Rectangle about centroidal x-axis
Ix = b h^3 / 12
Geometry calculator
Second Moment of Area Calculator
Find area moment of inertia for beam bending and section stiffness checks.
Calculator
Enter dimensions
Select a shape where available, choose units, and read the result as dimensions update.
Result
About this calculator
How it works
Second moment of area, also called area moment of inertia, describes how section area is distributed about an axis. It strongly affects bending stress and deflection.
Formulas
Formulas used
Circle about centroidal axis
I = pi d^4 / 64
Hollow circle
I = pi (Do^4 - Di^4) / 64
Rectangular tube
Ix = (B H^3 - b h^3) / 12
Worked example
Example: 100 mm by 50 mm rectangle
For a rectangle with b = 0.05 m and h = 0.10 m about its centroidal x-axis:
Second moment of area
Ix = 0.05 x 0.10^3 / 12 = 4.167e-6 m4
Section modulus
Zx = Ix / (h / 2) = 8.333e-5 m3
Guide
How to use this calculator
- Select the shape or section type if a shape menu is shown.
- Enter the known dimensions and choose units beside each length input.
- Read the highlighted result first, then use the supporting values for related checks.
Reference
What the results mean
Second moment of area
A geometric stiffness property used in beam bending and deflection formulas.
Section modulus
I divided by the extreme fiber distance, often used for bending stress checks.
Assumptions and limits
Before using the result
- Inputs are treated as ideal geometric dimensions with no tolerance, chamfer, fillet, draft, roughness, or manufacturing allowance.
- Section properties are centroidal for the listed standard shapes and do not include rotation, offsets, or parallel-axis corrections.
- Use project drawings, tolerances, material data, and applicable design standards for final engineering work.
FAQ
Second Moment of Area Calculator questions
Can I use different units?
Yes. Select the unit beside each input. The calculator converts dimensions internally before solving.
Are these geometry results suitable for final design?
Use the results for education, screening, drafting, and early design checks. Confirm final values against project requirements, tolerances, and applicable standards.
Why do dimensions need to use the same base units?
Geometry formulas require consistent dimensions. The calculator converts entered lengths to meters before calculating area, volume, or section properties.
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