Standard Rebar Weight Formulas and Derivations (d²/162)
The one-line rule W = d² / 162 (kg per metre, diameter d in mm) is the workhorse
of reinforcement estimating. This page derives it from first principles, shows where the 162
comes from, and lists the nominal values for the standard metric bar sizes — the same constant
used in the
Rebar Weight calculator.
1. Start from density, not from memory
Structural steel has a nominal density of 7850 kg/m³. A straight bar of diameter d (mm) is a cylinder, so its mass per unit length is the cross-sectional area times the density:
W (kg/m) = A × 7850
Expanding the constant: (π/4) × 7850 × 10−6 = 0.0061652..., and 1 / 0.0061652... = 162.2. That is the whole origin of the memorized 162:
The estimation engine in steel weight estimating uses the exact product of area × 7850; the rebar rule uses the rounded d²/162 form. The two agree to better than 0.2% for every practical diameter.
2. Nominal values for standard sizes
Rounded to three decimals, W = d²/162 gives the nominal kg/m for each size class. Metric and ASTM equivalent sizes are conventionally mapped to the same nominal mass per metre.
| Bar diameter d (mm) | d² | d² / 162 (kg/m) | ASTM size (approx.) |
|---|---|---|---|
| 8 | 64 | 0.395 | #3 (10 mm) |
| 10 | 100 | 0.617 | #3 (10 mm) |
| 12 | 144 | 0.888 | #4 (13 mm) |
| 16 | 256 | 1.580 | #5 (16 mm) |
| 20 | 400 | 2.469 | #6 (19 mm) |
| 25 | 625 | 3.858 | #8 (25 mm) |
| 32 | 1024 | 6.321 | #10 (32 mm) |
Units matter more than memory: the rule produces kilograms per metre, so a 6 m length of 12 mm bar is 6 × 0.888 = 5.33 kg, and a 1,000 m bar or bar-equivalent length is simply the kg/m value × 1,000.
3. Assumptions and honest limits
The d²/162 rule assumes plain solid circular nominal bars at 7850 kg/m³. Real rolled rebar carries deformations (ribs), which are accounted for in the published nominal masses that the rule reproduces; asking an engineer is always safer than trusting a rib-only section. The rule is linear mass only — for slabs, footings, or columns multiply by the cut length; for total weight add laps, hooks, and couplers separately. When a project specification has its own schedule of masses, use that in preference to the textbook constant.