Steel weight calculation: plate, bar, pipe and section
Every steel weight calculation is the same two steps: find the volume, then multiply by density. Get the density right, keep your units in metres, and a plate, a bar, a pipe or a beam all fall out of one formula. Here is that formula for each shape, with worked numbers you can trust for costing and RFQs.
The one rule behind every shape
Weight is volume times density. For steel the density is the number to memorise:
- Mild / carbon steel: 7850 kg/m³ (7.85 g/cm³)
So the master formula is Weight (kg) = Volume (m³) × 7850. Everything else is just working out the volume of the shape in front of you. The single most common error is mixing millimetres and metres, so decide on metres for the final volume and convert every dimension before you multiply.
Steel plate and sheet
A plate is a rectangular block, so the volume is length × width × thickness. Convert all three to metres and multiply by 7850.
Formula: Weight = L × W × t × 7850, with L, W and t in metres.
Example. A mild-steel plate 2 m × 1 m × 10 mm:
- Volume = 2 × 1 × 0.010 = 0.020 m³
- Weight = 0.020 × 7850 = 157 kg
A handy shortcut for sheet: weight per square metre = thickness in mm × 7.85. So 10 mm plate is 78.5 kg/m², and the 2 m² plate above is 2 × 78.5 = 157 kg, matching exactly.
Round bar and square bar
For a round bar the cross-section is a circle, so volume per metre is π/4 × D². Combine that with 7850 and it collapses to a shop-floor classic:
Round bar, weight per metre = D² / 162, with D in millimetres.
The 162 is simply 4 × 10&sup6; / (π × 7850), rounded. It is exact enough for quoting.
Example. A 25 mm round bar: 25² / 162 = 625 / 162 = 3.86 kg/m. A 6 m length weighs 23.1 kg.
For a square bar of side A (mm), the area is A² instead of π/4×D², so the divisor changes: weight per metre = A² / 127. A 25 mm square bar is 625 / 127 = 4.92 kg/m.
Pipe and hollow tube
A pipe is a bar with the centre removed, so subtract the bore. The clean version uses outside diameter and wall thickness:
Pipe, weight per metre = (OD − t) × t × 0.02466, with OD and t in millimetres.
The constant 0.02466 is π × 7850 / 10&sup6;. It already carries the density.
Example. A 60.3 mm OD pipe (2 inch NB) with 3.9 mm wall: (60.3 − 3.9) × 3.9 × 0.02466 = 56.4 × 3.9 × 0.02466 = 5.42 kg/m.
Angle, channel and standard sections
Rolled sections such as equal angles, channels and I-beams have areas that are not simple rectangles, so for these you take the weight per metre straight from the mill's section table rather than computing it by hand. Two routes work in practice:
- From the section table: an ISA 50×50×6 equal angle is listed at 4.5 kg/m; multiply by length.
- From area: if you have the cross-sectional area A in mm², then weight per metre = A × 7850 / 10&sup6; = A × 0.00785.
For an angle you can also approximate the area as (leg1 + leg2 − thickness) × thickness, which is close for equal-thickness legs.
When it is not mild steel
Only the density changes; the geometry stays identical. Swap 7850 for the right value:
| Material | Density (kg/m³) | Factor vs mild steel |
|---|---|---|
| Mild / carbon steel | 7850 | 1.000 |
| Stainless 304 / 316 | 8000 | 1.019 |
| Cast iron | 7200 | 0.917 |
| Aluminium 6061 | 2700 | 0.344 |
| Brass | 8500 | 1.083 |
| Copper | 8960 | 1.141 |
To convert a mild-steel answer, just multiply by the factor. A steel bar that weighs 3.86 kg/m becomes 3.86 × 1.019 = 3.93 kg/m in 316 stainless.
Common mistakes
- Unit mixing. Leaving thickness in mm inside a metre-based volume. Convert every dimension first.
- Wrong density. Using 7850 for stainless or aluminium. A 6061 part is only about a third of the steel weight.
- Forgetting the bore. Treating a pipe as a solid bar overstates weight badly; always subtract the inside.
- Using OD twice for pipe. The mean diameter (OD − t) is what carries the metal, not the full OD.
- Ignoring mill tolerance. Plate thickness can run under nominal, so a theoretical weight is an estimate, not a weighbridge reading.
Frequently asked questions
What density do I use for steel?
Use 7850 kg/m³ for mild and carbon steel. Stainless is about 8000, cast iron about 7200. The geometry formulas do not change, only the density.
Where does the D²/162 bar formula come from?
It is π/4 × D² (area) × 7850 (density) with unit conversions folded in. The divisor 162 gives kilograms per metre directly from a diameter in millimetres.
How do I weigh a pipe quickly?
(OD − wall) × wall × 0.02466 gives kg per metre. It subtracts the bore automatically, so you never treat a pipe as a solid bar.
Is theoretical weight the same as actual weight?
No. Rolling tolerances, mill scale and cut-length variation mean the weighbridge reading differs by a percent or two. Theoretical weight is for costing and estimating, not certification.