Moment of Inertia Calculator

Calculate the moment of inertia for common shapes. Select shape, dimensions, and axis of rotation. Get I, units, and formula. Based on standard physics formulas. Informational only—consult a physics textbook.

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Published: October 23, 2025 | Updated: October 23, 2025 | Reviewed by: Science/Physics Editor

Shape and Properties

Preset Objects

Formula Reference

ShapeFormula
Solid SphereI = (2/5)MR²
Cylinder (central)I = (1/2)MR²
Cylinder (diameter)I = (1/4)MR² + (1/12)ML²
Plate (center)I = (1/12)M(W² + H²)
Plate (edge)I = (1/3)MW²
Prism (center)I = (1/12)M(W² + H²)
Rod (end)I = (1/3)ML²

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How it works

I = ∫ r² dm. For common shapes, this simplifies to standard formulas like I = (2/5)MR² for a solid sphere. We use these formulas to calculate I based on the shape and dimensions you provide.

Inputs explained

  • Shape Type: The geometric shape and axis of rotation
  • Mass: Total mass of the object in kg or lbs
  • Radius: For spheres and cylinders
  • Length: For cylinders and rods
  • Width/Height: For plates and prisms

Example

Solid Sphere: M=10kg, R=0.5m

I = (2/5) × 10 × 0.5² = (2/5) × 10 × 0.25 = 1.0 kg·m²

Tips & notes

  • The moment of inertia depends on the shape's mass distribution and the axis of rotation
  • Objects with more mass farther from the axis have a higher moment of inertia
  • This is a key concept in rotational dynamics
  • The parallel axis theorem can shift calculations to different axes

FAQs

A measure of an object's resistance to angular acceleration about a given axis. It depends on the mass distribution relative to the rotation axis.

Using the integral I = ∫ r² dm, or standard formulas for common shapes like I = (2/5)MR² for a solid sphere.

kg·m² in the SI system and lbs·ft² in the imperial system.

No. Everything runs in your browser. Use Export/Share Link to save your configuration.

Disclaimer

Informational tool based on standard physics formulas for uniform density. Real-world objects may vary. Consult a physics textbook for detailed theory.

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