Section Properties Calculator

Features

• Six shapes: rectangle, circle, pipe, box (uniform wall), T section, I section (equal flanges)
• Area and centroid height from the bottom (plus from the top when the section is not symmetric)
• Moments of inertia Ix (strong axis) and Iy (weak axis)
• Answers to both names — "moment of inertia" (US) and "second moment of area" (UK, Australia, India, most Commonwealth texts) are the same quantity
• Section modulus given separately for the top and bottom fibre, so an asymmetric section cannot be used the wrong way round
• Radii of gyration ix and iy
• The section and its centroidal axis are drawn live and follow the dimensions
• A piece-by-piece breakdown for built-up shapes, so the result can be checked by hand
• Units mm / cm / m / in, the same in and out
• Impossible dimensions (zero, negative, a pipe wall that fills the bore) are explained instead of returning a plausible-looking wrong number

How to use

1. Choose a section shape
2. Fill in the dimensions it asks for — only the relevant boxes appear
3. Switch the unit if you need to
4. The section and its centroidal axis appear on the left, all results on the right
5. Use the per-row copy button, or copy the whole result

FAQ

Can it tell me how much load the member can carry?

No, and it is not meant to. This is section geometry only — a moment of inertia is a moment of inertia whether the material is concrete or steel. Capacity depends on material strength and a design code, which is a different order of problem, and getting it wrong has safety consequences that do not belong in a free web page.

Is "second moment of area" the same as "moment of inertia"?

Yes — the two names mean exactly the same thing, and this page answers to either. "Moment of inertia" is the usual term in the US; "second moment of area" is standard in the UK, Australia, India and most Commonwealth engineering texts (sometimes shortened to "second moment", and written I). It is *not* the same as the mass moment of inertia — the rotational one, in kg·m². This tool computes the area moment, in mm⁴: same formula shape, different quantity.

Why are the two section moduli different for a T section?

Because the centroid is not at mid-height. The section modulus is `I / y_max`, and the two fibres are at different distances from the centroid. A T section carries most of its material in the flange, so the centroid sits high and the bottom fibre is further away — which makes the bottom modulus the smaller one. Use that one when the tension side is at the bottom.

What is the dash-dot line on the drawing?

The centroidal axis. Moments of inertia and section moduli are taken about the centroid (parallel axis theorem: I about any axis = I about the centroid + A·d²). Drawing it makes it obvious which way the centroid leans — up for a T, centred for an I.

How do I convert the results between units?

Input and output share a unit and no conversion is done, so nothing is lost in between. To convert yourself: when lengths differ by 10, areas differ by 100, section moduli by 1000 and moments of inertia by 10000. So 5.4e9 mm⁴ is 5.4e5 cm⁴.

Why does the pipe ask for a wall thickness instead of a bore?

Because pipes are specified by outside diameter and wall (φ200×10). Taking the wall means the bore is derived — `OD − 2 × wall` — so the two can never contradict each other. Only one of them can be an input.

How precise are the numbers?

Six significant figures. Moments of inertia are often in the 10⁹ range, where trailing zeros are unreadable, so anything above ten million or below one thousandth switches to scientific notation (5.4e9).