Unit Weight of Steel Bar (D²/162 Formula + Full Chart)

The unit weight of a steel bar is D²/162 kg per metre, where D is the bar diameter in mm — so an 8 mm bar weighs 0.395 kg/m, a 12 mm bar 0.888 kg/m and a 16 mm bar 1.58 kg/m. This one formula quantifies every reinforcement estimate, checks every steel bill, and settles every bar-bending-schedule total on an Indian site. The complete chart is below, followed by the derivation (so you can trust it), the IS 1786 tolerances (so you can argue a bill correctly), and worked examples for slabs, columns and full houses.

Steel bar unit weight chart

(Bundle counts are the common market convention — bundles are made up to a liftable ~50 kg — and can vary by mill.)

6 mm

0.222 kg/m

8 mm

0.395 kg/m

10 mm

0.617 kg/m

12 mm

0.888 kg/m

16 mm

1.58 kg/m

20 mm

2.469 kg/m

25 mm

3.858 kg/m

32 mm

6.321 kg/m

Doubling the diameter quadruples the weight (compare 8 mm at 0.395 with 16 mm at 1.58). This quadratic growth is why substituting 'slightly bigger' bars quietly wrecks steel budgets.

6 mm

0.222

8 mm

0.395

10 mm

0.617

12 mm

0.888

16 mm

1.580

20 mm

2.469

25 mm

3.858

32 mm

6.321

From D²/162. The curve is quadratic, not linear — going from 12 mm to 25 mm makes the bar over FOUR times heavier, not twice. This is why substituting a 'close enough' size wrecks a steel estimate.

The D²/162 formula — where it comes from

Nothing about the formula is a mystery; it's the volume of a cylinder times the density of steel, compressed into site-friendly form.

Steel's density is 7,850 kg/m³ (the value IS 875 and structural practice use). For a round bar of diameter D mm, the cross-section area is (π/4)·D² mm². Converting units for a 1-metre length:

Weight per metre = (π/4) × D² × 7850 / 10⁶   kg
                 = D² × 0.0061654            kg
                 = D² / 162.2                kg  ≈  D²/162

Example — 12 mm bar: 12²/162 = 144/162 = 0.888 kg/m. A full 12 m factory length weighs 0.888 × 12 = 10.66 kg.

The "162" is just 1/0.0061654 rounded — using 162 instead of 162.2 overstates weight by about 0.15%, far inside rolling tolerance, which is why the site version of the rule drops the decimals.

The foot version and other variants

• Per foot: D²/533 kg (because 1 m = 3.281 ft; 162.2 × 3.281 ≈ 533). A 12 mm bar = 144/533 = 0.27 kg/ft.
• Per full bar: D² × 12/162 = D²/13.5 kg per 12 m length. A 16 mm bar: 256/13.5 = 18.96 kg.
• Bars per tonne (12 m): 1000 ÷ (D²/13.5) = 13,500/D². For 8 mm: ≈ 211 bars; 10 mm: 135; 12 mm: ≈ 94; 16 mm: ≈ 53; 20 mm: ≈ 34; 25 mm: ≈ 22.

IS 1786 tolerance — why delivered weight ≠ chart weight

Rolled bars are never perfectly nominal. IS 1786 (the Indian standard for high-strength deformed bars) permits the following tolerance on mass per metre:

Three practical consequences:

1. Billing follows the weighbridge, not bar counts — and that's legitimate. A "1 tonne" delivery of 8 mm bars may contain anywhere from ~197 to ~227 bars and still comply.
2. Persistent one-sided lightness is a red flag. Tolerance is a band, not a target; re-rollers running consistently at −6% to −7% are selling you air. Weigh a sample bundle against the chart once per supplier.
3. Your estimate should still use nominal weights. Design and BBS math use D²/162; tolerance is a procurement reality, not an estimating input. Add the customary 3–5% for cutting wastage and laps instead.

Worked examples

1. Slab steel check. A 12 ft × 15 ft room slab uses 8 mm @ 125 c/c main and 8 mm @ 150 c/c distribution. From the slab reinforcement calculator, total length ≈ 248 m → 248 × 0.395 = 98 kg, plus ~30% extras (top steel at supports, chairs, laps) ≈ 127 kg. If the contractor's bill claims 200 kg for this room, the formula just paid for itself.

2. Column cage. One 230 × 300 column, 3 m storey, 6 × 16 mm verticals + 8 mm stirrups @ 150: verticals 6 × 3.6 m (with lap allowance) × 1.58 = 34.1 kg; stirrups ≈ 21 pieces × 1.22 m × 0.395 = 10.1 kg → ≈ 44 kg per column per floor.

