Section properties
| Property | Symbol | Value |
|---|
Formula used
Calculation steps
Calculator inputs
Calculation history
What is the second moment of area?
The second moment of area measures how area spreads around an axis. It strongly affects bending resistance and beam deflection. Larger values usually indicate greater geometric stiffness.
Formula used
The exact formula depends on shape and reference axis. Centroidal properties are calculated before any axis translation. Rotated and composite sections use standard transformation relationships.
How to use this calculator
- Select the required calculation mode.
- Choose units, precision, and angle format.
- Select a shape and enter its dimensions.
- Choose a reference axis or rotation angle.
- Submit the form and review the detailed steps.
- Copy, print, or export the results when needed.
Example section data
| Shape | Example dimensions | Centroidal Ix | Centroidal Iy |
|---|---|---|---|
| Rectangle | b = 120 mm, h = 240 mm | 138,240,000 mm⁴ | 34,560,000 mm⁴ |
| Solid circle | D = 100 mm | 4,908,738.521 mm⁴ | 4,908,738.521 mm⁴ |
| Hollow circle | D = 120 mm, d = 90 mm | 6,958,136.854 mm⁴ | 6,958,136.854 mm⁴ |
| Ellipse | a = 80 mm, b = 40 mm | 4,021,238.597 mm⁴ | 16,084,954.387 mm⁴ |
Frequently asked questions
Is second moment of area the same as mass moment of inertia?
No. Area moment describes cross-sectional geometry. Mass moment describes rotational resistance based on distributed mass.
Why are the units raised to the fourth power?
The calculation integrates squared distance over an area. Length squared multiplied by area produces fourth-power length units.
Which axis should I use?
Use the bending axis relevant to the applied loading. Beam deflection depends on the second moment about that axis.
What does the parallel-axis theorem calculate?
It transfers a centroidal property to any parallel axis. The added term equals area multiplied by distance squared.
How are holes handled in composite sections?
Add holes as void components. Their areas and moments are subtracted from the solid section.
What is product moment of area?
It describes coupling between two perpendicular axes. It becomes important for unsymmetrical and rotated cross-sections.
What are principal axes?
Principal axes are orientations where product moment becomes zero. They provide the maximum and minimum second moments.
What is radius of gyration?
Radius of gyration represents an equivalent area-distribution distance. It is widely used in column slenderness calculations.
Does material type change the calculated value?
No. Geometry controls the second moment of area. Material modulus combines with it through bending stiffness EI.
Can I mix metric and imperial dimensions?
Enter every dimension using the selected unit. Convert dimensions first to avoid inconsistent section properties.