Section Properties
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XY / SECTION PLANE
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This free section properties calculator computes area, centroid position, moment of inertia (second moment of area), elastic section modulus and radius of gyration for standard steel profiles. Choose a region and a section — European IPE, HEA, HEB, HEM, UPE and UPN, American W-shapes, Australian sections or Russian GOST profiles — and get the cross-section drawing and the full property table instantly, with no sign-up. Values are calculated from the profile geometry, so they may differ slightly from the published tables; see the accuracy section below for details.
Area, A (mm²). The cross-sectional area of the material. It gives the axial stress under a normal force, σ = N / A, and the self-weight per metre of length.
Centroid. The geometric centre of the area. For doubly symmetric sections such as IPE, HEA or a rectangular tube, it lies in the middle of the profile. For channels, angles and tees, it shifts toward the heavier part. In elastic bending, the neutral axis passes through the centroid.
Moment of inertia, Ix and Iy (mm⁴). Also called the second moment of area. It describes how far the area is spread from an axis and controls bending stiffness EI, and therefore deflection. It is a geometric property with units of length to the fourth power, not the mass moment of inertia used in dynamics. Moving material farther from an axis raises I sharply.
Elastic section modulus, Wx and Wy (mm³). Calculated as W = I / c, where c is the distance from the axis to the extreme fibre. It gives the bending stress σ = M / W. If the distances to the top and bottom fibres differ, the farther fibre gives the smaller modulus and governs the stress.
Wx,max and Wx,min (asymmetric sections). If a section is not symmetric about the x-axis, such as a tee or a channel about its y-axis, the distances from the axis to the two extreme fibres differ, and so does the modulus. W = I / c is larger for the nearer fibre (Wx,max) and smaller for the farther fibre (Wx,min); the same applies to Wy,max and Wy,min. In steel, yield strength is the same in tension and compression, so the farther fibre with Wmin governs the stress and Wmax is rarely needed. In concrete the two faces behave differently: tension is limited by the tensile strength, compression by the compressive strength, and which face is in tension depends on the sign of the moment. Both moduli are therefore needed, for example for the cracking moment of an uncracked section, Mcr = fct · W, where W belongs to the tension face. The builder calculates gross sections only: reinforcement and cracking are not taken into account.
Plastic section modulus, Wpl,x and Wpl,y (mm³). The geometric term in the plastic bending moment, Mpl = fy · Wpl. It is calculated about the plastic neutral axis, which splits the area into two equal halves. Whether a section can actually develop Mpl depends on its class and local buckling, which this tool does not check.
Radius of gyration, ix and iy (mm). Defined as i = √(I / A). It is used to calculate the slenderness of a compression member, λ = L / i, and therefore relates to buckling. Buckling occurs about the axis with the smaller i, which for most I-sections is the weak axis.
Principal axes of angles, u and v (Wu and Wv). An angle is not symmetric about any axis parallel to its legs, so its product of inertia about the x and y axes is not zero. The centroidal axes about which it is zero are the principal axes: u–u carries the maximum moment of inertia and v–v the minimum. For an equal-leg angle they are rotated 45° from the leg axes. Wu and Wv are the elastic section moduli about these axes, defined like Wx and Wy. Single angles are usually checked about u and v, and buckling occurs about the weak axis v–v, which has the smallest radius of gyration.
The same quantities use different symbols depending on the design standard. This table maps RodX notation to common European, American and Russian conventions. Axis names matter as much as the letters.
| Quantity | RodX builder | Eurocode 3 | AISC (US) | GOST (RU) |
|---|---|---|---|---|
| Area | A | A | A | A |
| Strong-axis moment of inertia | Ix | Iy | Ix | Ix |
| Weak-axis moment of inertia | Iy | Iz | Iy | Iy |
| Elastic section modulus, strong axis | Wx | Wel,y | Sx | Wx |
| Elastic section modulus, weak axis | Wy | Wel,z | Sy | Wy |
| Plastic section modulus, strong axis | Wpl,x | Wpl,y | Zx | Wpl,x |
| Plastic section modulus, weak axis | Wpl,y | Wpl,z | Zy | Wpl,y |
| Radius of gyration, strong axis | ix | iy | rx | ix |
| Radius of gyration, weak axis | iy | iz | ry | iy |
The most common source of mistakes is the axis index. In Eurocode 3, the strong axis is y–y because the index names the axis the bending moment acts about. In AISC and GOST, the strong axis is x–x. AISC also uses S for the elastic and Z for the plastic modulus. Match each symbol to its definition rather than relying on the letter alone.
