Key takeaways
- Unit weight in kg/m = d²/162, where d is the nominal bar diameter in millimetres.
- The 162 is not arbitrary — it is 4,000,000 ÷ (7850 × π), the density of steel folded into the area of a circle.
- For US bar sizes the same derivation gives n²/24 lb/ft, where n is the bar number in eighths of an inch.
- IS 1786 allows the delivered bar to be up to 3–7% under nominal mass, so a tonne of steel may contain less running metre than the formula suggests.
Steel is drawn in metres and sold in tonnes. Every bar bending schedule, every steel indent and every reconciliation on site depends on converting one to the other, and almost everyone in construction does it with the same six characters: d²/162.
It is worth understanding once. Engineers who know where the 162 comes from can rebuild the formula from first principles when they meet a section it does not cover — a square bar, a hollow section, a different metal entirely.
Where the 162 comes from
Start with the physics. The mass of any prismatic bar is its cross-sectional area times its length times the density of the material:
Mass = Area × Length × Density
For a round bar of diameter d, the area is πd²/4. Take one metre of length, and take the density of structural steel as 7850 kg/m³ — the value used in IS 1786 and by every rolling mill. The only complication is units: d is quoted in millimetres, but the density is per cubic metre, so the area has to be divided by 1,000,000 to convert mm² to m².
Weight (kg/m) = (π × d² ÷ 4 ÷ 1,000,000) × 1 × 7850
= d² × 7850π ÷ 4,000,000 = d² × 0.0061654
Dividing by a number is friendlier on site than multiplying by a six-decimal constant, so invert it: 1 ÷ 0.0061654 = 162.2. That is the whole story. The constant is 4,000,000 ÷ (7850 × π), and the industry rounds it down to 162 because it makes the mental arithmetic clean and errs about 0.1% on the conservative side.
Unit weight (kg/m) = d² / 162
d = nominal bar diameter in mm. Valid for any plain or deformed round steel bar.
The standard bar weight table
These are the numbers most site engineers eventually memorise. Every one is simply d² ÷ 162.
| Diameter (mm) | d² | Weight (kg/m) | Weight per 12 m bar (kg) | Metres per tonne |
|---|---|---|---|---|
| 6 | 36 | 0.222 | 2.67 | 4505 |
| 8 | 64 | 0.395 | 4.74 | 2531 |
| 10 | 100 | 0.617 | 7.41 | 1620 |
| 12 | 144 | 0.889 | 10.67 | 1125 |
| 16 | 256 | 1.580 | 18.96 | 633 |
| 20 | 400 | 2.469 | 29.63 | 405 |
| 25 | 625 | 3.858 | 46.30 | 259 |
| 32 | 1024 | 6.321 | 75.85 | 158 |
| 40 | 1600 | 9.877 | 118.52 | 101 |
Nominal unit weights from d²/162. The 12 m column is the standard mill length supplied in India.
The last column is the one that saves arguments at the gate. If a truck delivers a tonne of 12 mm bars, it should contain roughly 1125 running metres — about 94 bars of 12 m. Counting bars is far quicker than weighing them.
Worked example: a slab bar list to a steel order
A one-way slab is reinforced with 10 mm main bars at 150 mm centres running 4.2 m, and 8 mm distribution bars at 200 mm centres running 6.0 m. The slab is 6.0 m × 4.2 m.
- Main bars. Across the 6.0 m width at 150 mm centres: (6000 ÷ 150) + 1 = 41 bars, each 4.2 m long.
- Main bar total length. 41 × 4.2 = 172.2 m
- Main bar weight. 172.2 × 0.617 = 106.3 kg
- Distribution bars. Along the 4.2 m span at 200 mm centres: (4200 ÷ 200) + 1 = 22 bars, each 6.0 m long.
- Distribution total length. 22 × 6.0 = 132.0 m
- Distribution weight. 132.0 × 0.395 = 52.1 kg
- Slab total. 106.3 + 52.1 = 158.4 kg. Add 3% for off-cuts → order 163 kg.
Note that this list ignores cover, hooks and laps for clarity. A real schedule adds all three — see how to prepare a bar bending schedule for the complete treatment.
The imperial equivalent
North American practice sizes bars by number, where the number is the diameter in eighths of an inch — a #4 bar is 4/8 inch, or 12.7 mm. Run the same derivation with a steel density of 0.2836 lb/in³ and you get an equally tidy rule:
Unit weight (lb/ft) = n² / 24
n = US bar number. #4 → 16/24 = 0.667 lb/ft, against a published 0.668 lb/ft.
If you work across both systems, the conversion between them is 1 kg/m = 0.672 lb/ft.
Why the delivered bar weighs less
The formula gives nominal weight. What arrives on the truck is allowed to differ. IS 1786 permits a tolerance on mass per metre of roughly ±7% for bars up to 10 mm, ±5% for 10 to 16 mm and ±3% above 16 mm, assessed on a batch rather than a single bar.
Reputable mills roll close to nominal. Some rolling mills roll consistently at the light end of the tolerance band — every bar passes specification, but a tonne of steel yields noticeably fewer running metres than the table predicts. If your reconciliation keeps showing a shortfall you cannot explain, weigh a measured 1 m sample from the batch and compare it with the nominal figure before blaming the site.
This matters structurally too. A bar rolled 5% under nominal has about 5% less steel area than the design assumed, which is why the tolerance is tighter for the larger diameters that carry the most load.
Frequently asked questions
Why 162 and not some other number?
It is 4,000,000 ÷ (7850 × π) = 162.2, rounded down. The 7850 is the density of steel in kg/m³ and the 4,000,000 converts square millimetres to square metres inside the circular area formula. Rounding to 162 keeps the arithmetic simple and errs about 0.1% on the safe side.
Does it work for TMT bars?
Yes. The formula uses nominal diameter, and TMT, TMX and plain mild steel all share a density of 7850 kg/m³. The surface ribs are not counted separately — the nominal diameter already represents the equivalent plain round bar of the same mass per metre.
What about square or hollow sections?
Go back to Mass = Area × Length × Density. A square bar of side a mm gives a²/127.4 kg/m; a hollow circular section is the outer-diameter weight minus the inner-diameter weight. Only the area term changes.
Should I order to nominal weight or measured weight?
Order to nominal, which is what the formula and every schedule give you, but reconcile against measured weight at delivery. The gap between the two is the mill's rolling tolerance, and knowing it for your supplier is worth more than any thumb rule.