Area, centroid, moment of inertia, section moduli and radius of gyration — 503 standard steel sizes from KS / JIS, AISC, EN, BS and IS (H-beams, angles, channels, tubes), any custom shape, PSC girders and box girders. Exact polygon integration with root fillets.
Every size below loads with the root fillet or corner radius of its standard, and the properties are computed from that outline. Sections sharing the same rolled profile (KS D 3503 / JIS G 3192 / GB/T 11263 H-beams, KS D 3502 / JIS angles and channels) are listed once. AISC shapes are in inches on the label and millimetres in the model; HSS use the AISC design wall thickness (0.93 tnom).
H / I beams — H-beams (Korea · Japan · China) (KS D 3503 · JIS G 3192 · GB/T 11263): H 100×100×6×8 · H 125×125×6.5×9 · H 150×150×7×10 · H 175×175×7.5×11 · H 200×200×8×12 · H 250×250×9×14 · H 300×300×10×15 · H 350×350×12×19 · H 400×400×13×21 · H 148×100×6×9 · H 194×150×6×9 · H 244×175×7×11 · H 294×200×8×12 · H 340×250×9×14 · H 390×300×10×16 · H 440×300×11×18 · H 488×300×11×18 · H 588×300×12×20 · H 100×50×5×7 · H 125×60×6×8 · H 150×75×5×7 · H 175×90×5×8 · H 198×99×4.5×7 · H 200×100×5.5×8 · H 248×124×5×8 · H 250×125×6×9 · H 298×149×5.5×8 · H 300×150×6.5×9 · H 346×174×6×9 · H 350×175×7×11 · H 396×199×7×11 · H 400×200×8×13 · H 446×199×8×12 · H 450×200×9×14 · H 496×199×9×14 · H 500×200×10×16 · H 596×199×10×15 · H 600×200×11×17 · H 700×300×13×24 · H 800×300×14×26 · H 900×300×16×28
H / I beams — W-shapes (AISC / ASTM A6 (USA)): W4×13 · W5×16 · W6×9 · W6×15 · W6×20 · W6×25 · W8×10 · W8×18 · W8×24 · W8×31 · W8×40 · W8×58 · W10×12 · W10×22 · W10×33 · W10×49 · W10×68 · W12×14 · W12×26 · W12×40 · W12×53 · W12×72 · W12×96 · W12×136 · W14×22 · W14×30 · W14×48 · W14×68 · W14×90 · W14×132 · W14×176 · W14×257 · W16×26 · W16×31 · W16×40 · W16×57 · W16×77 · W18×35 · W18×50 · W18×76 · W18×106 · W21×44 · W21×62 · W21×93 · W21×132 · W24×55 · W24×76 · W24×104 · W24×146 · W27×84 · W27×114 · W27×161 · W30×90 · W30×116 · W30×173 · W33×118 · W33×141 · W33×201 · W36×135 · W36×160 · W36×210 · W36×300 · W40×167 · W40×215 · W40×297 · W44×230 · W44×290
H / I beams — IPE (EN 10365 (Europe)): IPE 80 · IPE 100 · IPE 120 · IPE 140 · IPE 160 · IPE 180 · IPE 200 · IPE 220 · IPE 240 · IPE 270 · IPE 300 · IPE 330 · IPE 360 · IPE 400 · IPE 450 · IPE 500 · IPE 550 · IPE 600
H / I beams — HEA (EN 10365 (Europe)): HEA 100 · HEA 120 · HEA 140 · HEA 160 · HEA 180 · HEA 200 · HEA 220 · HEA 240 · HEA 260 · HEA 280 · HEA 300 · HEA 320 · HEA 340 · HEA 360 · HEA 400 · HEA 450 · HEA 500 · HEA 550 · HEA 600 · HEA 650 · HEA 700 · HEA 800 · HEA 900 · HEA 1000
H / I beams — HEB (EN 10365 (Europe)): HEB 100 · HEB 120 · HEB 140 · HEB 160 · HEB 180 · HEB 200 · HEB 220 · HEB 240 · HEB 260 · HEB 280 · HEB 300 · HEB 320 · HEB 340 · HEB 360 · HEB 400 · HEB 450 · HEB 500 · HEB 550 · HEB 600 · HEB 650 · HEB 700 · HEB 800 · HEB 900 · HEB 1000
