Area, second moment of area, section modulus and radius of gyration for European rolled I-sections, derived from nominal geometry including root fillets and cross-checked against EN 10365.
Direct answer. The textbook three-rectangle formula I = [bh³ − (b−tw)hw³]/12 under-predicts the real properties of a rolled I-section, because it ignores the four root fillets at the web-to-flange junctions. Across the 27 sections below those fillets add 2.6–4.9% to area and 2.5–5.7% to Iy. Include them and the derivation matches the published table to within 0.29%.
Elastic mid-span deflection of a simply supported beam under uniform load. Pure mechanics, no code factors — this is a serviceability sanity check, not a design verification.
Narrow-flange beams. Scroll the table sideways for the full property set.
| Section | h (mm) | b (mm) | tw | tf | r | Mass (kg/m) | A (cm²) | Iy (cm⁴) | Wy (cm³) | iy (cm) | Iz (cm⁴) | Wz (cm³) | iz (cm) | Max dev. |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| IPE 100 | 100 | 55 | 4.1 | 5.7 | 7 | 8.1 | 10.32 | 171 | 34.2 | 4.07 | 16 | 5.8 | 1.24 | 0.05% |
| IPE 120 | 120 | 64 | 4.4 | 6.3 | 7 | 10.4 | 13.21 | 318 | 53.0 | 4.90 | 28 | 8.6 | 1.45 | 0.29% |
| IPE 140 | 140 | 73 | 4.7 | 6.9 | 7 | 12.9 | 16.43 | 541 | 77.3 | 5.74 | 45 | 12.3 | 1.65 | 0.04% |
| IPE 160 | 160 | 82 | 5.0 | 7.4 | 9 | 15.8 | 20.09 | 869 | 108.7 | 6.58 | 68 | 16.7 | 1.84 | 0.18% |
| IPE 180 | 180 | 91 | 5.3 | 8.0 | 9 | 18.8 | 23.95 | 1,317 | 146.3 | 7.42 | 101 | 22.2 | 2.05 | 0.02% |
| IPE 200 | 200 | 100 | 5.6 | 8.5 | 12 | 22.4 | 28.48 | 1,943 | 194.3 | 8.26 | 142 | 28.5 | 2.24 | 0.18% |
| IPE 220 | 220 | 110 | 5.9 | 9.2 | 12 | 26.2 | 33.37 | 2,772 | 252.0 | 9.11 | 205 | 37.3 | 2.48 | 0.02% |
| IPE 240 | 240 | 120 | 6.2 | 9.8 | 15 | 30.7 | 39.12 | 3,892 | 324.3 | 9.97 | 284 | 47.3 | 2.69 | 0.02% |
| IPE 270 | 270 | 135 | 6.6 | 10.2 | 15 | 36.1 | 45.95 | 5,790 | 428.9 | 11.23 | 420 | 62.2 | 3.02 | 0.09% |
| IPE 300 | 300 | 150 | 7.1 | 10.7 | 15 | 42.2 | 53.81 | 8,356 | 557.1 | 12.46 | 604 | 80.5 | 3.35 | 0.10% |
| IPE 330 | 330 | 160 | 7.5 | 11.5 | 18 | 49.1 | 62.61 | 11,767 | 713.1 | 13.71 | 788 | 98.5 | 3.55 | 0.09% |
| IPE 360 | 360 | 170 | 8.0 | 12.7 | 18 | 57.1 | 72.73 | 16,266 | 903.6 | 14.95 | 1,043 | 122.8 | 3.79 | 0.03% |
| IPE 400 | 400 | 180 | 8.6 | 13.5 | 21 | 66.3 | 84.46 | 23,128 | 1156.4 | 16.55 | 1,318 | 146.4 | 3.95 | 0.04% |
| IPE 450 | 450 | 190 | 9.4 | 14.6 | 21 | 77.6 | 98.82 | 33,743 | 1499.7 | 18.48 | 1,676 | 176.4 | 4.12 | 0.03% |
| IPE 500 | 500 | 200 | 10.2 | 16.0 | 21 | 90.7 | 115.52 | 48,199 | 1927.9 | 20.43 | 2,142 | 214.2 | 4.31 | 0.02% |
| IPE 550 | 550 | 210 | 11.1 | 17.2 | 24 | 105.5 | 134.42 | 67,117 | 2440.6 | 22.35 | 2,668 | 254.1 | 4.45 | 0.02% |
| IPE 600 | 600 | 220 | 12.0 | 19.0 | 24 | 122.4 | 155.98 | 92,083 | 3069.4 | 24.30 | 3,387 | 307.9 | 4.66 | 0.04% |
Wide-flange columns, depth roughly equal to width.
