Section weight: theoretical geometry versus published mass
A weight estimate must state whether it comes from ideal geometry and density or from a published standard-section mass. Rolled flanges, radii and manufacturing tolerances make these different methods; never replace a tabulated section mass with a simplified sketch area.
Worked numbers are illustrative. Use your own operating conditions and documented material/process data.
Required inputs
- Custom dimensions or an exact available standard designation.
- Material density for theoretical geometry; length per piece and quantity.
- Units and whether coatings, holes, welds or tolerances are included.
Governing equations
Custom section: A = πd²/4 for a solid round bar
m′(kg/m) = ρ A(mm²) × 10⁻⁶
mpiece = m′ L(m); mtotal = n mpiece
Variables and units
- A: mm²; ρ: kg/m³; m′: kg/m; L: m; n: piece count.
- For a published record, use its tabulated m′ rather than recalculating it from nominal density.
Assumptions
- Uniform cross-section along each length.
- Custom density in the example is an illustrative entered 7850 kg/m³, not a certificate.
Calculation workflow
- Choose theoretical/custom or published-standard basis before entering dimensions.
- Convert length into metres and calculate each item separately.
- Sum item masses in the project list; report allowances or scrap separately.
Worked example
- Custom round bar d = 25 mm: A = 490.873852 mm²; at ρ = 7850 kg/m³, m′ = 3.853360 kg/m.
- Three 2 m pieces have volume 0.002945243 m³ and total mass 23.120158 kg.
- Existing SAIL ISMC 100 record instead uses 9.56 kg/m: three 2 m pieces total 57.36 kg, without substituting a theoretical density result.
Limitations
- Structural capacity and cut optimization are NOT EVALUATED.
- Other catalogue families remain unavailable until actual records are supplied; custom geometry is not a substitute for a verified rolled designation.
Common mistakes
- Using mm length directly with kg/m.
- Counting quantity twice after entering a combined total length.
- Treating sharp-corner geometry as the mass of a rolled standard section.
Practical interpretation
The two cases illustrate different section bases, not interchangeable masses. A cut list is an arithmetic quantity list: it does not establish nesting, kerf, available stock lengths or a waste-minimizing cutting plan.
Related formulas
The governing equations, units and calculation steps above provide the formula basis for this guide. The related workspace also shows its calculation trace.
Dimensional and unit bases →Section geometry reference
Shapes & Sections — dimensions and section-area relationships →Related workspace
Open Materials & Shape Weight →Sources and reference basis
Equations and worked examples are independently explained here. References reviewed 2026-10-17; no copyrighted standard tables are reproduced.