Moment of Inertia Converter
Convert between moment of inertia units — kilogram square meter, kilogram square centimeter, kilogram square millimeter, gram square centimeter, gram square millimeter, pound square foot, pound square inch, ounce square inch, and slug square foot.
Results from this calculator are estimates provided for general informational purposes only, based on formulas, rates, and standards commonly accepted as of 2026. Figures may differ slightly from other calculators or professional sources due to rounding methods, differing assumptions, or regional regulations, and rules may change over time. Always consult a qualified professional — such as a financial advisor, healthcare provider, or other relevant specialist — before making decisions based on these results.
Result
1 lb·ft² = 0.04214011 kg·m²
1 Pound Square Foot = 0.04214011 Kilogram Square Meters
1 Kilogram Square Meter = 23.73036 Pound Square Feet
1 lb·ft² in every supported unit
What is a Moment of Inertia Converter?
A moment of inertia converter translates a rotating object's resistance to changes in its angular velocity from one unit into its equivalent in another — for example, turning pound square feet into kilogram square meters, or slug square feet into gram square centimeters. Moment of inertia (also called the second moment of mass or rotational inertia) is the rotational counterpart of ordinary mass in Newton's second law: just as mass resists linear acceleration under a force, moment of inertia resists angular acceleration under a torque (torque = I × angular acceleration). It depends not only on how much mass an object has but on how that mass is distributed relative to the axis of rotation, which is why flywheels, rotors, and vehicle wheels are engineered around this specific quantity.
Every unit below is defined relative to the kilogram square meter, the SI derived unit of moment of inertia, so any conversion — metric to metric, imperial to imperial, or across systems — reduces to a single multiplication.
Conversion chart: Pound Square Foot to Kilogram Square Meters
Conversion table
| Pound Square Foot (lb·ft²) | Kilogram Square Meter (kg·m²) |
|---|---|
| 0.01 lb·ft² | 0.0004214011 kg·m² |
| 0.1 lb·ft² | 0.004214011 kg·m² |
| 1 lb·ft² | 0.04214011 kg·m² |
| 2 lb·ft² | 0.08428022 kg·m² |
| 3 lb·ft² | 0.12642033 kg·m² |
| 5 lb·ft² | 0.21070055 kg·m² |
| 10 lb·ft² | 0.4214011 kg·m² |
| 20 lb·ft² | 0.8428022 kg·m² |
| 50 lb·ft² | 2.1070055 kg·m² |
| 100 lb·ft² | 4.214011 kg·m² |
| 1000 lb·ft² | 42.14011 kg·m² |
Supported Units
| Unit | Symbol | In Kilogram Square Meters |
|---|---|---|
| Kilogram Square Meter | kg·m² | 1 kg·m² |
| Kilogram Square Centimeter | kg·cm² | 0.0001 kg·m² |
| Kilogram Square Millimeter | kg·mm² | 1E-06 kg·m² |
| Gram Square Centimeter | g·cm² | 1E-07 kg·m² |
| Gram Square Millimeter | g·mm² | 1E-09 kg·m² |
| Pound Square Foot | lb·ft² | 0.04214011 kg·m² |
| Pound Square Inch | lb·in² | 0.0002926397 kg·m² |
| Ounce Square Inch | oz·in² | 1.829E-05 kg·m² |
| Slug Square Foot | slug·ft² | 1.355818 kg·m² |
About These Parameters
- Value
- The number you want to convert, expressed in the "From" unit. Accepts decimals.
- From Unit
- The moment of inertia unit your input value is currently measured in.
- To Unit
- The moment of inertia unit you want the result converted into. Use the swap button to flip From and To instantly.
How Moment of Inertia Conversion Works
The Formula
Every unit here is defined by a fixed multiplier relative to the kilogram square meter. To convert a value from one unit to another:
result = value × (factor of "From" unit ÷ factor of "To" unit)
For Pound Square Foot → Kilogram Square Meter: multiply by 0.04214011. For example, 1 lb·ft² × 0.04214011 = 0.04214011 kg·m².
Moment of Inertia vs. Mass: Distribution Matters
Mass tells you how much matter an object has; moment of inertia tells you how hard it is to spin that object, and the two are not simply proportional. For a point mass m at distance r from the rotation axis, moment of inertia is I = m·r² — the distance is squared, so mass located far from the axis contributes far more resistance to rotation than the same mass located close to it. This is why a solid disk and a thin ring of identical mass and radius have different moments of inertia (the ring's mass all sits at the rim, at maximum distance), and why figure skaters spin faster by pulling their arms in — reducing r reduces I, and angular momentum conservation forces angular velocity to increase.
SI vs. US Customary Engineering Units
The kilogram square meter is the SI standard used in physics and mechanical engineering worldwide. US automotive and aerospace engineers instead work in pound square foot or, when applying Newton's second law directly without conversion factors, the slug square foot — built on the slug, the US customary mass unit defined so that a 1 lbf force accelerates a 1-slug mass at exactly 1 ft/s². Smaller components — gears, motors, precision instruments — are typically specified in centimeter, millimeter, or inch-based variants to keep the numbers in a readable range for their scale.
Example
1 lb·ft² equals 0.04214011 kg·m². For scale, a small automotive flywheel might have a moment of inertia around 0.5 kg·m² — about 11.86518 lb·ft² — meaning it takes a torque of 0.5 N·m to give it an angular acceleration of exactly 1 radian per second squared.
Frequently Asked Questions
What's the difference between moment of inertia and mass?
Mass measures how much matter an object contains and resists linear acceleration; moment of inertia measures how that mass is distributed around a rotation axis and resists angular acceleration. Two objects with identical mass can have very different moments of inertia depending on how far their mass sits from the axis — a ring resists spinning far more than a solid disk of the same mass and radius.
Why does the US customary system use the slug?
The slug is the US customary unit of mass defined so that Newton's second law (F = ma) and its rotational analog (torque = I·α) work directly with pound-force and foot units, without extra conversion factors. Using ordinary "pounds" for both force and mass creates ambiguity, so engineering calculations that need internal consistency use the slug and slug square foot instead.
How accurate are these conversions?
Every conversion factor used here is derived from the exact, internationally recognized definitions of the underlying mass and length units (the international pound, the international foot, and the slug's definition from pound-force and standard gravity) — results are limited only by floating-point display precision, not by rounded conversion constants.