The builder contains standard section catalogs for four regions, and new catalogs are added regularly.
| Region | Standards and series |
|---|---|
| EU | I-beams IPE, HEA, HEB, HEM; channels UPE and UPN; equal and unequal angles; tees cut from IPE; hollow sections CHS, RHS and SHS |
| US | W-shapes (wide-flange I-beams); C channels; equal and unequal angles; HSS round, rectangular and square tubes |
| AU | AS/NZS 3679.1: parallel-flange and tapered-flange I-beams, parallel-flange channels, equal and unequal angles. AS/NZS 1163:2009: circular, rectangular and square hollow sections |
| RU (CIS) | I-beams: GOST 8239-89, GOST 19425-74, GOST 26020-83, GOST R 57837-2017. Channels: GOST 8240-97, GOST 8278-83. Angles: GOST 8509-93, GOST 8510-86, GOST 19771-93, GOST 19772-93. Pipes and tubes: GOST 8732-78, GOST 8734-75, GOST 10704-91, GOST 8639-82, GOST 8645-68, GOST 30245-2003 |
All the most common section types are covered: I-beams and H-sections, channels, angles, square, rectangular and circular hollow sections (tubes), and, in the European catalog, tees cut from IPE beams. Simple solid and hollow shapes, such as a rectangle or a circle, are also available and are calculated from the dimensions you enter.
Choose a region and a section from the list, or find a profile by its height or required moment of inertia. The builder draws the cross-section with the centroid marked and shows the full property table. The dimensions of a catalog profile can be edited, so the tool also works for modified and non-standard sizes.
The tool gives geometric properties only. Torsion, warping and code checks are not included.
The profile geometry, including the flange slope for sections with tapered flanges, is taken exactly from the tables of the standards. The section properties are then calculated from this geometry, not copied from the tables. The builder takes the outline of the section, computes the area, centroid and moments of inertia with Green's theorem, and replaces every arc with 16 straight segments. Circles and circular tubes use exact formulas. For a rectangle and an I-section the results match the analytical formulas exactly.
Compared with the values published in the catalogs, the difference is usually about 0.5%. In rare cases, mostly on small sections, it can reach 1%. Three things contribute to it:
For preliminary design, comparing options and checking a section, the calculated values are accurate enough. For final calculations and code checks, take the section properties from the official table of the standard or the manufacturer.
Solid and hollow rectangles and circles are calculated as gross sections. Reinforcement, cracking and transformed sections are not taken into account.
Say you want to see which channels are available with a height of about 120 mm. Choose the region, select h as the search parameter, enter 120 in the field and press Enter or the search button (the magnifier). The search shows the three nearest sections by height. Click the one you need and it is loaded into the builder and drawn.
Searching by the required moment of inertia, which is the more common case, works the same way.
Choose a section type and set the heights, widths, thicknesses and other parameters in the Geometry section. The properties are recalculated instantly. Parameters can also be changed with the mouse wheel.
Once you have the properties, you can download the section drawing as a DXF file and the properties as a TXT file.
It is free and needs no sign-up. Results appear instantly as soon as you choose a section.
Catalogs for four regions: Europe (IPE, HEA, HEB, HEM, UPE, UPN, angles and hollow sections), the United States (W-shapes, C channels, angles and HSS), Australia (AS/NZS 3679.1 and AS/NZS 1163) and Russia/CIS (GOST). New catalogs are added regularly.
The builder gives geometric properties only and does not perform code checks. For final calculations, take the section properties from the official table of the standard or the manufacturer.
No. Torsion and warping are not included; the builder reports area, centroid, moments of inertia, section moduli and radii of gyration.
The profile geometry comes from the standards, but the properties are calculated from it, so rounding in the tables, arcs replaced by segments and rolling tolerances create small differences. They are usually about 0.5% and in rare cases up to 1% on small sections.
The builder works in millimetres. Most tables list cm⁴ and cm³, so divide the results by 10,000 for moments of inertia (1 cm⁴ = 10,000 mm⁴), by 1,000 for section moduli (1 cm³ = 1,000 mm³) and by 100 for area (1 cm² = 100 mm²).
Choose the region, select Ix or Iy as the search parameter, enter the value and press Enter. The search shows the three nearest sections, and clicking one loads it into the builder.
Yes. Choose a section type, such as an I-beam, channel, angle, tee, tube, rectangle or circle, and set its dimensions in the Geometry section. You are not limited to catalog sizes, and the properties update instantly.
The moment of inertia I describes the stiffness of the section and controls deflection through EI. The section modulus W is I divided by the distance to the extreme fibre, and it gives the bending stress, σ = M / W.
Eurocode 3 names the axis the bending moment acts about, so its strong axis is y–y, while AISC and GOST use x–x. AISC also writes S for the elastic and Z for the plastic section modulus. See the notation table above for the full comparison.
Section properties are the input for beam and frame analysis. Two RodX tools take it from here.