Moment of Inertia Calculator - Free Online Cross-Section Tool
Moment of Inertia Calculator
Calculate area moment of inertia, section modulus, and other geometric properties for various cross-sectional shapes.
Select Cross-Section Shape
Dimensions
Calculation Options
Composite Section Builder
Section Properties
Cross-Section Visualization
Geometric Properties
- Section Modulus (Sx):
- -
- Section Modulus (Sy):
- -
- Radius of Gyration (rx):
- -
- Radius of Gyration (ry):
- -
Additional Properties
- Polar Moment (J):
- -
- Product of Inertia (Ixy):
- -
- Distance to Top Fiber:
- -
- Distance to Bottom Fiber:
- -
📐 Formulas Used
Common Section Properties
| Shape | Area | Ix | Iy |
|---|---|---|---|
| Rectangle (b×h) | bh | bh³/12 | hb³/12 |
| Circle (d) | πd²/4 | πd⁴/64 | πd⁴/64 |
| Triangle (b×h) | bh/2 | bh³/36 | hb³/48 |
How to use this calculator
📐 How to Use This Calculator
- Select the cross-sectional shape from the options
- Enter the dimensions for your selected shape
- Choose the reference axis for calculations
- Click calculate to find moment of inertia and other properties
- For composite sections, add multiple shapes and calculate combined properties
📐 Key Formulas
Moment of Inertia
I = ∫ y² dA
Second moment of area about an axis
Parallel Axis Theorem
I = I_c + A × d²
Where:
I_c = Moment about centroid
A = Area
d = Distance between axes
Section Modulus
S = I / c
c = Distance to extreme fiber
🌟 Practical Applications
Calculate bending stress: σ = M·c/I
Use section modulus for quick sizing
Critical load: P_cr = π²EI/(KL)²
Radius of gyration determines slenderness
Shear stress: τ = T·r/J
Use polar moment J for circular shafts
💡 Design Tips
- • Maximize I by placing material far from neutral axis
- • I-beams and hollow sections are efficient for bending
- • Circular sections are best for torsion
- • Consider buckling for compression members
- • Use composite sections for complex loading
- • Check both Ix and Iy for biaxial bending
⚠️ Important Notes
- • Results assume homogeneous, isotropic material
- • Thin-walled sections may require special analysis
- • Consider shear deformation for short beams
- • Local buckling may govern for thin plates
- • Always verify with applicable design codes
About this calculator
Calculate moment of inertia, section modulus, and radius of gyration for various cross-sections.
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