Choose the section that matches your drawing
Choose solid rectangle, rectangular hollow section, doubly symmetric I section, solid circle or circular hollow section. The I-section option assumes equal top and bottom flanges.
BEAMS & SECTIONS / TOOL 11
Beam Section Properties Calculator
Use this when comparing candidate beam sections or preparing geometric inputs for an elastic beam calculation. It calculates section geometry from dimensions; it does not convert a beam into a rated crane capacity.
Before you start: required inputs
- Use a section drawing viewed square-on to the beam length. Identify the section shape and its outside dimensions in millimetres.
- For a box or tube, obtain the wall thickness. For an I section, obtain the separate flange and web thicknesses. Confirm which physical direction is vertical in the intended installation.
Calculation diagram
A PRACTICAL WALKTHROUGH
How to use this calculator
Measure B, H and the actual thicknesses
B is the outside width and H is the overall vertical height. Use t for a uniform hollow wall, tf for flange thickness, tw for web thickness, or D for outside diameter. Enter mm, not cm or m.
Read the property about the correct axis
The x axis is horizontal through the centroid; y is vertical through the centroid. Read Ix for bending about x and Iy for bending about y, then carry the matching value and unit into your next calculation.
Rectangular hollow section: 200 × 300 × 10 mm
THE INPUTS
Shape rectangular hollow section; outside width B = 200 mm; vertical height H = 300 mm; uniform wall t = 10 mm.
THE RESULT
Ix = 120,720,000 mm⁴; Iy = 63,920,000 mm⁴; area = 9,600 mm². The centroid is 100 mm from the left and 150 mm from the bottom. Zx = 804,800 mm³ and Zy = 639,200 mm³.
What does the result mean?
01
Area describes how much material lies in the section. The centroid locates its geometric centre within the outside bounding rectangle.
02
Ix and Iy are second moments of area about two different centroidal axes. They quantify geometric resistance to bending curvature, not the load the beam may carry.
03
Elastic section moduli Zx and Zy relate elastic bending moment to extreme-fibre bending stress. They are different from I: Z uses mm³, while I uses mm⁴.
Watch for this
Copying a catalogue value in cm⁴ into a field marked mm⁴. Multiply cm⁴ by 10,000 to obtain mm⁴. Also keep the section orientation: rotating a rectangle or box by 90° swaps its x- and y-axis properties.
Formula & model conditions +
Rectangle: Ix = B × H³ / 12; Iy = H × B³ / 12
Box: subtract the inner rectangle, width B−2t and height H−2t, from the outer rectangle
I section: Ix = [BH³ − (B−tw)(H−2tf)³] / 12
I section: Iy = [2tf B³ + (H−2tf)tw³] / 12; tf = flange thickness, tw = web thickness
Circle: Ix = Iy = πD⁴ / 64; tube: Ix = Iy = π[D⁴ − (D−2t)⁴] / 64
Elastic section modulus: Zx = Ix / extreme vertical distance; Zy = Iy / extreme horizontal distance
- x is the horizontal centroidal axis and y is the vertical centroidal axis. Dimensions are in millimetres.
- Centroid coordinates are measured from the lower-left corner of the section bounding rectangle.
- Sharp corners, equal flanges and uniform wall thickness are assumed; fillets, welds and section classification are excluded.
- Elastic section modulus is I divided by the distance to the extreme fibre. These geometric properties do not establish member resistance.
Common questions
How do I convert a section property from cm⁴ to mm⁴?
Multiply by 10,000: 1 cm⁴ = 10,000 mm⁴. For example, 12,072 cm⁴ equals 120,720,000 mm⁴. Do not use the factor of 10 that applies to a simple length.
Can Ix tell me how many tonnes a crane girder can lift?
No. Capacity also depends on span, loading, material, stability, deflection, fatigue, connections and the applicable design method. Ix is one geometric input to those checks.