Calculate area, second moments of area, and section moduli for rectangles, circles, and hollow sections.
Set the inputs and run the calculation.
Calculate area, second moments of area and section moduli for idealized sections.
Shape and dimensions such as width, height, diameter and wall thickness define geometry.
Height places material farther from the neutral axis and therefore has a stronger bending effect. This is why a taller slender section raises I and W more than an equally heavy widening.
The area distribution gives I and W; W = I/yₘₐₓ feeds bending stress σ = M/W.
Doubling rectangle height at constant width roughly quadruples I and doubles W.
Sources and limits: Classical section theory; include radii, cut-outs and local buckling for real geometry.
Calculate area, second moments of area and section moduli for idealized sections.
Mechanical calculators translate geometry and load into a response such as torque, stress, deflection, spring force or bearing life. The position of the load relative to the effective axis is often decisive.
The area distribution gives I and W; W = I/yₘₐₓ feeds bending stress σ = M/W.
Shape and dimensions such as width, height, diameter and wall thickness define geometry. Height places material farther from the neutral axis and therefore has a stronger bending effect. This is why a taller slender section raises I and W more than an equally heavy widening.
Select the section shape (rectangle, solid circle, hollow circle or rectangular hollow section) and enter the corresponding dimensions. The calculator returns area, second moment of area and section modulus for a later bending-stress calculation.
Doubling rectangle height at constant width roughly quadruples I and doubles W.
Height places material farther from the neutral axis and therefore has a stronger bending effect. This is why a taller slender section raises I and W more than an equally heavy widening. The result shows the idealized component response for the selected load case. A small change in diameter, height, length or load can have a large effect because of power laws.
Dimensions in millimetres, area in mm², second moment of area in mm⁴, section modulus in mm³ or cm³.
Providing second moment of area and section modulus as an input for bending-stress or deflection calculators, or comparing different section shapes at equal material use.
Classical section theory; include radii, cut-outs and local buckling for real geometry.
Common mistake: For a hollow section, don't swap inside and outside dimensions – the inside diameter must stay geometrically smaller than the outside one. Height and width of a rectangular section don't act equally: only the dimension in the bending direction enters the second moment of area cubically.
Material far from the neutral axis contributes disproportionately (with the second to third power of distance) to bending stiffness; a taller, slimmer shape is therefore more material-efficient than a wider, flatter one.
Second moment of area I describes pure geometry and stiffness; section modulus W = I/yₘₐₓ additionally accounts for the edge-fiber distance and is used directly for bending stress σ = M/W.
Only approximately. Radii, cut-outs, welds or local section weakening must be additionally accounted for in a real component check.
Dimensions are converted into the geometric basis for stress, stiffness, and preliminary sizing. For example, a rectangular beam's section modulus can feed the bending-stress calculator directly.
The calculation uses ideal nominal geometry. Profile radii, tolerances, local buckling, and plastic reserve are excluded.