Calculator · Engineering Mechanics
Mass Moment of Inertia Calculator
Rotational inertia of a rigid body about a stated axis, in kg·m². This is a mass property — dimensionally different from the second moment of area in m⁴.
Case
I_G = m·L²/12 — about the centroidal axis perpendicular to the rod.
Inputs
Results
| Mass m | 2 kg |
|---|---|
| Mass moment of inertia I | 0.1667 kg·m² |
| Axis | about the centroidal axis perpendicular to the rod |
| Radius of gyration k = √(I/m) | 0.2887 m |
Diagnostics
Technical reference
I = ∫r² dm
- r
- perpendicular distance of a mass element from the stated axis[m]
- dm
- differential mass element[kg]
- I
- mass moment of inertia about that axis[kg·m²]
Standard-body cases implemented here: point mass I = m·d²; slender rod I_G = mL²/12 (centre) or I_O = mL²/3 (end); solid disk I = mR²/2; thin hoop I = mR²; rectangular plate I_G,z = m(b²+h²)/12.
Each formula already states its axis — the same body has a different I about a different axis, and moving between them is the parallel-axis theorem, not a new formula.
This is a mass property in kg·m², dimensionally distinct from the area moment of inertia in m⁴ used for bending of cross-sections.
Assumptions
- · Rigid, homogeneous bodies with the idealisation named by the case (a slender rod has negligible cross-section).
- · Every result is about the axis stated with it; moving to another axis is the parallel-axis theorem.
- · Mass moment of inertia [kg·m²] is never interchangeable with an area moment of inertia [m⁴].
- · Mass must be finite and non-negative; a size must be strictly positive, while a distance may be zero.