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Moment of Inertia Calculator | Free Online Tool

Moment of Inertia Calculator

Global Standard for Rotational Dynamics & Mechanical Design

Engineering Precision: This moment of inertia calculator provides accurate results for 8 standard shapes with full input validation and SI units.

Calculate moment of inertia for a solid cylinder about central or end axis using our moment of inertia calculator.

Range: 0.001 to 10,000 kg
Range: 0.001 to 10 m
Range: 0.01 to 50 m

Enter values to calculate

Calculate I for thick or thin-walled hollow cylinder using our moment of inertia calculator.

Range: 0.001 to 10,000 kg
Range: 0.001 to 10 m
Must be > inner radius

Enter values to calculate

Uniform solid sphere moment of inertia using our moment of inertia calculator.

Range: 0.001 to 10,000 kg
Range: 0.001 to 10 m

Enter values to calculate

Thin spherical shell using our moment of inertia calculator.

Range: 0.001 to 10,000 kg
Range: 0.001 to 10 m

Enter values to calculate

Flat rectangular plate or slab using our moment of inertia calculator.

Range: 0.001 to 10,000 kg
Range: 0.01 to 20 m
Range: 0.01 to 20 m

Enter values to calculate

Uniform thin rod or bar using our moment of inertia calculator.

Range: 0.001 to 5,000 kg
Range: 0.01 to 50 m

Enter values to calculate

Solid cone about apex or base center using our moment of inertia calculator.

Range: 0.001 to 10,000 kg
Range: 0.01 to 10 m
Range: 0.01 to 20 m

Enter values to calculate

Apply parallel axis theorem to any shape using our moment of inertia calculator.

Range: 0.0001 to 1Ɨ10ā¹ kgĀ·mĀ²
Range: 0.001 to 10,000 kg
Range: 0 to 50 m

Enter values to calculate

Moment of Inertia Calculator: The Global Engineering Standard

Trusted by mechanical engineers, roboticists, and physicists worldwide, our moment of inertia calculator delivers precision for flywheels, motors, drones, satellites, and automotive components.

"Inertia est vis rotationis" ā€” Inertia is the force of rotation.

How the Moment of Inertia Calculator Works

The moment of inertia (I) quantifies an object's resistance to angular acceleration:

I = āˆ« rĀ² dm
Iparallel = ICM + m dĀ²

Our moment of inertia calculator uses exact analytical formulas for uniform density objects.

Moment of Inertia Calculator: Eight Standard Shapes

Solid Cylinder

Central axis: (1/2) m rĀ²
End axis: (1/3) m LĀ² + (1/4) m rĀ²

Hollow Cylinder

Central axis: (1/2) m (rā‚Ā² + rā‚‚Ā²)

Solid Sphere

(2/5) m rĀ² ā€” Classic result in our moment of inertia calculator.

Hollow Sphere

(2/3) m rĀ² ā€” Thin shell approximation.

Rectangular Plate

Center X: (1/12) m hĀ² | Center Y: (1/12) m wĀ² | Edge: (1/3) m hĀ²

Rod

Center: (1/12) m LĀ² | End: (1/3) m LĀ²

Cone

Apex: (3/10) m rĀ² | Base center: (3/5) m rĀ² + (3/20) m hĀ²

Custom Shape

Parallel axis theorem: I = ICM + m dĀ²

Moment of Inertia Calculator: Standard Reference Table

Shape Axis Formula Example I (kgĀ·mĀ²)
Solid Cylinder Central (1/2) m rĀ² 1.250
Hollow Cylinder Central (1/2) m (rā‚Ā² + rā‚‚Ā²) 2.080
Solid Sphere Any diameter (2/5) m rĀ² 3.840
Hollow Sphere Any diameter (2/3) m rĀ² 8.000
Rod Center (1/12) m LĀ² 3.750

Moment of Inertia Calculator: Real-World Applications

  • Flywheel Energy Storage: Maximize I for kinetic energy
  • Electric Motors: Minimize I for fast acceleration
  • Spacecraft Attitude Control: Precise I for reaction wheels
  • Robotics: I affects joint torque requirements
  • Automotive: Crankshaft and wheel inertia
  • Wind Turbines: Rotor inertia for grid stability

Pro Tips for Using the Moment of Inertia Calculator

  1. Use SI units: kg and meters ā†’ kgĀ·mĀ²
  2. Apply parallel axis theorem when axis is offset
  3. For composites: Itotal = Ī£ Ii
  4. Minimize I for rapid rotational acceleration
  5. Maximize I for energy storage (flywheels)
  6. Verify with FEA for complex geometries

Calculate with Confidence

From student projects to mission-critical systems, our moment of inertia calculator ensures rotational accuracy worldwide.

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