Moment of Inertia Calculator

Moment of inertia is a fundamental property in physics and engineering. It quantifies an object’s resistance to rotational acceleration and is essential for designing mechanical parts, analyzing vehicle stability, simulating robotic joints, and studying celestial motion.

Compute the moment of inertia I using I = ∫ r² dm. Select your mass and length units, then enter dimensions for your chosen shape.

• Thin Rod (center): I = (1/12) M L²
• Solid Cylinder: I = (1/2) M R²
• Solid Sphere: I = (2/5) M R²
• Rectangular Plate (center): I = (1/12) M (A² + B²)
• Thin Ring / Hoop: I = M R²