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.