3. Whole-house tonnage. Thumb rule 3.5–4.5 kg/sq ft of built-up area (details): a 1,200 sq ft G+1 house → 4.2–5.4 t. At ₹57/kg (current rates) that's ₹2.4–3.1 lakh — steel is usually the second-largest single line in the budget after cement.

4. Bundle sanity check at delivery. Two bundles of 12 mm should weigh ≈ 2 × 5 × 10.66 = 106.6 kg. Weighbridge says 101 kg → −5.3%, right at the IS limit for 12 mm. Accept, but note the supplier; three deliveries all at the floor of the band deserve a conversation.

How much steel per cubic metre of concrete?

For estimates before a bar schedule exists, Indian residential practice uses these ranges (kg of steel per m³ of concrete):

Multiply element concrete volumes by these densities, sum, add 3–5% wastage — that's the procurement tonnage. The full detailing rules that generate these densities are on reinforcement details for column, beams and slab.

Reading weight off a mill test certificate

Every branded TMT delivery can (and should) come with a mill test certificate (MTC) for its cast/lot. Alongside chemistry and strength results, the MTC lists the measured mass per metre for the lot — e.g. "12 mm: 0.876 kg/m" — and that number is the honest bridge between the chart and your weighbridge slip:

• Chart (nominal): 0.888 kg/m. MTC (actual): 0.876 kg/m → the lot runs 1.35% light, well inside the ±5% band.
• Expected delivered weight for 94 bars: 94 × 12 × 0.876 = 988 kg — so a weighbridge reading of ~990 kg is exactly right, and one of 940 kg is not explained by tolerance.

Asking for the MTC does more than settle weight questions: it confirms the grade (Fe 500D vs Fe 500 changes ductility, not weight) and proves the bundle tags belong to a real lot — useful in markets where brand tags get recycled.

From weights to a bar bending schedule (BBS)

The unit-weight chart becomes money through the BBS — the sheet that converts drawings into kilograms. The arithmetic chain for every bar mark:

1. Cutting length from geometry (member length − covers + hooks/bends; for stirrups see the cutting length guide).
2. Number of bars from spacing: (span ÷ spacing) + 1.
3. Length × count × D²/162 = weight for that mark.
4. Sum all marks per diameter → order list by diameter (dealers price per size).

Two BBS habits protect the budget. Group cut lengths so 12 m stock divides with minimum offcut (a 3.9 m bar cuts 3 per length with 0.3 m waste; a 4.1 m bar cuts 2 with 3.8 m waste — same design intent, wildly different wastage). And record laps explicitly: every lap of 50d on a 16 mm bar is 0.8 m × 1.58 = 1.26 kg of pure overlap, which is why lap planning is a weight item, not just a detailing rule.

Does rust change the weight?

Practically, for sound bars: no. Mill scale and light surface rust are microns thick; the mass change is far below weighbridge resolution, and light rust is actually acceptable for bond per long-standing site practice — loose, flaky rust must be brushed off before casting. What does change weight noticeably is heavy pitting corrosion from months of unprotected open storage: pitted bars lose section (strength) before they lose meaningful weight, so the correct response to visibly pitted steel is rejection on engineering grounds, not a billing adjustment. Store bars off the ground on sleepers, covered, and this never becomes a question.

Chart in feet (for footage-based estimates)

Some older estimators and most fabricators still measure in feet. Same bars, per-foot weights (D²/533):

Mild steel, binding wire and structural sections

The D²/162 rule applies to any round steel bar, TMT or mild steel, because it's pure geometry × density. Related weights that show up in the same estimate:

• Binding wire: ordered by weight directly; the thumb allowance is 8–12 kg per tonne of reinforcement.
• MS square bar (side S mm): S²/127 kg/m (square section, same density).
• MS flat (W × T mm): W × T / 127.3 kg/m — a 50 × 6 flat is 2.36 kg/m.
• Structural sections (ISMB/ISA/ISMC): use the IS handbook weights — an ISMB 200 is 25.4 kg/m by section tables, not by any simple formula.

Grade changes strength, not weight

A recurring site confusion: Fe 500, Fe 500D and Fe 550D bars of the same diameter weigh the same. Grade describes yield strength (500 vs 550 MPa) and ductility (the "D"), which come from chemistry and the quenching process — not from putting more steel in the bar. So a higher-grade quote at the same per-kg rate is genuinely better value structurally, and no grade choice will rescue an estimate that used the wrong diameters. Choose grade with your engineer (Fe 500D is the common residential specification; seismic zones often prefer 550D's ductility), and choose tonnage with this page's charts — the two decisions are independent.

