Polar Moment of Inertia Calculator

Calculate polar moment of inertia (J) for engineering applications. Free tool with instant results, no login required.

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What is Polar Moment of Inertia?

The polar moment of inertia (J) is a measure of an object’s resistance to twisting (torsion). It depends only on the object’s shape and size, not the material.

J = I_x + I_y

Where I_x and I_y are moments of inertia about the x and y axes. A larger J value means greater resistance to twisting.

Formulas for Common Shapes

Solid Circle: J = (π × D⁴) / 32

Hollow Circle: J = (π × (D⁴ – d⁴)) / 32

Rectangle: J = (w × h × (w² + h²)) / 12

Square: J = w⁴ / 6

I-beam: Sum of rectangular components

Our calculator automatically selects the correct formula for your chosen shape.

Engineering Applications

Shaft Design

Designing drive shafts, propeller shafts, and torque tubes.

Structural Engineering

Analyzing beams and columns under torsional loads.

Automotive

Designing axles, crankshafts, and suspension components.

Machine Design

Calculating torsional stiffness in machine parts.

Junaid Ahmed

Creator

A high school teacher with ten years of experience and a lifelong love for physics. Holds a Bachelor of Engineering in computer science and enjoys making scientific ideas simple, clear, and engaging. Quiet by nature, but fully expressive when exploring motion, energy, and the wonders of the physical world. See full profile

Zaheer Ahmed

Reviewer

A civil engineer with a strong love for numbers, teaching, and building practical digital tools. With a Bachelor’s in Civil Engineering, a postgraduate degree in Project Management, and 12 years of teaching experience, he blends technical expertise with creativity. His passion for math and web development drives him to create clear, useful calculators that simplify everyday problem-solving. See full profile

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