Free Moment of Inertia Calculator

Calculate moment of inertia for common shapes including solid sphere, hollow sphere, solid cylinder, and thin rod.

Save
kg
m

Moment of Inertia

0.080000 kg·m²

Moment of Inertia vs Mass

View formula & how it works →

Moment of Inertia

Moment of inertia (I) is the rotational analogue of mass. It depends on mass distribution relative to the rotation axis.

Formulas by Shape

  • Solid Sphere: I = (2/5) * m * r²
  • Hollow Sphere: I = (2/3) * m * r²
  • Solid Cylinder/Disk: I = (1/2) * m * r²
  • Thin Rod (center): I = (1/12) * m * L²

    • Example Calculation

    A solid sphere of mass 5 kg and radius 0.2 m.

    1. 01For a solid sphere: I = (2/5) * m * r²
    2. 02I = 0.4 * 5 * 0.04
    3. 03I = 0.4 * 0.2
    4. 04I = 0.08 kg·m²

    Frequently Asked Questions

    Learn More

    Understanding Newton's Laws of Motion

    A comprehensive guide to Newton's three laws of motion. Learn about inertia, force and acceleration, action-reaction pairs, and how these principles govern everyday physics.

    Related Calculators

    Torque Calculator

    Calculate torque from force and lever arm.

    Angular Acceleration Calculator

    Find angular acceleration from torque and inertia.

    Kinetic Energy Calculator

    Compute kinetic energy from mass and velocity.