Moment of Inertia Converter: kg·m², slug·ft², lb·ft² & More
Convert moment of inertia between kg·m² (kilogram square meter), slug·ft², lb·ft², lbf·ft·s², and 14 units. Whether you need kg·m² to slug·ft², pound square foot to kg·m², or any SI, gravitational, or imperial unit, this converter uses the SI base (kg·m²) for accurate results. Free, runs in your browser, no sign-up required.
What is moment of inertia?
Moment of inertia (I) is the rotational analogue of mass, it quantifies how mass is distributed relative to an axis of rotation. Its dimension is mass × length² (e.g. kg·m²). The SI unit is the kilogram square meter (kg·m²). In US customary units you’ll see slug·ft², lb·ft², and lbf·ft·s² (pound-force foot square second); in metric engineering, kgf·m·s² and g·cm² appear. This converter supports 14 units including SI (kg·m², kg·cm², kg·mm², g·cm², g·mm²), gravitational (kgf·m·s², kgf·cm·s²), and imperial (slug·ft², lb·ft², lb·in², oz·in², and force-time² variants). Every value is normalized to kg·m² under the hood.
How moment of inertia conversion works
Moment of inertia has dimension mass × length². The SI unit is the kilogram square meter (kg·m²). Convert your value into kg·m² using the source unit’s factor, then divide by the target unit’s factor:
Example: 10 slug·ft² to kg·m² → 10 × 1.35582 ÷ 1 ≈ 13.56 kg·m². The converter supports SI (kg·m², kg·cm², kg·mm², g·cm², g·mm²), gravitational (kgf·m·s², kgf·cm·s²), and imperial (slug·ft², lb·ft², lb·in², oz·in², and lbf·ft·s², lbf·in·s², ozf·in·s²).
Key moment of inertia units explained
Each unit’s factor to kg·m², what this converter uses. Moment of inertia = mass × length²; mass-length² units (kg·m², lb·ft², slug·ft²) and force-length-time² units (lbf·ft·s², kgf·m·s²) both reduce to kg·m².
Kilogram square meter (kg·m²)
Factor: 1 (SI base unit)
The SI derived unit for moment of inertia. Used in physics, structural dynamics, and rotational mechanics worldwide.
Slug square foot (slug·ft²)
Factor:
Common in US engineering. 1 slug = 14.5939 kg, 1 ft = 0.3048 m, so 1 slug·ft² ≈ 1.356 kg·m². Same numeric factor as lbf·ft·s².
Pound square foot (lb·ft²)
Factor: 1 lb·ft² ≈ 0.04214 kg·m²
Mass-length² form in US units. 1 lb = 0.4536 kg, 1 ft = 0.3048 m. Used in machinery and rotor specs when mass and radius are in lb and ft.
Pound-force foot square second (lbf·ft·s²)
Factor: 1 lbf·ft·s² ≈ 1.35582 kg·m²
Force × length × time² equals mass × length² dimensionally. 1 lbf = 4.448 N, so 1 lbf·ft·s² = 4.448 × 0.3048 kg·m². Common in US engineering tables.
Kilogram-force meter square second (kgf·m·s²)
Factor: 1 kgf·m·s² = 9.80665 kg·m²
Gravitational metric unit. 1 kgf = 9.80665 N (standard gravity). Used in some regional specs and textbooks.
Gram square centimeter (g·cm²)
Factor: 1 g·cm² = 10−7 kg·m²
CGS-style unit. Convenient for small rotating parts, flywheels, and beam cross-sections in cm and grams.
When to use kg·m² vs slug·ft² vs lb·ft²
kg·m² is the SI unit and is preferred in physics and international specs. slug·ft² and lbf·ft·s² are the US customary standards for rotational dynamics (1 slug·ft² = 1 lbf·ft·s² ≈ 1.356 kg·m²). lb·ft² (pound square foot) is mass-length² and smaller: 1 lb·ft² ≈ 0.04214 kg·m². kgf·m·s² appears in some metric regions. g·cm² and kg·cm² are handy for small parts and beam theory. This converter supports all of these so you can match datasheets and formulas.
