Steel Weight Formula D²/162: Derivation, Weight Table and Example

The weight of a steel bar in kg per metre is D²/162, where D is the bar diameter in mm. For example, a 12 mm bar weighs 12²/162 = 0.889 kg/m, so a standard 12 m length weighs about 10.67 kg. The formula comes straight from the density of steel, 7850 kg/m³, and is accurate to within about 0.1% of the exact value.

This one formula is used every day on Indian sites for BBS, ordering steel, checking supplier bills and spotting under-weight bars. Below is the derivation, a full table and worked examples.

Derivation of D²/162

Take a round bar of diameter D (mm) and length 1 m.

1. Cross-sectional area = πD²/4 mm² = πD²/4 × 10⁻⁶ m².
2. Volume of 1 m length = πD²/4 × 10⁻⁶ × 1 = πD²/4 × 10⁻⁶ m³.
3. Mass = volume × density = πD²/4 × 10⁻⁶ × 7850 kg.
4. π × 7850 / (4 × 10⁶) = 0.0061654.
5. So mass per metre = 0.0061654 D² = D² / 162.2. This is rounded to D²/162.

Because 162 is slightly smaller than 162.2, the formula overestimates by about 0.12%, which is negligible. If you prefer kg per foot, multiply by 0.3048: D²/162 × 0.3048 = D²/531.5. This is often quoted loosely as D²/533.

Steel weight table: 6 mm to 32 mm

Quick memory aid: 10 mm ≈ 0.62 kg/m, 12 mm ≈ 0.89, 16 mm ≈ 1.58, and 20 mm ≈ 2.47. Doubling the diameter makes the bar four times heavier (8 mm 0.395 → 16 mm 1.58).

Bundle counts (typical, check with your dealer)

TMT bars of 8–20 mm are usually sold in bundles of roughly 45–60 kg so that two workers can carry them; large diameters are often single bars. Bundle size is not fixed by the code and varies by brand and plant. The counts below are common in the Indian market. Bundle weights are calculated with D²/162 on 12 m bars.

6 mm is mostly sold as coils or loose by weight. Always count bars, not bundles, when receiving material.

Worked example 1: steel for a slab and beams

From a BBS you have: 120 bars of 12 mm, each 6.5 m long, and 25 bars of 16 mm, each 9 m long.

1. 12 mm total length = 120 × 6.5 = 780 m.
2. 12 mm unit weight = 12²/162 = 144/162 = 0.889 kg/m.
3. 12 mm weight = 780 × 0.8889 = 693.3 kg.
4. 16 mm total length = 25 × 9 = 225 m.
5. 16 mm unit weight = 16²/162 = 256/162 = 1.580 kg/m.
6. 16 mm weight = 225 × 1.5802 = 355.6 kg.
7. Total = 693.3 + 355.6 = 1048.9 kg ≈ 1.05 tonnes, before wastage.

Ordering: a 12 m bar gives only one 6.5 m piece (5.5 m left over) and one 9 m piece (3 m left over). Unless the offcuts are used for shorter bars, you need 120 + 25 bars, not 780/12 = 65 + 225/12 ≈ 19. This is why a cutting plan matters. With a good plan, allow about 3–5% for cutting wastage (a common assumption; it varies with the job). See our BBS guide and steel quantity guide.

Worked example 2: length from weight

Rearranging gives length (m) = weight (kg) × 162 / D².

You received 2 tonnes of 10 mm bars. Length = 2000 × 162 / 10² = 324000 / 100 = 3240 m, which is 3240 / 12 = 270 bars of 12 m. If the count is far below 270, the bars are heavier than nominal (you are paying for extra steel by weight). If the count is far above, they are under-weight.

Worked example 3: checking an under-weight bar

Bars are sold by weight, but they are designed by area. An under-weight bar has less steel area than the design assumed. IS 1786 allows a small mass tolerance. The batch tolerance is about ±7% for bars up to 10 mm, ±5% for over 10 up to 16 mm, and ±3% above 16 mm. Confirm the exact figures for your contract.

1. Theoretical weight of a 12 m, 12 mm bar = 12 × 0.888 = 10.66 kg (IS nominal; D²/162 gives 10.67 kg).
2. Bars weighed at site: average 10.2 kg.
3. Deviation = (10.2 − 10.66) / 10.66 × 100 = −4.3%. This is within ±5%, so acceptable.
4. If the average were 10.0 kg: (10.0 − 10.66) / 10.66 × 100 = −6.2%. This is outside ±5%, so stop and take it up with the supplier, and get lab tests.

Weigh at least 3–5 full bars of each diameter from different bundles (cut ends straight), on a calibrated scale.

Where the formula is used

• Converting BBS lengths into kg for ordering and billing.
• Estimating steel for a house. Our house estimator does this automatically from member sizes.
• Checking supplier invoices: theoretical weight vs actual weighbridge weight.
• Exams: PSC, SSC JE and diploma papers regularly ask "weight of 1 m of 16 mm bar".

Site tips

• D must be in mm and the answer is in kg/m. Do not put D in cm or inches.
• Agree in the purchase order whether billing is by actual weight or by theoretical weight. Many disputes start here.
• Stirrups use small diameters but many pieces. Their weight adds up, so do not skip them in estimates.
• Laps, hooks and bends add length. Include them in the BBS before converting to weight.
• The formula applies to all round steel bars (mild steel, Fe415, Fe500, Fe550), because density does not change with grade.