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Polar Moment of Area Calculator — result sheet
Find the polar second moment of area for a solid circular shaft or an annular tube and show its torsional section modulus.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For a circular section, J = π(Do⁴ − Di⁴) ÷ 32; a solid circle has Di = 0.
The polar second moment of area J is a geometry property used in circular-shaft torsion. Because the diameter is raised to the fourth power, a small change in outer or inner diameter can materially change torsional stiffness and stress capacity; the tool reports the geometry without pretending to approve a structural design.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Circular section type — 2 choices
- Outer diameter — m; minimum 1.0E-6; maximum 1000000
- Inner diameter — m; minimum 0; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Circular section type | solid |
| Outer diameter | 0.05 |
| Inner diameter | 0 |
A 50 mm solid circular section has J ≈ 6.136×10⁻⁷ m⁴.
Assumptions and limits
- The section is circular, concentric, and uniform along the length being considered.
- Diameters are entered in metres, so J is returned in m⁴ and the section modulus in m³.
- The result does not choose material strength, allowable stress, fatigue life, stress concentrations, or a design factor.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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