Physics

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Polar Moment of Inertia Calculator.

Calculate the polar second moment for a solid circular shaft.

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Polar moment: 0.000001 m⁴

Polar moment

0.000001m⁴

Results update automatically as you type.

Use Cases

Mechanical engineering coursework

Students can verify hand calculations of polar moment of inertia for solid circular cross-sections, aiding in homework and exam preparation.

Example: Checking J for a 0.1 m diameter shaft.

Frequently Asked Questions

What is the polar moment of inertia?
The polar moment of inertia (J) measures an object's resistance to torsion (twisting). For a solid circular shaft, it depends on the diameter and is calculated as J = (π × d^4) / 32, where d is the shaft diameter.
How do I use this calculator?
Enter the shaft diameter in meters into the 'Shaft diameter' field. The calculator will compute the polar second moment of area (J) for a solid circular shaft using the formula J = (π × d^4) / 32. The result is in m^4.
What units does the calculator use?
The calculator requires the shaft diameter in meters (m). The resulting polar moment of inertia is given in meters to the fourth power (m^4). Ensure you convert your diameter to meters before entering it.

Tips & Common Mistakes

Tips

  • Ensure the shaft diameter is in meters. If you have millimeters, divide by 1000 before entering.
  • The polar moment of inertia is proportional to the fourth power of diameter, so small changes in diameter significantly affect the result.
  • This calculator is for solid circular shafts only. For hollow shafts, use a different formula that accounts for inner and outer diameters.
  • Use the result to compute angle of twist or shear stress with appropriate formulas, but remember this is a reference tool, not a substitute for professional engineering analysis.

Common Mistakes to Avoid

  • Forgetting to convert diameter to meters. Entering millimeters directly will give a result that is off by a factor of 10^12.
  • Using the formula for a hollow shaft or a different cross-section. This calculator is specifically for solid circular shafts.
  • Confusing polar moment of inertia (J) with area moment of inertia (I). They are different properties used for different loading types.

Last updated: August 13, 2026