Free Engineering Tool
Moment of Inertia Unit Converter
Convert mass moment of inertia between all common metric and imperial units instantly. Enter a value and see all conversions simultaneously.
All Conversions
What is Moment of Inertia?
The mass moment of inertia (also called rotational inertia) quantifies a body’s resistance to angular acceleration about a given axis. It is the rotational analog of mass in linear motion.
Where m is mass and r is the perpendicular distance from the axis of rotation.
Conversion Table
| Unit | Symbol | = kg·m² |
|---|---|---|
| kilogram meter squared | kg·m² | 1 |
| kilogram centimeter squared | kg·cm² | 1 × 10⁻⁴ |
| gram centimeter squared | g·cm² | 1 × 10⁻⁷ |
| pound foot squared | lb·ft² | 0.042140 |
| pound inch squared | lb·in² | 2.9264 × 10⁻⁴ |
| ounce inch squared | oz·in² | 1.8290 × 10⁻⁵ |
| slug foot squared | slug·ft² | 1.35582 |
Common Formulas for Simple Shapes
| Shape | Axis | Formula |
|---|---|---|
| Solid cylinder/disk | Central axis | J = ½ m r² |
| Hollow cylinder | Central axis | J = ½ m (r₁² + r₂²) |
| Solid sphere | Through center | J = ⅖ m r² |
| Thin rod | Through center | J = ¹⁄₁₂ m L² |
| Thin rod | Through end | J = ⅓ m L² |
Note: In the imperial system, slug·ft² is the dynamically consistent unit (force = mass × acceleration without a conversion factor). 1 slug = 1 lb·s²/ft = 14.594 kg.
Relationship to Torque and Angular Motion
Where τ is torque (N·m), J is moment of inertia (kg·m²), and α is angular acceleration (rad/s²).
Parallel Axis Theorem
The moment of inertia about any parallel axis equals the inertia about the center of mass plus m × d², where d is the distance between axes.
Professional field balancing instruments and software. Used in 50+ countries.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
