Area and linear mass
Area is assembled from solid geometry or calculated by subtracting the idealized inner void. Linear mass uses the entered density: m′ = Aρ with the required unit conversion.
INDUNECT / KNOWLEDGE / RF-002DERIVED REFERENCE
Section properties.
From geometry, visibly.
Generate idealized geometric properties for five common symmetric section shapes. Every result comes from the dimensions you enter—never from a copied manufacturer or standards table.
FORMULA DERIVEDFIVE SHAPESNO CATALOGUE SERIES
01REFERENCE SCOPE
IDEALIZED CROSS-SECTIONS
Compare stiffness geometry before selecting a real profile.
Use these values for preliminary comparison and transparent hand-checks. Catalogue values can differ because real rolled and hollow sections include root radii, rounded corners, tapers, manufacturing tolerances, and product-specific geometry.
INPUT / SECTION GEOMETRY
SELECTED PROFILEIdealized I / H section
Geometry boundary
Parallel flanges, centred web, sharp internal corners, and equal top/bottom flange dimensions. Root radii and flange taper are excluded.
CALCULATION STATUSI / H SECTION READY
RF-002- Cross-sectional area
- 5,808 mm² A
- Mass per metre
- 45.593 kg/m m′ = A · ρ
- Major-axis second moment
- 88.709 × 10⁶ mm⁴ Iₓ
- Minor-axis second moment
- 6.762 × 10⁶ mm⁴ Iᵧ
- Major-axis elastic modulus
- 591.395 × 10³ mm³ Wₓ = Iₓ / cᵧ
- Minor-axis elastic modulus
- 90.157 × 10³ mm³ Wᵧ = Iᵧ / cₓ
- Major-axis radius of gyration
- 123.586 mm rₓ = √(Iₓ / A)
- Minor-axis radius of gyration
- 34.121 mm rᵧ = √(Iᵧ / A)
ACTIVE GEOMETRY
A = 2bt_f + (h − 2t_f)tᵥ02FORMULA MAP
WHAT IS CALCULATED
Properties about centroidal x–x and y–y axes.
Second moment of area
Iₓ and Iᵧ describe how the cross-sectional area is distributed about each centroidal axis. They are geometric properties, not material stiffness by themselves.
Elastic section modulus
W = I/c divides the second moment by the distance to the extreme idealized fibre. The result supports elastic bending-stress checks when the loading and design method are known.
Radius of gyration
r = √(I/A) is useful in slenderness calculations. It does not independently establish a buckling resistance or effective member length.
VISIBLE SHAPE EQUATIONS
Area models used by the calculator
A = 2bt_f + (h − 2t_f)tᵥTwo flanges plus the clear webA = BH − (B − 2t)(H − 2t)Outside rectangle minus inside voidA = π(D² − dᵢ²) / 4Outside circle minus inside voidA = BHSolid rectangular areaA = πD² / 4Solid circular area03LIMITS & USE
PRELIMINARY GEOMETRY ONLY
A section property is not a member design.
Confirm the real product
Use the manufacturer’s current, authorized catalogue for actual dimensions, radii, mass, tolerances, section properties, steel grade, and product availability.
Apply the governing design method
Strength, deflection, local buckling, lateral-torsional buckling, effective lengths, shear, torsion, fatigue, connections, and fire design are outside this reference.
Treat hollow corners correctly
RHS and SHS results here use sharp idealized corners. Real cold-formed or hot-finished corner radii change area and axis properties.
Do not infer catalogue status
Entered dimensions do not imply that a standardized or commercially available section exists. This page intentionally contains no preferred section series.
04SOURCE BOUNDARY
ORIGINAL CALCULATION
Geometry derived—not a catalogue extract.
The equations are evaluated from first principles for idealized symmetric shapes using rectangle and circle area properties plus subtraction of voids. No EN, DIN, ISO, AISC, manufacturer, or commercial section-database rows are reproduced.
For a real project, take the selected product’s authoritative properties from the applicable supplier documentation and verify the governing structural or machine-design requirements.
RF-002 calculates geometry only. Units are millimetres, square millimetres, cubic millimetres, fourth-power millimetres, kilograms, and metres as labelled.