Formula
W = π × d² × ρ ÷ 4000
- W
- Unit weight (kg/m)
- d
- Diameter (mm)
- ρ
- Density (g/cm³)
Multiplying the cross-section πd²/4 (mm²) by 1 m (1000 mm) gives the volume per metre (mm³). Multiplying by density (g/cm³ = 0.001 g/mm³) gives grams, and converting to kilograms gives the formula above.
Example: a 3 m length of 20 mm carbon steel bar weighs 2.466 kg/m × 3 m ≈ 7.398 kg in theory. The table is for round bar; hexagons and squares use a different cross-section.
Theoretical unit weight of round bar (kg/m)
Unit: kg/m (theoretical, rounded to three decimals) · the figure under each heading is the density used (g/cm³)
| Diameter d (mm) | Carbon steelρ 7.85 | Type 304 stainlessρ 7.93 | Type 316 stainlessρ 7.98 | Aluminum alloy (6061)ρ 2.70 | Titanium (commercially pure)ρ 4.51 |
|---|---|---|---|---|---|
| 3 | 0.055 | 0.056 | 0.056 | 0.019 | 0.032 |
| 4 | 0.099 | 0.100 | 0.100 | 0.034 | 0.057 |
| 5 | 0.154 | 0.156 | 0.157 | 0.053 | 0.089 |
| 6 | 0.222 | 0.224 | 0.226 | 0.076 | 0.128 |
| 8 | 0.395 | 0.399 | 0.401 | 0.136 | 0.227 |
| 9 | 0.499 | 0.504 | 0.508 | 0.172 | 0.287 |
| 10 | 0.617 | 0.623 | 0.627 | 0.212 | 0.354 |
| 12 | 0.888 | 0.897 | 0.903 | 0.305 | 0.510 |
| 14 | 1.208 | 1.221 | 1.228 | 0.416 | 0.694 |
| 16 | 1.578 | 1.594 | 1.604 | 0.543 | 0.907 |
| 18 | 1.998 | 2.018 | 2.031 | 0.687 | 1.148 |
| 20 | 2.466 | 2.491 | 2.507 | 0.848 | 1.417 |
| 22 | 2.984 | 3.014 | 3.033 | 1.026 | 1.714 |
| 25 | 3.853 | 3.893 | 3.917 | 1.325 | 2.214 |
| 28 | 4.834 | 4.883 | 4.914 | 1.663 | 2.777 |
| 30 | 5.549 | 5.605 | 5.641 | 1.909 | 3.188 |
| 32 | 6.313 | 6.378 | 6.418 | 2.171 | 3.627 |
| 35 | 7.553 | 7.630 | 7.678 | 2.598 | 4.339 |
| 38 | 8.903 | 8.994 | 9.050 | 3.062 | 5.115 |
| 40 | 9.865 | 9.965 | 10.028 | 3.393 | 5.667 |
| 45 | 12.485 | 12.612 | 12.692 | 4.294 | 7.173 |
| 50 | 15.413 | 15.571 | 15.669 | 5.301 | 8.855 |
| 55 | 18.650 | 18.840 | 18.959 | 6.415 | 10.715 |
| 60 | 22.195 | 22.422 | 22.563 | 7.634 | 12.752 |
| 65 | 26.049 | 26.314 | 26.480 | 8.959 | 14.966 |
| 70 | 30.210 | 30.518 | 30.711 | 10.391 | 17.357 |
| 75 | 34.680 | 35.034 | 35.255 | 11.928 | 19.925 |
| 80 | 39.458 | 39.861 | 40.112 | 13.572 | 22.670 |
| 85 | 44.545 | 44.999 | 45.283 | 15.321 | 25.592 |
| 90 | 49.940 | 50.448 | 50.767 | 17.177 | 28.691 |
| 95 | 55.643 | 56.210 | 56.564 | 19.138 | 31.968 |
| 100 | 61.654 | 62.282 | 62.675 | 21.206 | 35.421 |
| 110 | 74.601 | 75.361 | 75.836 | 25.659 | 42.860 |
| 120 | 88.781 | 89.686 | 90.252 | 30.536 | 51.007 |
| 130 | 104.195 | 105.257 | 105.920 | 35.838 | 59.862 |
| 140 | 120.841 | 122.073 | 122.843 | 41.563 | 69.426 |
| 150 | 138.721 | 140.135 | 141.018 | 47.713 | 79.698 |
| 160 | 157.834 | 159.442 | 160.447 | 54.287 | 90.679 |
| 180 | 199.758 | 201.794 | 203.066 | 68.707 | 114.766 |
| 200 | 246.615 | 249.128 | 250.699 | 84.823 | 141.686 |