Governing Formula
The weight of any steel member is the product of its volume and the density of structural steel (≈ 7,850 kg/m³). For prismatic members this reduces to the cross-sectional area times the length times the density.
W = A × L × ρ Where:
-
ρ= Density of structural steel [7,850 kg/m³] -
A= Cross-sectional area of the section (per shape geometry) [mm²] -
w= Unit weight per meter of length (w = A × ρ) [kg/m] -
L= Length of a single member [m] -
n= Number of identical members [pieces]
Derived Equations:
A_bar = (π/4) × d² A_pipe = (π/4) × (OD² – ID²) A_square = s² A_plate = b × t W_total = w × L × n How the Calculation Works
The calculator first derives the cross-sectional area from the geometry of the selected shape: a round bar from its diameter, a pipe from its outside diameter and wall thickness, a square bar from its side, and a plate from its breadth and thickness. For standard rolled sections, the area step is replaced by the catalog unit weight you supply.
The area (converted to m² by ×10⁻⁶) is multiplied by the steel density to obtain the unit weight in kg/m. Scaling by the member length and the number of identical members gives the total weight, with a metric tonne equivalent for procurement and transport planning.
Worked Engineering Example
Design Scenario: Four Ø20 mm Round Bars at 12 m
- Cross-section area:
A = (π/4) × 20² = 314.16 mm² - Unit weight per meter:
w = 314.16 × 10⁻⁶ × 7,850 = 2.47 kg/m - Total weight for 4 bars at 12 m:
W = 2.47 × 12 × 4 = 118.34 kg = 0.118 tonnes
Engineering Notes & Design Benchmarks
| Ø20 Round Bar (kg/m) | 300×10 Plate (kg/m) | 100×5 Pipe (kg/m) |
|---|---|---|
| 2.47 (A615 Grade 60) | 23.55 (A36 plate) | 11.71 (ASTM A53) |
| ≈ d²/162 shortcut | 0.3 × 0.01 × 7,850 | (π/4) × (0.1² − 0.09²) × 7,850 |
All section weights use the structural steel density of 7,850 kg/m³ consistent with ASTM and AISC practice. For reinforcement, deformed geometry is neglected in this density-based estimate — the small extra steel in the lugs is offset by manufacturing tolerances.
Assumptions & Limitations
- Assumes a uniform structural steel density of 7,850 kg/m³; alloys with different densities (stainless ≈ 8,000 kg/m³) require an adjustment.
- For pipes, the ID is derived as OD − 2t; threaded, socketed, or lined ends are not included.
- Standard-section results depend entirely on the catalog unit weight you enter — verify it against the relevant standard table.
- Add 2–5% for cutting waste, laps, and coating when ordering; weight alone is not a substitute for a bar-bending schedule.
Frequently Asked Questions
Why is a Ø20 mm round bar about 2.47 kg/m?
Its area is (π/4) × 20² = 314.16 mm². Converting to m² (×10⁻⁶) and multiplying by 7,850 kg/m³ gives 2.47 kg/m — equivalent to the familiar d²/162 shortcut used for rebar.
What density should I use for steel?
Structural carbon steel is 7,850 kg/m³ per ASTM A36/A615 practice. Stainless steels run about 7,900–8,100 kg/m³ and aluminum about 2,700 kg/m³. Entering a custom material in the companion Material Quantity calculator lets you vary the density.
Does this calculator replace a steel takeoff from drawings?
It provides fast section weights for estimates. For reinforcement, a bar-bending schedule derived from placing drawings is the authoritative quantity, including laps, hooks, couplers, and chairs that a density-based estimate does not capture.
Engineering Disclaimer
Engineering Note: This calculator provides estimating weights for planning and procurement. Final tonnage and details (laps, hooks, cut lengths, coatings) must be derived from approved placing drawings and section tables, and verified by a qualified engineer.
Technical References
- ASTM A615/A615M: Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement, ASTM International.
- ASTM A36/A36M: Standard Specification for Carbon Structural Steel (plates, shapes, and bars), ASTM International.
- AISC Steel Construction Manual, American Institute of Steel Construction.