H / I beams — UB / UC (BS 4-1 (UK)): UB 127×76×13 · UB 152×89×16 · UB 178×102×19 · UB 203×133×25 · UB 203×133×30 · UB 254×146×31 · UB 254×146×43 · UB 305×165×40 · UB 305×165×54 · UB 356×171×51 · UB 356×171×67 · UB 406×178×60 · UB 406×178×74 · UB 457×191×82 · UB 457×191×98 · UB 533×210×101 · UB 533×210×122 · UB 610×229×125 · UB 610×229×140 · UB 686×254×152 · UB 762×267×173 · UB 838×292×194 · UB 914×305×224 · UB 914×305×289 · UC 152×152×23 · UC 152×152×30 · UC 152×152×37 · UC 203×203×46 · UC 203×203×52 · UC 203×203×60 · UC 254×254×73 · UC 254×254×89 · UC 305×305×97 · UC 305×305×118 · UC 305×305×158 · UC 356×368×129 · UC 356×368×153 · UC 356×368×202
H / I beams — ISMB (tapered flanges, mean tf) (IS 808 (India)): ISMB 100 · ISMB 125 · ISMB 150 · ISMB 175 · ISMB 200 · ISMB 225 · ISMB 250 · ISMB 300 · ISMB 350 · ISMB 400 · ISMB 450 · ISMB 500 · ISMB 550 · ISMB 600
Channels — Channels ㄷ (Korea · Japan) (KS D 3502 · JIS G 3192): ㄷ 100×50×5×7.5 · ㄷ 125×65×6×8 · ㄷ 150×75×6.5×10 · ㄷ 150×75×9×12.5 · ㄷ 180×75×7×10.5 · ㄷ 200×80×7.5×11 · ㄷ 200×90×8×13.5 · ㄷ 250×90×9×13 · ㄷ 250×90×11×14.5 · ㄷ 300×90×9×13 · ㄷ 300×90×10×15.5 · ㄷ 300×90×12×16 · ㄷ 380×100×10.5×16 · ㄷ 380×100×13×16.5 · ㄷ 380×100×13×20
Channels — C-shapes (AISC (USA)): C3×4.1 · C4×5.4 · C5×6.7 · C6×8.2 · C6×13 · C8×11.5 · C8×18.75 · C9×15 · C10×15.3 · C10×20 · C10×30 · C12×20.7 · C12×30 · C15×33.9 · C15×40 · C15×50
Channels — UPN (EN 10365 / DIN 1026 (Europe)): UPN 80 · UPN 100 · UPN 120 · UPN 140 · UPN 160 · UPN 180 · UPN 200 · UPN 220 · UPN 240 · UPN 260 · UPN 280 · UPN 300 · UPN 320 · UPN 350 · UPN 380 · UPN 400
Channels — ISMC (mean tf) (IS 808 (India)): ISMC 75 · ISMC 100 · ISMC 125 · ISMC 150 · ISMC 175 · ISMC 200 · ISMC 250 · ISMC 300 · ISMC 350 · ISMC 400
Angles — Angles L (Korea · Japan) (KS D 3502 · JIS G 3192): L 40×40×5 · L 50×50×6 · L 60×60×6 · L 65×65×6 · L 65×65×8 · L 75×75×6 · L 75×75×9 · L 75×75×12 · L 90×90×10 · L 90×90×13 · L 100×100×10 · L 100×100×13 · L 120×120×8 · L 130×130×9 · L 130×130×12 · L 150×150×12 · L 150×150×15 · L 150×150×19 · L 175×175×12 · L 175×175×15 · L 200×200×15 · L 200×200×20 · L 200×200×25 · L 250×250×25 · L 250×250×35 · L 90×75×9 · L 100×75×7 · L 100×75×10 · L 125×75×7 · L 125×75×10 · L 125×75×13 · L 125×90×10 · L 125×90×13 · L 150×90×9 · L 150×90×12 · L 150×100×12 · L 150×100×15
Angles — Equal & unequal angles (EN 10056-1 (Europe)): L 40×40×4 · L 45×45×4.5 · L 50×50×5 · L 60×60×6 · L 70×70×7 · L 75×75×8 · L 80×80×8 · L 90×90×9 · L 100×100×10 · L 120×120×12 · L 130×130×12 · L 150×150×15 · L 160×160×16 · L 180×180×18 · L 200×200×20 · L 100×65×8 · L 100×75×8 · L 120×80×10 · L 150×90×12 · L 150×100×12 · L 200×100×12 · L 200×150×15
Angles — L-shapes (AISC (USA)): L2×2×¼ · L2½×2½×¼ · L3×3×¼ · L3×3×⅜ · L3×3×½ · L3½×3½×⅜ · L4×4×¼ · L4×4×⅜ · L4×4×½ · L4×4×¾ · L5×5×⅜ · L5×5×½ · L5×5×¾ · L6×6×⅜ · L6×6×½ · L6×6×¾ · L6×6×1 · L8×8×½ · L8×8×¾ · L8×8×1 · L8×8×1⅛ · L3×2×¼ · L4×3×⅜ · L4×3×½ · L5×3×⅜ · L5×3½×⅜ · L6×4×⅜ · L6×4×½ · L6×4×¾ · L7×4×½ · L8×4×½ · L8×6×½ · L8×6×¾ · L8×6×1
