TL;DR: Steel unit weight, as site engineers use the term, starts from a density of 7850 kg/m³ (7.85 g/cm³), the figure Engineering ToolBox's density table, reproduced by kg-m3.com, lists for steel. The D²/162 rule for round bars folds steel's 7850 kg/m³ density into a unit conversion, so a bar's diameter in millimetres gives its weight in kilograms per metre. For flats, angles and pipes, cross-section area in mm² multiplied by 0.00785 gives kilograms per metre, because 0.00785 is 7850 kg/m³ expressed per square millimetre per metre. Formula weights for steel are theoretical, so D²/162 suits estimates and bar bending schedules, while a weighment of the delivered steel settles what a site actually received.
Reference tables put the density of steel at 7850 kg/m³
Steel unit weight is the weight of steel per unit volume or per unit length, and on an Indian site three different numbers go by that one name. Density is the mass of a material per unit volume, and Engineering ToolBox's reference value for steel is 7850 kg/m³. Structural engineers reserve "unit weight" for a force per volume, while a bar bending schedule uses the same words for kilograms per metre of bar.
- Unit weight
- the weight force of one cubic metre of a material, measured in kN/m³; in Indian site usage the same term also means kilograms per metre of a bar or section.
Kilograms measure mass, and kg-m3.com, reproducing the Engineering ToolBox value, reminds readers that weight is properly a force in newtons: mass times g. Amardeep Steel's September 2025 weight formula guide gives mild steel a unit weight of 78.5 kN/m³, the figure that follows from taking g as 10 m/s²; at 9.81 m/s² the same density gives about 77.0 kN/m³. Use kN/m³ for dead loads in a structural model and kilograms for quantities and billing, the unit that weight charts and invoices carry.
Treat 7850 kg/m³ as the conventional value for mild and carbon steel rather than a physical constant, since individual grades sit slightly either side of it. The reference tables and calculators that publish the figure do not quote IS 800 or the SP 6 handbook for it, so a senior who wants a code clause needs the BIS text itself.
Why do engineers divide D² by 162 to get rod weight?
Engineers divide D² by 162 because 162 is the reciprocal of π/4 × 7850 × 10⁻⁶: the circle's area constant, steel's density and the conversion from square millimetres to square metres, multiplied together. Nothing in that number is empirical. The Civil Engineering YouTube channel's 2019 D²/162 derivation builds it in four steps (area, volume over one metre, density, then weight per metre), with the diameter entered in millimetres.
Find the cross-section area. A round bar of diameter D mm has an area of πD²/4 mm². Dividing by 10⁶ converts that to πD²/4 × 10⁻⁶ m².
Fix the length at one metre. One metre of bar then holds πD²/4 × 10⁻⁶ m³ of steel. Choosing one metre is what turns the answer into a weight per metre.
Multiply by density. At 7850 kg/m³, that metre has a mass of π/4 × 7850 × 10⁻⁶ × D² kg. The constant multiplies out to 0.0061654, so the bar weighs 0.0061654 × D² kg per metre.
Turn the constant into a divisor. Dividing 1 by 0.0061654 gives 162.19, so the exact form is D²/162.19 kg/m. Rounding the divisor to 162 gives the version printed on weight charts.
, last updated in August 2026, gives the constant as (π/4) × (10⁻³)² × 7850 = 1/162.19, approximated to 1/162 for TMT bars with the diameter in millimetres and the length in metres.
Rounding 162.19 down to 162 makes D²/162 read about 0.1% heavy, far less than the tightest batch tolerance on Amrit Steels' chart. An online answer that prints an unrounded constant other than 162.19 has slipped in the arithmetic, and the four steps are the check. Run the derivation on 7800 kg/m³ instead and the divisor lands near 163.2, so the 162 is tied to the 7850 kg/m³ assumption.
Hand calculations for 8 mm, 12 mm and 20 mm bars match the weight chart
Squaring the diameter and dividing by 162 is the whole method. Lakshmanan Sankaran, a former chief civil engineer at The Ramco Cements, works the 8 mm case on Quora: 8 × 8 = 64, and 64 ÷ 162 = 0.395 kg per metre. Amrit Steels supplies TMT bars from 8 mm to 32 mm in 12 m lengths, so the table also gives the weight per 12 m bar.
| Bar diameter | D² | D² ÷ 162 (kg/m) | Per 12 m bar by formula (kg) | Amrit Steels chart (kg/m, kg per 12 m bar) |
|---|---|---|---|---|
| 8 mm | 64 | 0.395 | 4.74 | 0.395, 4.74 |
| 12 mm | 144 | 0.889 | 10.67 | 0.888, 10.66 |
| 20 mm | 400 | 2.469 | 29.63 | 2.47, 29.64 |
Three slightly different figures for a 12 m length of 12 mm bar can all be right. Omni Calculator's worked 12 mm example, using π in full and 7850 kg/m³, gives 10.654 kg; D²/162 gives 10.67 kg; and Amrit Steels' chart lists 10.66 kg. The spread is under 0.2%, so a reviewer who questions it is asking about rounding, not method.
