kg. Dealers may also charge separately for cutting and bending, and the price per kg can change with bar diameter, with thinner bars often costing a little more.
Mistakes that throw the figure off
Diameter and radius. The D²/162 rule uses the full diameter. Using the radius by mistake gives a quarter of the true weight.
Inches. Older drawings and fabrication shops may give sizes in inches. Multiply by 25.4 first, so a 2 inch flat is 50.8 mm wide. The calculator takes sizes in millimetres.
Outer size only. Treating a pipe as a solid rod gives several times the real weight. Enter the wall thickness, which is what you are paying for.
Metal. Aluminium is about a third of the weight of steel, so a sum with the wrong density will be badly out. Pick the metal before reading the result.
What this calculator assumes
- The section is a plain geometric shape, without the rounded corners or ribs of a real rolled section. TMT ribs are allowed for by nominal diameter.
- Densities are standard values. Particular grades of stainless steel and brass differ slightly.
- All pieces are the same size and length.
- The table of bars uses the D²/162 rule, and the main result uses the exact π ÷ 4 sum for a round bar, so the two can differ in the last decimal place.
- The figures are theoretical weights. They exclude tolerances, laps, bends and offcuts.