Mass Moment of Inertia Converter

This moment of inertia converter changes a mass moment of inertia between kilogram square meters, kilogram square centimeters, pound square feet, pound square inches and slug square feet. Formula: 1 kg·cm² = 0.0001 kg·m²; 1 g·cm² = 0.0000001 kg·m². All values go through kg·m², the SI unit. 1 lb·ft² is about 0.0421401 kg·m², 1 lb·in² is about 0.000292640 kg·m², and 1 kg·cm² is exactly 0.0001 kg·m².

How to use the moment of inertia converter

1. Enter the value, for example 12 from a motor datasheet in kg·cm².
2. In the moment of inertia converter, choose its unit and the target unit, such as kg·cm² to kg·m².
3. Read the moment of inertia converter result: 12 kg·cm² = 0.0012 kg·m².

This page covers mass moment of inertia (resistance to angular acceleration). Area moment of inertia, used for beam bending, has units of length to the fourth power (m⁴, in⁴) and is a different quantity.

What is moment of inertia?

Mass moment of inertia measures how hard it is to change an object’s rotation about an axis. It depends on mass and how far that mass sits from the axis; the SI unit is kilogram square meter (kg·m²).

Conversion formula

The moment of inertia converter stores every unit as a multiple of the base unit, the kilogram square meter (kg·m²). To convert:

value in target unit = value × (factor of source unit ÷ factor of target unit)

where each factor is the size of the unit in kilogram square meters.

Common moment of inertia conversions

From	To	1 unit equals
pound square foot (lb·ft²)	kilogram square meter (kg·m²)	0.04214011 kg·m²
kilogram square meter (kg·m²)	pound square inch (lb·in²)	3,417.172 lb·in²
gram square centimeter (g·cm²)	kilogram square meter (kg·m²)	1 × 10−7 kg·m²

Moment of inertia converter worked example

Convert 25 pound square feet to kilogram square meters:

1. Factor of lb·ft² = 0.04214011 kg·m²
2. Factor of kg·m² = 1 kg·m²
3. 25 × 0.04214011 ÷ 1 = 1.053503 kg·m²

Moment of inertia unit reference

Unit	Symbol	Group	Equals (kg·m²)
Kilogram Square Meter	kg·m²	SI	1
Kilogram Square Centimeter	kg·cm²	Metric	0.0001
Gram Square Centimeter	g·cm²	Metric	1 × 10−7
Pound Square Foot	lb·ft²	US/Imperial	0.04214011009
Pound Square Inch	lb·in²	US/Imperial	0.0002926396543
Slug Square Foot	slug·ft²	US Engineering	1.355817948
Ounce Square Inch	oz·in²	US/Imperial	1.829 × 10−5

Reverse factors for each moment of inertia unit

The moment of inertia converter reference table gives each unit in kilogram square meters. To go the other way, divide by that factor; the list below does the division for you.

• Kilogram Square Centimeter (kg·cm²), Metric: 1 kg·cm² = 0.0001 kg·m², so 1 kg·m² = 10,000 kg·cm².
• Gram Square Centimeter (g·cm²), Metric: 1 g·cm² = 1 × 10⁻⁷ kg·m², so 1 kg·m² = 1 × 10⁷ g·cm².
• Pound Square Foot (lb·ft²), US/Imperial: 1 lb·ft² = 0.04214011 kg·m², so 1 kg·m² = 23.73036 lb·ft².
• Pound Square Inch (lb·in²), US/Imperial: 1 lb·in² = 0.0002926397 kg·m², so 1 kg·m² = 3,417.172 lb·in².
• Slug Square Foot (slug·ft²), US Engineering: 1 slug·ft² = 1.355818 kg·m², so 1 kg·m² = 0.7375621 slug·ft².
• Ounce Square Inch (oz·in²), US/Imperial: 1 oz·in² = 1.829 × 10⁻⁵ kg·m², so 1 kg·m² = 54,674.75 oz·in².

Mass moment of inertia of common shapes

For simple uniform shapes, the inertia follows from mass and size. The example column uses a 2 kg body with radius or length 0.5 m:

Shape and axis	Formula	Example (m = 2 kg, r or L = 0.5 m)
Solid disc or cylinder, central axis	I = ½ m r²	0.25 kg·m²
Thin ring or hoop, central axis	I = m r²	0.5 kg·m²
Solid sphere, through center	I = ⅖ m r²	0.2 kg·m²
Thin rod, about its center	I = 1⁄12 m L²	0.0417 kg·m²
Thin rod, about one end	I = ⅓ m L²	0.1667 kg·m²

Inertia scales with the square of distance, so moving mass outward raises it quickly.

Motor and load inertia in practice

Servo and motor datasheets list rotor inertia in kg·cm² or lb·in², and drive sizing compares load to motor inertia. Convert both to the same unit first. For kg·m² to lb·ft², divide by 0.0421401; for lb·in² to kg·m², multiply by 0.000292640. With inertia in kg·m² and angular acceleration in rad/s², torque = I × α; see the angular acceleration converter.

WK² and GD² in motor data

US motor and gearbox catalogs often list rotating inertia as WK², in lb·ft². It is the same quantity as the mass moment of inertia J, just in pound and foot units. Enter 25 lb·ft² in the moment of inertia converter and you get about 1.054 kg·m², since one lb·ft² equals 0.04214 kg·m².

Some European and Japanese data sheets use GD² instead, with G as weight and D as the diameter of gyration. Because the diameter is twice the radius, GD² in kgf·m² is numerically four times J in kg·m². A GD² of 2.0 therefore means J = 0.5 kg·m². Check which one the sheet uses before you compare two motors.

Load inertia matters for drive sizing. Servo vendors usually recommend keeping the ratio of load inertia to motor inertia below about 10:1, and often much lower for fast positioning. If the motor rotor is 0.0012 kg·m² and the reflected load is 0.009 kg·m², the ratio is 7.5. A moment of inertia converter lets you put both values into the same unit first, which is where most of the mistakes in these ratio checks happen.

Small parts are usually quoted in g·cm² or lb·in². One kg·m² is 10,000,000 g·cm² and about 3,417 lb·in², so small numbers in one system can look huge in the other.

Related converters and calculators

Related rotation tools:

• Torque unit converter: N·m and lbf·ft
• Angular acceleration converter: rad/s²
• Angular velocity converter: rpm and rad/s
• Weight converter: kg and lb
• Length converter: m, ft and in

Sources

NIST Special Publication 811, Appendix B; BIPM: SI Brochure.

Questions about this calculator