Hot-finished RHS section properties to EN 10210-2: area, second moments, moduli and radii of gyration. Pick a section and read the values.
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About this RHS Section Properties Calculator
This calculator returns the section properties of any hot-finished rectangular hollow section in the standard range, computed from the published depth, width, wall thickness and corner radii. Pick a designation and it gives you the area, the second moments of area about both axes, the elastic and plastic section moduli and the radii of gyration, along with a scale drawing of the section.
- Structural engineer: take the properties of a candidate RHS into a bending or column check without retyping a table row.
- Design engineer: compare depths, widths and wall thicknesses during concept sizing, with the section drawn to scale as you change it.
- Checker: confirm the properties used in a submitted calculation, with the corner geometry and every step of the derivation visible.
Every property is computed on the page in visible MathJS rather than read from a stored table, and each one is checked against an independent geometric integration of the same section before it ships. It is an engineering-grade calculator you can audit, duplicate and adapt in CalcTree.
More info on RHS Section Properties
What defines an RHS
Five published dimensions define the section: the overall depth, the overall width, the wall thickness, and the outer and inner corner radii. The radii matter, particularly on smaller sections with thicker walls, where the corners are a real fraction of the cross-section.
How the properties are derived
The section is the outer rounded rectangle less the inner one. Each rounded corner removes a corner piece, the square of side r minus the quarter disc inside it, so the properties are the plain rectangle plus four corner corrections carried out to the corner by their parallel-axis terms. Because the section is doubly symmetric, the plastic neutral axis coincides with the centroidal axis and the plastic modulus is twice the first moment of the half section.
Using the library in your own calculation
The section range is attached to the page as a dataset rather than pasted in as a table, so the same file can be inserted into any other calculation in your workspace. Duplicate the page and the data comes with it, which means a member check you build on top of it stays tied to one copy of the section range rather than a retyped subset of it.
Where the numbers are checked
Each section is verified against an independent numerical integration of the same geometry, carried out by a different method to the closed-form expressions used on the page. Both have to agree to four significant figures for every section in the range.
Common Calculation Errors to Avoid
- Mixing hot-finished and cold-formed sections: A hot-finished section and a cold-formed section of the same nominal size are not interchangeable. The cold-formed corner radii are larger, which removes more material and lowers the area and the second moment of area. Use the library that matches the standard you are specifying to.
- Ignoring the corner radii: Treating a hollow section as a sharp-cornered tube overstates both the area and the second moment of area, and the error grows as the wall gets thicker relative to the size. The radii are part of the section definition, not a detailing nicety.
- Using plastic properties without classifying the section: The plastic modulus only applies if the cross-section can reach and sustain its plastic moment. Classify the section for the relevant load case first; a Class 3 section is limited to its elastic modulus and a Class 4 section needs effective properties, not the gross ones given here.
- Confusing nominal and design thickness: The thickness in the product standard is the nominal wall thickness. Some cold-formed design rules work from a design thickness that deducts the zinc coating or a rolling tolerance, so check which one the clause you are applying expects.
- Treating gross properties as net properties: These are gross section properties. Bolt holes, cope cuts and corrosion allowances all reduce the section, and none of them are accounted for here.
Engineering templates
Common calculators
Design guides
FAQs
What is the difference between hot-finished and cold-formed RHS?
Corner radii. A cold-formed section of the same overall size has larger corners, which removes more material and gives a slightly lower area and second moment of area. Use the library that matches what you are specifying: EN 10210 for hot finished, EN 10219 for cold formed.
Why do the corner radii matter?
On a small section with a thick wall the corners are a significant fraction of the cross-section. Treating the section as a sharp-cornered tube overstates both the area and the second moment of area.
Which axis is y-y?
The y-y axis is the strong axis, bending about the depth of the section. The z-z axis bends about the width. Both are given, along with the radius of gyration about each, because the weak axis usually governs buckling.
Can I use this inside my own calculation?
Yes. The section range is a dataset attached to the page, so duplicating the page brings the data with it and you can look up any section from your own maths.
Does it account for cross-section classification?
No. The properties given are the gross section. Classification, and any reduction to effective properties for a slender section, belong in the member check.
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