| Section | h (mm) | b (mm) | tw | tf | r | Mass (kg/m) | A (cm²) | Iy (cm⁴) | Wy (cm³) | iy (cm) | Iz (cm⁴) | Wz (cm³) | iz (cm) | Max dev. |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| HEB 100 | 100 | 100 | 6.0 | 10.0 | 12 | 20.4 | 26.04 | 450 | 89.9 | 4.16 | 167 | 33.5 | 2.53 | 0.19% |
| HEB 120 | 120 | 120 | 6.5 | 11.0 | 12 | 26.7 | 34.01 | 864 | 144.1 | 5.04 | 318 | 52.9 | 3.06 | 0.03% |
| HEB 140 | 140 | 140 | 7.0 | 12.0 | 12 | 33.7 | 42.96 | 1,509 | 215.6 | 5.93 | 550 | 78.5 | 3.58 | 0.06% |
| HEB 160 | 160 | 160 | 8.0 | 13.0 | 15 | 42.6 | 54.25 | 2,492 | 311.5 | 6.78 | 889 | 111.2 | 4.05 | 0.03% |
| HEB 180 | 180 | 180 | 8.5 | 14.0 | 15 | 51.2 | 65.25 | 3,831 | 425.7 | 7.66 | 1,363 | 151.4 | 4.57 | 0.04% |
| HEB 200 | 200 | 200 | 9.0 | 15.0 | 18 | 61.3 | 78.08 | 5,696 | 569.6 | 8.54 | 2,003 | 200.3 | 5.07 | 0.01% |
| HEB 220 | 220 | 220 | 9.5 | 16.0 | 18 | 71.5 | 91.04 | 8,091 | 735.5 | 9.43 | 2,843 | 258.5 | 5.59 | 0.05% |
| HEB 240 | 240 | 240 | 10.0 | 17.0 | 21 | 83.2 | 105.99 | 11,259 | 938.3 | 10.31 | 3,923 | 326.9 | 6.08 | 0.01% |
| HEB 260 | 260 | 260 | 10.0 | 17.5 | 24 | 93.0 | 118.44 | 14,919 | 1147.6 | 11.22 | 5,135 | 395.0 | 6.58 | 0.04% |
| HEB 300 | 300 | 300 | 11.0 | 19.0 | 27 | 117.0 | 149.08 | 25,166 | 1677.7 | 12.99 | 8,563 | 570.9 | 7.58 | 0.02% |
A rolled I-section is not three rectangles. Where the web meets each flange there is a root fillet of radius r, and there are four of them. Each fillet is the region left when a quarter disc is removed from a square of side r:
Each fillet is then shifted onto the section's neutral axis by the parallel-axis theorem:
These constants are exact, integrated from the geometry — not fitted to make the numbers agree. That distinction matters: a fudge factor tuned to one catalogue tells you nothing about the next section you meet.
Verification result: all 27 sections agree with EN 10365. The largest deviation across area, Iy, Wy and mass for every section is 0.29%, comfortably inside the 1.0% flag threshold applied site-wide. Deviations at this level reflect rounding in the published tables.
European practice (EN 1993, EN 10365) labels the major axis y-y and the minor axis z-z. US practice (AISC) labels them x-x and y-y. Same physical quantity, different name — so an American Ix is the European Iy. Getting this backwards is a common and expensive mistake when working across the two systems.
Use the published table for your governing standard. These derived values exist to verify that table and to show where the numbers come from, not to replace it. They agree to within 0.29%, so if your source disagrees with both, the source is worth checking.
No. The load w is whatever you enter. Add the section's own mass (the Mass column, in kg/m × 9.81 ÷ 1000 = kN/m) if you want it included. The formula is elastic deflection only — it applies no partial factors, no buckling check and no serviceability limit.
i = √(I/A) expresses how far the area sits from the axis. It is the property that drives slenderness, λ = Lcr/i, and therefore buckling capacity — which is why a wide-flange HEB makes a far better column than an IPE of the same mass.