Who uses a moment of inertia converter?
Mechanical and structural engineers convert between kg·m² and slug·ft² for rotors, flywheels, and dynamics. Students and educators use it for rotational kinetics (τ = Iα, kinetic energy = ½Iω²) and to switch between SI and US units. Manufacturing and machinery specs often mix kg·m², lb·ft², and lbf·ft·s². Aerospace and automotive work with rotational inertia in both metric and imperial. All conversions run in your browser, no data is sent to a server.
Common moment of inertia conversions at a glance
Handy reference for kg·m² to slug·ft², lb·ft² to kg·m², and other everyday conversions.
| From | To | Formula | Example |
|---|---|---|---|
| kg·m² | slug·ft² | ÷ 1.35582 | 13.56 kg·m² ≈ 10 slug·ft² |
| slug·ft² | kg·m² | × 1.35582 | 10 slug·ft² ≈ 13.56 kg·m² |
| lb·ft² | kg·m² | × 0.04214 | 100 lb·ft² ≈ 4.21 kg·m² |
| lbf·ft·s² | kg·m² | × 1.35582 | 1 lbf·ft·s² ≈ 1.356 kg·m² |
| kg·cm² | kg·m² | ÷ 10000 | 10000 kg·cm² = 1 kg·m² |
Why kilogram square meter is the SI unit
Moment of inertia I has dimension mass × length², so the coherent SI unit is kg·m². In τ = Iα (torque = I × angular acceleration), I must be in kg·m² when τ is in N·m and α in rad/s². Gravitational units (kgf·m·s², lbf·ft·s²) express the same dimension using force and time²; the converter uses fixed factors so results are consistent across all 14 units.
Avoiding common mistakes
Don’t confuse lb·ft² (pound square foot, mass × length²) with lbf·ft·s² (pound-force foot square second), they differ by a factor of about 32.2 (g). Don’t mix slug·ft² and lb·ft² without converting (1 slug·ft² ≈ 32.2 lb·ft²). Area moment of inertia (for beams, in m⁴ or in⁴) is a different quantity; this tool is for mass moment of inertia (kg·m²). Always convert to one unit (we recommend kg·m²) before using in τ = Iα or ½Iω².
Moment of Inertia Conversion FAQ
How do I convert kg·m² to slug·ft²?
Divide kg·m² by 1.35582 to get slug·ft². So 13.56 kg·m² ≈ 10 slug·ft². To convert slug·ft² to kg·m², multiply by 1.35582.
What is the difference between lb·ft² and lbf·ft·s²?
lb·ft² is mass × length² (1 lb·ft² ≈ 0.04214 kg·m²). lbf·ft·s² is force × length × time², which has the same dimension as mass × length²; 1 lbf·ft·s² ≈ 1.35582 kg·m². So 1 lbf·ft·s² ≈ 32.2 lb·ft². Don’t mix them without converting.
What is the SI unit for moment of inertia?
The kilogram square meter (kg·m²). Moment of inertia has dimension mass × length², so in SI the coherent unit is kg·m². This converter uses kg·m² as the base for all 14 units.
Is slug·ft² the same as lbf·ft·s²?
Numerically yes: 1 slug·ft² = 1 lbf·ft·s² ≈ 1.35582 kg·m². The slug is defined so that 1 lbf = 1 slug·ft/s², so 1 slug·ft² = 1 lbf·ft·s². Both are common in US engineering for rotational inertia.
How do I convert gram square centimeter to kg·m²?
Multiply g·cm² by 10−7 to get kg·m². So 10⁷ g·cm² = 1 kg·m². To convert kg·m² to g·cm², multiply by 10⁷. Gram square centimeter is convenient for small parts and CGS-style calculations.
Is this for mass moment of inertia or area moment of inertia?
This converter is for mass moment of inertia (dimension mass × length², unit kg·m²), used in rotational dynamics (τ = Iα, kinetic energy = ½Iω²). Area moment of inertia (second moment of area, dimension length⁴, units m⁴ or in⁴) is used in beam bending and is a different quantity, use a dedicated area-moment converter for that.