In a bar bending schedule, the per-metre figure multiplies the total cut length of each bar mark. Forty 12 mm bars at a 3.2 m cutting length make 128 m, and 128 × 0.889 gives 113.8 kg for that mark. For ordering, Amrit Steels' TMT bar weight chart turns the same figures into bars per tonne: roughly 94 bars of 12 mm and 34 of 20 mm.
How do you calculate an MS angle's weight without a table?
An MS angle's weight in kilograms per metre is (A + B − T) × T × 0.00785, with leg sizes A and B and thickness T in millimetres, the shortcut SteelMath's IS 808 angle weight calculator uses. Its 0.00785 is 7850 kg/m³ rescaled to one square millimetre of section over one metre of length. Any steel section weighs its cross-section area in mm² times 0.00785 kilograms per metre, and D²/162 is the special case where that area is πD²/4.
A flat bar is the simplest section to weigh
A flat's area is its width times its thickness, so a 50 × 6 mm flat holds 300 mm² of steel and weighs 300 × 0.00785 = 2.355 kg/m. Plate works the same way per square metre: one square metre at 1 mm thick is 0.001 m³ of steel, so each millimetre of thickness adds 7.85 kg/m².
Angles are two flats that overlap in one corner square
An equal angle is two legs, each leg × thickness, that overlap in one thickness × thickness square at the corner. Amardeep Steel's guide writes the equal-angle area as 2at − t², and (A + B − T) × T is the same expression with both legs written out, which is how Sachiya Steel's November 2025 MS angle weight guide presents it. For the 50 × 50 × 6 angle that Amrit Steels uses to show buyers how to specify one, the area is 94 × 6 = 564 mm², and 564 × 0.00785 comes to 4.427 kg/m, which Sachiya Steel's guide gives as 4.42.
Published angle charts sit slightly off the formula
| Equal angle (mm) | Formula weight (kg/m) | Published chart weight (kg/m) | Chart publisher |
|---|---|---|---|
| 50 × 50 × 6 | 4.42 | 4.50 | Sachiya Steel |
| 65 × 65 × 6 | 5.84 | 5.80 | Sachiya Steel |
| 75 × 75 × 6 | 6.78 | 6.77 | SteelMath (IS 808-based) |
Sachiya Steel attributes its 4.50 kg/m chart figure to the fillet radius at the inside corner, which the two-flat model leaves out. The 65 × 65 × 6 row runs the other way, with the chart lighter than the formula, and SteelMath's IS 808-based angle chart lists 75 × 75 × 6 at 6.77 kg/m, or 40.62 kg per 6 m piece, against 6.78 kg/m by formula. Because the gaps run in both directions, no single correction factor fixes the angle shortcut: use the formula for estimates and the chart value on the purchase order. Amrit Steels stocks MS angles in equal and unequal sizes, quoted by leg sizes and thickness.
Pipe weight comes from the ring of steel between two circles
An MS pipe's cross-section is the outer circle minus the inner one, π/4 × (D² − (D − 2t)²), with D the outside diameter and t the wall thickness in millimetres. Amardeep Steel's pipe formula multiplies that ring area by length and 7850 kg/m³, which per metre means ring area in mm² × 0.00785. The bracket simplifies to 4t(D − t), so the area is also π × t × (D − t), the quicker form on a site calculator.
Take a pipe measured at 50 mm outside diameter with a 3 mm wall, dimensions chosen to show the arithmetic. Its ring area is π × 3 × 47 = 443 mm², and 443 × 0.00785 gives about 3.48 kg/m, or 20.9 kg over a 6 m length. A pipe described by its outside diameter alone has no calculable weight, and Amrit Steels asks for size and wall thickness when it quotes MS pipes for sheds, railings and fabrication.
How far can delivered steel differ from its theoretical weight?
Amrit Steels' chart puts the batch tolerance on TMT bars at ±7% for 8 and 10 mm, ±5% for 12 and 16 mm, and ±3% for 20 to 32 mm. At ±5%, a metre of 12 mm bar charted at 0.888 kg can weigh from about 0.844 kg to 0.932 kg and stay within the band. Weighing a one-metre piece against that tolerance is one of the on-site checks Amrit Steels gives for confirming a bar is genuine.
Sections carry the same caveat. Sachiya Steel's guide calls its angle weights theoretical, notes that actual weight varies with rolling tolerances and points critical work to the mill test certificate. BuildingClub's steel volume-to-weight calculator adds that this kind of conversion leaves out waste, voids and product tolerances, so a theoretical weight is an estimate, not a weighbridge reading.
