The Formula Behind Rebar Weight per Metre
Every bar bending schedule ends with a weight column, and every one of those weights comes from the same simple formula: divide the bar diameter squared by 162. It's used so universally that it's easy to take on faith without knowing where it actually comes from — this post derives it from first principles, so you know exactly what it assumes and where its limits are.
The formula
Where D is the bar's nominal diameter in millimetres. This is the figure used across BS 8666:2020, IS 2502:1963 and most international rebar references, and it's exactly what this calculator uses to compute the weight column of a schedule automatically.
Deriving it from first principles
The formula falls out of three things: the density of steel, the geometry of a circular bar, and a unit conversion. Here's the derivation step by step.
- Start with steel's density. Mild and reinforcing steel has a density of approximately 7,850 kg per cubic metre (kg/m³).
- Find the cross-sectional area of a circular bar. For a bar of diameter D (in metres), the cross-sectional area is πD²/4.
- Multiply area by length to get volume, then by density to get weight. For a 1-metre length of bar: weight = πD²/4 × 1 × 7,850 kg/m³.
- Convert diameter from metres to millimetres. Since D is normally expressed in mm on a drawing, substitute Dmm/1000 for D (in metres) and simplify the constants together: π/4 × 7,850 ÷ 1,000,000 ≈ 1/162.
- The result. Weight (kg/m) = Dmm² ÷ 162 — the constant 162 is simply π × steel density × a unit-conversion factor, all folded into one number so the formula only needs the bar diameter as an input.
Checking it against real bar sizes
| Diameter (D, mm) | D² | Weight (D² ÷ 162) |
|---|---|---|
| 6mm | 36 | 0.2222 kg/m |
| 8mm | 64 | 0.3951 kg/m |
| 10mm | 100 | 0.6173 kg/m |
| 12mm | 144 | 0.8889 kg/m |
| 16mm | 256 | 1.5802 kg/m |
| 20mm | 400 | 2.4691 kg/m |
| 25mm | 625 | 3.8580 kg/m |
| 32mm | 1024 | 6.3210 kg/m |
| 40mm | 1600 | 9.8765 kg/m |
These figures match published reinforcement weight tables closely, confirming the formula holds across the standard bar size range. For a fuller reference table with typical uses per size, see our rebar sizes guide.
Why this matters for a schedule
Every row in a bar bending schedule ends in a weight figure, and that figure is what a quantity surveyor prices the steel package against and what a supplier uses to plan delivery. Since weight is purely a function of diameter (not shape or bend), it's one of the more mechanical parts of preparing a schedule — but errors still creep in if the wrong diameter is used against a bar mark, or if a schedule mixes up nominal diameter with some other dimension. Cross-checking a handful of weight figures by hand against this formula is a fast way to catch that kind of error before a schedule is issued.
Where the formula's precision runs out
D²/162 assumes a perfectly circular bar at nominal diameter and the standard 7,850 kg/m³ steel density. In practice, ribbed reinforcing bar has a slightly larger effective cross-section than a perfectly smooth circular bar of the same nominal diameter (to account for the ribs), and real bars carry small manufacturing tolerances on both diameter and mass per metre. None of this meaningfully changes the figure for scheduling and ordering purposes — it's the reason the formula is described as a very close approximation rather than an exact physical measurement, and it's precise enough that it's the basis for every published rebar weight table in the industry.
Let the calculator do the arithmetic
Enter your bar sizes and the calculator applies this formula automatically to every bar mark in your schedule, along with the correct cutting-length formula for the shape.
Open the BS 8666 calculator →Frequently asked questions
What is the formula for rebar weight per metre?
Rebar weight per metre in kilograms is calculated as the bar diameter in millimetres squared, divided by 162: weight (kg/m) = D² ÷ 162.
Where does the 162 in the rebar weight formula come from?
The 162 comes from combining the density of steel (approximately 7,850 kg per cubic metre) with the geometry of a circular bar and the unit conversion between millimetres and metres, simplifying into a single constant so the formula only needs the bar diameter as an input.
How accurate is the D²/162 rebar weight formula?
The D²/162 formula is a very close approximation of a ribbed reinforcing bar's actual weight, and is the standard figure used across BS 8666, IS 2502 and most international rebar references — actual delivered weight can vary marginally within standard manufacturing tolerances, but the formula is accurate enough for scheduling and ordering purposes.
More calculations
See the full rebar size reference table, or understand the bend deduction that affects cutting length.
Rebar sizes & weight table → Bend deduction & bend diameter →This is a general reference. Always confirm weight and quantity figures against the actual project specification and the relevant national standard.