Moment of Inertia Converter
Convert mass moment of inertia, the resistance of a body to changes in its rotation, between kilogram square meters, gram square centimeters, pound square feet, slug square feet and other units. Pick two units, enter a value and read the result instantly.
Select two units to see the conversion factor.
This tool converts mass moment of inertia (mass × length², kg·m²) only. It is not the area moment of inertia (second moment of area, m⁴) used for beam bending, and not torque or mass.
Mass Moment of Inertia Formula
Mass moment of inertia is the sum of each mass element times the square of its distance from the axis: I = Σ m × r². Every unit is a fixed multiple of the kilogram square meter. Result = value × (source factor ÷ target factor). The building blocks are exact: 1 g = 10⁻³ kg, 1 cm = 0.01 m, 1 lb = 0.45359237 kg, 1 ft = 0.3048 m, 1 in = 0.0254 m, standard gravity 9.80665 m/s², and force-based units such as kgf·m·s² or lbf·ft·s² add a factor of standard gravity.
What Is Mass Moment of Inertia?
Mass moment of inertia, also called rotational inertia, measures how strongly a body resists a change in its rotation about a given axis. It plays the role for rotation that mass plays for straight-line motion. It depends on both the mass and how far that mass is from the axis: I = Σ m × r². Because distance is squared, mass far from the axis counts much more than mass near it, which is why a flywheel concentrates its mass at the rim. The SI unit is the kilogram square meter (kg·m²).
Standard results help check a number: a point mass is m r², a thin ring about its axis is m r², a solid cylinder or disc about its axis is ½ m r², and a solid sphere about a diameter is ⅖ m r². A 10 kg solid disc of radius 0.2 m has I = ½ × 10 × 0.2² = 0.2 kg·m². The units in this converter fall into two groups. Mass-based units such as kg·m², g·cm², lb·ft², lb·in², oz·in² and slug·ft². Force-based (gravitational) units such as lbf·ft·s², lbf·in·s², ozf·in·s², kgf·m·s² and kgf·cm·s², which contain standard gravity. The slug·ft² and the lbf·ft·s² are the same size.
Do not confuse mass moment of inertia with the area moment of inertia. The area moment of inertia, or second moment of area, has units of length to the fourth power (m⁴, in⁴, mm⁴). It describes how a cross-section resists bending and has nothing to do with mass or rotation dynamics. This converter handles only the mass moment of inertia (kg·m²). It is also not mass (kg) or torque (Torque Converter).
Supported Units
This converter supports the following 14 mass moment of inertia units. The last column gives the value of each unit in the base unit, the kilogram square meter. Pay attention to the difference between pound-mass units (lb·ft²) and force-based units (lbf·ft·s²): 1 lbf·ft·s² equals 32.17404856 lb·ft².
| Unit | Symbol | Value in kg·m² |
|---|---|---|
| Kilogram square meter | kg·m² | 1 |
| Kilogram square centimeter | kg·cm² | 0.0001 |
| Kilogram square millimeter | kg·mm² | 1e-6 |
| Gram square centimeter | g·cm² | 1e-7 |
| Gram square millimeter | g·mm² | 1e-9 |
| Pound square foot | lb·ft² | 0.04214011009 |
| Pound square inch | lb·in² | 0.0002926396534 |
| Ounce square inch | oz·in² | 1.828997834e-5 |
| Slug square foot | slug·ft² | 1.355817948 |
| Pound-force foot square second | lbf·ft·s² | 1.355817948 |
| Pound-force inch square second | lbf·in·s² | 0.112984829 |
| Ounce-force inch square second | ozf·in·s² | 0.007061551814 |
| Kilogram-force meter square second | kgf·m·s² | 9.80665 |
| Kilogram-force centimeter square second | kgf·cm·s² | 0.0980665 |
How to Use the Moment of Inertia Converter
- Type the moment of inertia in the value box. Decimals and scientific notation such as 0.0025 or 2.5e-3 are accepted.
- Choose the From unit and the To unit.