Amrit Steels supplies ISI-marked TMT bars made to IS 1786, and its chart weights are D²/162 values rather than figures quoted from that standard; the calculators that publish d²/162 for rebar, SteelMath among them, do not quote IS 1786 either. Amrit Steels weighs material on its own machines and customers can recheck it on public weighing scales, so keep D²/162 for the estimate and treat the weighment as the record of what arrived.
Does a higher grade of TMT bar weigh less?
A higher grade does not make a bar lighter by any amount a weight chart records. Amrit Steels' chart gives one weight per diameter, with no split by brand or between Fe 550 and Fe 550D.
Omni Calculator's density table lists carbon steels, from carbon tool steel to mild steel, between 7820 and 7870 kg/m³, a spread well under 1%; its mild steel entry of 7870 is a grade-table value, not the 7850 estimating convention. Stainless sits at 8030 kg/m³ in the same table, so a stainless or alloy bar needs its own data-sheet density. A stronger grade saves steel only when the design uses fewer or thinner bars.
Sources
Steel density (kg-m3.com)
Weight Formula for Steel | Steel Weight Calculator - ASC (Amardeep Steel (AMC), 2025-09-25)
Derivation of D²/162 - Unit weight of steel bar Formula - YouTube (Civil Engineering (YouTube channel), 2019-04-22)
Why is 162 used for steel weight calculation? - Quora (Quora answer by Lakshmanan Sankaran (Former Chief Civil Engineer, The Ramco Cements))
Steel Weight Calculator (Omni Calculator, 2026-08-17)
Steel Angle Weight Calculator — Equal & Unequal IS 808 Chart | SteelMath (SteelMath (calculator site; chart labelled IS 808))
MS Angle Weight Chart Guide | PDF | Pipe (Fluid Conveyance) | Steel (Sachiya Steel International Private Limited, 2025-11-15)
Steel from m³ to kg and Tonnes Calculator (BuildingClub (Misha Noyr, M.Eng.))
Frequently asked questions about steel unit weight
- What is the unit weight of steel in kg per cubic metre?
- Steel's density is 7850 kg/m³ (7.85 g/cm³) in reference tables such as Engineering ToolBox, and that is the figure people mean by steel's unit weight in kg per cubic metre. Strictly, steel's unit weight is a force per volume: about 77 to 78.5 kN/m³, depending on the value taken for g.
- Why is 162 used in the steel bar weight formula?
- The 162 in the steel bar weight formula is the reciprocal of π/4 × 7850 × 10⁻⁶, which Omni Calculator works out to 162.19 before rounding. As the Civil Engineering YouTube channel's four-step derivation shows, dividing D² by 162 turns a diameter in millimetres into kilograms per metre of solid round bar at 7850 kg/m³.
- How much does a 12 mm TMT bar weigh per metre?
- A 12 mm TMT bar weighs about 0.889 kg per metre by D²/162 (144 ÷ 162). Amrit Steels' weight chart lists a 12 mm TMT bar at 0.888 kg/m and 10.66 kg per 12 m bar, roughly 94 bars per tonne. Delivered 12 mm bars can vary within the ±5% batch tolerance Amrit Steels' chart gives for that size.
- Can I work out an MS angle's weight without a chart?
- Yes: MS angle weight in kg per metre is (Leg 1 + Leg 2 − Thickness) × Thickness × 0.00785, with all dimensions in millimetres. A 50 × 50 × 6 MS angle comes to about 4.42 kg/m by that formula, while Sachiya Steel's chart lists 4.50 kg/m because the chart allows for the corner fillet. Use the MS angle formula for estimates and the chart for orders.
- How do I find the weight of a steel pipe from its size?
- Steel pipe weight per metre is the ring area π/4 × (D² − (D − 2t)²) in mm² multiplied by 0.00785, the method in Amardeep Steel's weight guide, where D is the outside diameter and t the wall thickness. A steel pipe of 50 mm outside diameter and 3 mm wall works out to about 3.48 kg/m. Without the wall thickness, steel pipe weight cannot be calculated.
- What does a steel I-beam weigh if I know its measurements?
- A steel I-beam weighs its cross-section area in mm² times 0.00785 kg per metre, which needs four measurements: depth, flange width, flange thickness and web thickness. Add the areas of the two flanges and the web between them, then multiply by 0.00785 and the length. Rolled corner radii make the result approximate, so match the I-beam to an ISMB section table before ordering.
Send your bar bending schedule to Amrit Steels for a quote
Amrit Steels, a family-run steel business trading in Bengaluru's City Market since 1972, quotes TMT bars, angles, channels, beams and pipes against a bar bending schedule or structural drawing. Send the schedule with your hand-calculated weights and ask Amrit Steels for the day's rate; TMT arrives with test reports, and project supplies include free loading, unloading and delivery.