Angles — ISA (IS 808 (India)): ISA 50×50×6 · ISA 65×65×6 · ISA 75×75×8 · ISA 90×90×10 · ISA 100×100×10 · ISA 130×130×12 · ISA 150×150×15 · ISA 200×200×20 · ISA 100×75×8 · ISA 125×75×10 · ISA 150×100×12
Square & rectangular hollow sections — Square / rectangular tubes □ (cold-formed) (KS D 3568 · JIS G 3466): □ 50×50×3.2 · □ 60×60×3.2 · □ 75×75×3.2 · □ 100×100×4.5 · □ 100×100×6 · □ 125×125×4.5 · □ 125×125×6 · □ 150×150×6 · □ 150×150×9 · □ 175×175×6 · □ 200×200×9 · □ 200×200×12 · □ 250×250×9 · □ 250×250×12 · □ 300×300×9 · □ 300×300×12 · □ 350×350×12 · □ 400×400×12 · □ 100×50×3.2 · □ 125×75×4.5 · □ 150×100×6 · □ 200×100×9 · □ 250×150×9 · □ 300×200×12
Square & rectangular hollow sections — HSS square & rectangular (design wall) (AISC / ASTM A500 (USA)): HSS2×2×¼ · HSS3×3×¼ · HSS4×4×¼ · HSS4×4×⅜ · HSS5×5×⅜ · HSS6×6×¼ · HSS6×6×⅜ · HSS6×6×½ · HSS8×8×⅜ · HSS8×8×½ · HSS10×10×½ · HSS12×12×½ · HSS12×12×⅝ · HSS14×14×½ · HSS16×16×⅝ · HSS6×4×⅜ · HSS8×4×⅜ · HSS8×6×½ · HSS10×6×½ · HSS12×6×½ · HSS12×8×½ · HSS16×8×½ · HSS20×12×⅝
Square & rectangular hollow sections — SHS / RHS (EN 10210 (Europe, hot-finished)): SHS 40×40×3 · SHS 50×50×4 · SHS 60×60×4 · SHS 70×70×5 · SHS 80×80×5 · SHS 90×90×5 · SHS 100×100×5 · SHS 100×100×8 · SHS 120×120×6 · SHS 140×140×6 · SHS 150×150×8 · SHS 160×160×8 · SHS 180×180×8 · SHS 200×200×8 · SHS 200×200×10 · SHS 250×250×10 · SHS 300×300×12 · SHS 350×350×12 · SHS 400×400×16 · RHS 100×50×4 · RHS 120×60×5 · RHS 150×100×6 · RHS 200×100×8 · RHS 250×150×8 · RHS 300×200×10 · RHS 400×200×12
Circular hollow sections — Round tubes Ø (Korea · Japan) (KS D 3566 · JIS G 3444 (STK)): Ø 48.6×2.8 · Ø 60.5×3.2 · Ø 76.3×3.2 · Ø 89.1×3.2 · Ø 101.6×4.2 · Ø 114.3×4.5 · Ø 139.8×4.5 · Ø 165.2×5.0 · Ø 190.7×5.3 · Ø 216.3×5.8 · Ø 267.4×6.6 · Ø 318.5×6.9 · Ø 355.6×7.9 · Ø 406.4×9.5 · Ø 457.2×9.5 · Ø 508.0×9.5 · Ø 609.6×12.0
Circular hollow sections — HSS round (design wall) (AISC / ASTM A500 (USA)): HSS4.000×0.250 · HSS5.563×0.258 · HSS6.625×0.280 · HSS8.625×0.322 · HSS10.000×0.375 · HSS12.750×0.375 · HSS14.000×0.500 · HSS16.000×0.500 · HSS18.000×0.500 · HSS20.000×0.500
Circular hollow sections — CHS (EN 10210 (Europe)): CHS 60.3×3.2 · CHS 76.1×3.2 · CHS 88.9×4 · CHS 114.3×5 · CHS 139.7×5 · CHS 168.3×6.3 · CHS 193.7×8 · CHS 219.1×8 · CHS 244.5×10 · CHS 273×10 · CHS 323.9×10 · CHS 355.6×12.5 · CHS 406.4×12.5 · CHS 457×16 · CHS 508×16 · CHS 610×20
For bending, the section modulus S is the number that matters, not I alone — and for asymmetric sections like a PSC girder, always check which fibre governs: the bulb pulls the centroid down, so the bottom modulus usually controls at release and the top in service. When comparing steel shapes, weight per metre is the honest denominator — an efficient section is the one with the most S per kg. Catalogue values include the root fillets — pick a standard size and they come with it; with the sliders at r = 0 the model is sharp-cornered and sits 1–3% low on I. One more habit: when a code gives two thicknesses for the same nominal size (HSS design wall, tapered-flange channels), check which one the table you are matching uses.