- The result appears instantly, or press Convert Now. Very large or very small results are shown in scientific notation.
- Use Swap Units to reverse the conversion, Copy Result to copy the answer, open Show this value in all units for a full list, and Clear to start again.
Step-by-step by hand
- Find the size of each unit in the common base unit (kg·m²): 1 lb·ft² = 0.04214011009 kg·m² and 1 kg·m² = 1 kg·m².
- Divide the source size by the target size to get the conversion factor: 0.04214011009 ÷ 1 = 0.04214011009, so 1 lb·ft² = 0.04214011009 kg·m².
- Multiply by your value: 25 lb·ft² × 0.04214011009 = 1.053502752 kg·m².
Mass moment of inertia cannot be negative, so only zero and positive values are accepted.
Common Moment of Inertia Conversions
- Pound square feet to SI: 25 lb·ft² equals 1.053502752 kg·m².
- Solid disc flywheel: 0.2 kg·m² equals 4.746072081 lb·ft² and 0.1475124299 slug·ft².
- Small rotor: 2,500 g·cm² equals 0.00025 kg·m².
- Servo motor datasheet: 0.5 kg·cm² equals 5e-5 kg·m² and 500 g·cm².
- Small parts: 12 oz·in² equals 0.0002194797401 kg·m².
- Gravitational unit: 1 kgf·m·s² equals 9.80665 kg·m².
Pound Square Foot to Other Moment of Inertia Units
Quick reference for frequently used values
| lb·ft² | kg·m² | g·cm² | slug·ft² |
|---|---|---|---|
| 0.01 | 0.0004214011009 | 4,214.011009 | 0.0003108095017 |
| 0.1 | 0.004214011009 | 42,140.11009 | 0.003108095017 |
| 1 | 0.04214011009 | 421,401.1009 | 0.03108095017 |
| 5 | 0.2107005505 | 2,107,005.505 | 0.1554047509 |
| 10 | 0.4214011009 | 4,214,011.009 | 0.3108095017 |
| 25 | 1.053502752 | 10,535,027.52 | 0.7770237543 |
| 50 | 2.107005505 | 21,070,055.05 | 1.554047509 |
| 100 | 4.214011009 | 42,140,110.09 | 3.108095017 |
Where and Why This Conversion Is Used
- Motor and drive sizing: the torque needed to accelerate a load is τ = I × α, so inertia in kg·m² is a core input.
- Flywheels, rotors and turbines: energy storage ½ I ω² and run-up behaviour.
- Automotive and aerospace: crankshaft, wheel, propeller and spacecraft attitude-control inertia, often quoted in lb·ft² or slug·ft².
- Robotics and servo systems: inertia matching between motor and load, with datasheets in kg·cm² or g·cm².
- Physics education: rotational dynamics problems.
Limitations
- The converter changes units only. It does not calculate the moment of inertia of a shape; use a formula or CAD software for that.
- A moment of inertia depends on the chosen axis. Make sure the value you convert refers to the axis you need.
Important Differences Between Related Measurements
- Mass moment of inertia vs area moment of inertia: mass moment of inertia (kg·m²) describes rotational inertia. Area moment of inertia, or second moment of area (m⁴), describes how a cross-section resists bending. They have different units and are never interchangeable.
- Moment of inertia vs mass: mass resists linear acceleration. Moment of inertia resists angular acceleration and depends on where the mass is, not only how much there is.
- Moment of inertia vs torque: torque is the twisting action (N·m). Moment of inertia is the resistance to it (kg·m²). They are linked by τ = I × α.
- Pound-mass units vs force-based units: lb·ft² uses the pound of mass. lbf·ft·s² (equal to the slug·ft²) is a gravitational unit and is about 32.17 times larger, since it includes standard gravity.
Each converter on this site changes units within one quantity only, and none of them mixes quantities. The related tools are: Velocity - Angular, Acceleration, Acceleration - Angular, Density, Specific Volume, Moment of Inertia, Moment of Force and Torque.