Cylinder Moment of Inertia Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/6/2026
The moment of inertia of a solid cylinder rotating about its axis is calculated with I = ½ × m × r². For a 5 kg cylinder with a 0.2 m radius, the moment of inertia is 0.1 kg·m².
Explanation
Moment of inertia measures an object's resistance to a change in its rotational speed, exactly as mass measures an object's resistance to a change in its linear (translational) speed. For a homogeneous solid cylinder rotating about its central axis of symmetry, the moment of inertia is calculated with I = ½ × m × r², where m is the cylinder's total mass and r its radius. This formula differs from that of other rotating geometric shapes (a thin ring, a solid sphere, a rod): it accounts for the fact that a solid cylinder's mass is distributed throughout its whole volume, not just at the rim, giving a lower moment of inertia than a hollow ring of the same mass and radius (whose entire weight would be concentrated at the maximum distance from the axis, giving I = m×r² without the ½ factor). Moment of inertia enters directly into the torque needed to accelerate or slow down a rotating object (torque = moment of inertia × angular acceleration, the rotational equivalent of F = ma), an essential parameter in designing flywheels, wheels, motor rotors, or any rotating mechanical component. A flywheel, for example, is designed with a high moment of inertia (a large mass, often concentrated at the rim) precisely to store rotational kinetic energy and smooth out a motor's speed fluctuations. For the rotational speed itself, see our angular velocity calculator.
Example: a 5 kg cylinder, 0.2 m radius
Inputs
Mass: 5 kg. Radius: 0.2 m.
Calculation
Moment of inertia = 0.5 × 5 × 0.2² = 0.5 × 5 × 0.04 = 0.1 kg·m².
Result
This cylinder's moment of inertia is 0.1 kg·m².
Frequently asked questions
Why is the factor ½ for a solid cylinder, but 1 for a hollow ring of the same mass?
Because in a solid cylinder, the mass is distributed across all distances from the axis, from 0 (at the center) up to the maximum radius, with an average effective distance lower than the full radius. In a hollow ring (all the mass concentrated at the rim, at exactly radius r), every particle of mass contributes maximally to the moment of inertia, hence a higher coefficient (I = m×r², without the ½ factor) for the same mass and radius.
Why does a flywheel often have its mass concentrated at the rim?
Because moment of inertia depends on the square of the radius (r²): for the same mass, concentrating it as far as possible from the rotation axis (at the rim, rather than the center) maximizes the moment of inertia obtained. This is why an effective flywheel often looks more like a thick ring than a uniform solid disk, to store as much rotational kinetic energy as possible with the least added mass.
Does this formula apply to a hollow cylinder (a tube)?
No, this formula is specific to a solid, homogeneous cylinder. For a hollow cylinder (a thick-walled tube, with distinct inner and outer radii), the moment of inertia formula is different and involves both radii: I = ½ × m × (r(outer)² + r(inner)²), a more general formula that correctly reduces to the solid cylinder's when the inner radius is zero.