Governing Formula
The widely used structural-steel estimating shortcut for metric deformed bars gives the unit weight directly from the nominal diameter. It is exact only for plain round bars (density 7850 kg/m³); the d²/162 form combines the bar area and steel density.
w_unit = d² / 162 Where:
-
d= Nominal bar diameter [mm] -
w_unit= Unit weight of steel per meter (w = d²/162) [kg/m] -
L= Bar length [m] -
n= Number of bars [bars]
Derived Equations:
w_unit = d² / 162 W_bar = w_unit × L W_total = w_unit × L × n How the Calculation Works
Starting from the cross-sectional area A = (π/4) × d² and the density of structural steel (≈7850 kg/m³), the unit weight in kg/m reduces to d²/162 when the diameter is expressed in mm:
w = (π/4) × d² × 7850 / 10⁶ = d²/162 (kg/m)
The unit weight is scaled by the bar length and bar count to give the individual and total weights, with tonnage for procurement planning.
Worked Engineering Example
Design Scenario: Twenty Ø16 Bars at 12 m
- Unit weight:
w = 16² / 162 = 256 / 162 = 1.58 kg/m - Weight per bar:
W_bar = 1.58 × 12 = 18.96 kg - Total weight:
W_total = 18.96 × 20 = 379.26 kg = 0.379 tonnes
Engineering Notes & Design Benchmarks
| Bar Ø (mm) | Unit Weight (kg/m) | Typical Use |
|---|---|---|
| 8 | 0.395 | Stirrups, ties, mesh |
| 12 | 0.888 | Slabs, beams secondary |
| 16 | 1.580 | Beams, columns, footings |
| 20 | 2.469 | Main girders, heavy slabs |
| 25 | 3.858 | Columns, transfer structures |
Assumptions & Limitations
- Assumes a structural steel density of 7850 kg/m³ and round bars; deformed surface geometry is neglected in the standard shortcut.
- Does not include laps, couplers, chairs, tie wire, or gallery/merchant bar stock lengths.
- Add 2–5% for unusable offcuts and bending allowances when ordering.
Frequently Asked Questions
Why is rebar unit weight "d²/162"?
The formula derives from the bar cross-section area and steel density: w = (π/4) d² ρ / 10^6. With ρ = 7850 kg/m³ and d in mm, the constants combine to 1/162.03 ≈ 1/162.
What is a safe ordering allowance for cutting waste?
Allow roughly 2–5% over the calculated tonnage for offcuts, laps beyond drawings, splices, and site losses. For tight or heavily detailed structures use the higher end.
Does this calculator account for lapping lengths?
No. Enter the total in-place length per bar (including specified laps and anchorage/bends) as the bar length, or add a lap allowance separately on top of the calculated tonnage.
Engineering Disclaimer
Engineering Note: This calculator provides estimating weights for planning and procurement. Final tonnage and details (laps, hooks, couplers, cut lengths) must be derived from approved placing drawings and bar-bending schedules.
Technical References
- BS 4449: Steel for the Reinforcement of Concrete – Weldable reinforcing steel, BSI.
- ASTM A615/A615M: Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement.
- ACI 318: Building Code Requirements for Structural Concrete (Chapter 25 – Reinforcement Details).