Why the chart matters more than the price chart

Buyers spend hours comparing per-kg rates across brands and minutes checking quantity — which is backwards. A ₹2/kg rate negotiation on a 4-tonne house order saves ₹8,000. Getting the tonnage right — ordering 4.0 t because the bar schedule says 4.0 t, rather than 4.6 t because somebody rounded soot sizes up and added "thoda extra" — saves ₹34,000 at the same rate. The unit-weight chart is where that money lives.

The same asymmetry runs through the whole steel line of a budget. Diameter errors are quadratic (a 16 mm bar where a 12 mm was designed carries 78% more weight and cost); spacing errors are linear; rate errors are trivial by comparison. Spend your attention in that order.

Why your delivered weight never matches the chart exactly

Steel is sold by weight and used by length, and those two facts do not reconcile as cleanly as the D²/162 table suggests. A bundle billed as 1,000 kg of 12 mm will not contain exactly 1,126 metres.

IS 1786 permits a rolling tolerance on mass per metre — ±7% for bars up to 10 mm, ±5% for 12–16 mm, and ±3% for 20 mm and above, measured on individual samples, with a tighter limit on the batch average. A mill rolling consistently at the light end of tolerance is not cheating; it is operating inside the standard. But across a 6-tonne order for a house, 3% is 180 kg of steel you paid for and did not receive as length.

This is why the chart weight is the basis of the estimate, not an acceptance test. What protects you is checking the actual delivery:

• Weigh a known length. Cut a clean 1 m sample, weigh it, compare against the chart. Do this per diameter, per delivery — it takes ten minutes.
• Read the test certificate. The mill's TC states actual mass per metre for the heat. A supplier who cannot produce one for the batch on your site is a supplier to walk away from.
• Count the bars. If you ordered by weight, the bar count tells you what you actually got. 1,000 kg of 12 mm should be about 94 bars of 12 m (10.66 kg each). Eighty-eight bars means the bars are heavy or short — either way, ask.

None of this matters much on a bathroom slab. On a full house it is a few thousand rupees, and on anything larger it is the difference between an estimate and a guess.

Frequently asked questions

What is the unit weight of an 8 mm steel bar? An 8 mm bar weighs 0.395 kg per metre, or about 4.74 kg per standard 12 m length.

What is the formula for steel bar weight? Weight in kg per metre = D²/162, where D is the diameter in mm. For a full bar multiply by its length (standard factory length is 12 m).

How many 12 mm bars are in one tonne? One 12 m long 12 mm bar weighs 10.66 kg, so one tonne has about 94 bars.

Why is my delivered steel weight different from the chart? IS 1786 permits a rolling tolerance of ±3–7% depending on diameter, so actual weight differs slightly from theoretical. Billing follows the weighbridge slip — but consistent lightness at the bottom of the band is worth challenging.

Where does the 162 in D²/162 come from? From steel's density: (π/4) × 7,850 kg/m³ converted to mm-and-metre units gives D² × 0.0061654 kg/m, and 1/0.0061654 ≈ 162.2 — rounded to 162 for site use.

What is the weight of a 16 mm bar? 1.58 kg per metre, 18.96 kg per 12 m bar; about 53 bars per tonne.

Does the formula work for mild steel and stainless bars? For mild steel yes (same 7,850 kg/m³ density). Stainless grades run slightly denser (~7,900–8,000 kg/m³), so add roughly 1–2% if you ever price stainless rebar.

How much extra steel should I order over the calculated weight? 3–5% covers cutting wastage and non-schedule laps on a typical house; complex shapes with many short bars waste more than long straight runs.

What lengths do steel bars come in? The standard factory length is 12 m; many dealers also stock 9 m, and some markets cut 6 m for retail. Confirm the length behind any per-piece price — a "cheap rod" is sometimes just a shorter rod.

What is the weight of a 6 mm bar, and where is it used? 0.222 kg/m (2.66 kg per 12 m). Its structural use has shrunk — 8 mm is today's minimum for most slab steel — but 6 mm survives in chairs, spacers, fan hooks and light fabrication.

How do I quickly estimate stirrup steel for a beam? Stirrup count × cutting length × 0.395 (for 8 mm). A 4 m beam with stirrups at 150 c/c and 1.2 m cutting length: 28 × 1.2 × 0.395 ≈ 13 kg — a number you can produce at the tea stall faster than the contractor can object to it.

Why do engineers memorise 0.395, 0.617 and 0.888? Because 8, 10 and 12 mm bars make up the bulk of a house's steel, those three per-metre weights — plus 1.58 for 16 mm — cover 90% of everyday mental checks without a calculator.

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• Steel Price Per Kg
• TMT Steel Price List (All Brands)
• Slab Reinforcement Calculator
• Cutting Length of Stirrups
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