Inputs are saved on this device · reset to defaults
Every beam, column and girder check starts from a handful of geometric numbers. This calculator works them out exactly from the outline of the shape, including the root fillets of rolled sections, so the values match the steel tables. Here is what each one means and how to get it by hand for the common shapes.
| Property | Symbol | What it controls |
|---|---|---|
| Area | A | axial stress N/A, self-weight, shear area |
| Centroid | x̄, ȳ (ct, cb) | where the elastic neutral axis sits; distance to the top and bottom fibres |
| Second moment of area | Ix, Iy | bending stiffness EI, deflection, buckling load |
| Elastic section modulus | S = I / c | first-yield moment My = fy S, extreme-fibre stress M / S |
| Plastic section modulus | Z | full plastic moment Mp = fy Z for compact steel sections |
| Radius of gyration | r = √(I / A) | column slenderness KL / r |
| Torsion constant | J | St Venant torsional stiffness GJ, lateral-torsional buckling |
| Shape | I about the centroid | S | Z | Z / S |
|---|---|---|---|---|
| Rectangle b × h | b h³ / 12 | b h² / 6 | b h² / 4 | 1.50 |
| Solid circle, diameter d | π d⁴ / 64 | π d³ / 32 | d³ / 6 | 1.70 |
| Tube, D outside, d inside | π (D⁴ − d⁴) / 64 | 2 I / D | (D³ − d³) / 6 | about 1.3 |
| Doubly symmetric I-section | (B H³ − (B − tw) hw³) / 12 | 2 I / H | flanges + web halves about the centre | 1.10 to 1.15 |
For any built-up shape, split it into rectangles and use the parallel-axis theorem: I = Σ (Iown + A d²), where d is the distance from each part's centroid to the centroid of the whole section. The plastic modulus is taken about the equal-area axis, which for unsymmetric sections (tees, angles, PSC girders) is not the elastic centroid. For thin-walled open sections J ≈ Σ b t³ / 3; closed boxes are far stiffer in torsion, J = 4 A0² / Σ (s / t) with A0 the area enclosed by the wall mid-line.
Choose a shape family (H / I beam, channel, angle, tube), then CODE · SIZE to load a rolled section from KS / JIS / GB, AISC, EN, BS or IS tables. The outline carries the standard's root fillet or corner radius, so I and S agree with the catalogue within about 1 %. Switch to the sliders for a welded or custom size, or to Bridge sections for PSC I-girders and single or multi-cell box girders. The step view shows how each number is integrated from the polygon.
Flanges 300 × 20 mm, web 560 × 12 mm, overall depth H = 600 mm (sharp corners).
Enter the same plate sizes in the H / I beam sliders with zero fillet and the calculator returns these values. With fy = 355 MPa the girder yields at My = 355 × 3.95 = 1,400 kN·m and reaches Mp = 355 × 4.42 = 1,570 kN·m if the flanges and web are compact.
Next steps on TheBridgeEng: put the section into the beam analyzer or frame and truss solver, check a reinforced concrete section in RC beam design, or size a girder depth with girder depth.