Moment of Inertia Converter

The moment of inertia (I) is how hard an object is to spin up or slow down about an axis, the rotational counterpart of mass. It depends on the mass and on how far it sits from the axis: for small masses, I = Σ m * r². Its SI unit is the kilogram square meter (kg·m²).

Two common shapes:

• A solid disc of mass m and radius r, about its center: I = m * r² / 2. A 10 kg flywheel of radius 0.2 m has I = 10 × 0.2² / 2 = 0.2 kg·m².
• A thin ring of the same mass and radius: I = m * r², twice the disc's, since all of its mass is at the rim.

How to convert moment of inertia units

Type a value into any field, and every other unit is calculated at once. Motor and servo data sheets often give the rotor's inertia in kg·cm² or oz·in². For example, 0.2 kg·m²:

1. In kg·cm²: multiply by 10,000, since 1 m² = 10,000 cm².

   0.2 × 10,000 = 2,000 kg·cm²

2. In lb·ft²: multiply by 23.7304.

   0.2 × 23.7304 = 4.746 lb·ft²

Common conversions

Moment of inertia units

• Kilogram-meter² (kg•m²): The kilogram meter squared is the standard SI unit for moment of inertia. One kilogram meter squared is defined as the moment of inertia of a mass of one kilogram rotating in a circular path with a radius of one meter.
  Conversion factor: 1 kg•m² = 10,000 kg•cm² = 1,000,000 kg•mm²

• Kilogram-centimeter² (kg•cm²): Kilogram centimeter squared is another commonly used unit for moment of inertia. One kilogram centimeter squared is defined as the moment of inertia of a mass of one kilogram rotating in a circular path with a radius of one centimeter.
  Conversion factor: 1 kg•cm² = 0.0001 kg•m² = 100 kg•mm²

• Kilogram-millimeter² (kg•mm²): Kilogram millimeter squared is a smaller unit for expressing moment of inertia. One kilogram millimeter squared is defined as the moment of inertia of a mass of one kilogram rotating in a circular path with a radius of one millimeter.
  Conversion factor: 1 kg•mm² = 0.000001 kg•m² = 0.01 kg•cm²

• Gram-centimeter² (g•cm²): The gram centimeter squared is a common unit for moment of inertia in applications where smaller values are encountered. One gram centimeter squared is defined as the moment of inertia of a mass of one gram rotating in a circular path with a radius of one centimeter.
  Conversion factor: 1 g•cm² = 0.0000001 kg•m² = 100 g•mm²

• Gram-millimeter² (g•mm²): Gram-millimeter² is an even smaller unit for expressing moment of inertia. One gram millimeter squared is defined as the moment of inertia of a mass of one gram rotating in a circular path with a radius of one millimeter.
  Conversion factor: 1 g•mm² = 0.000000001 kg•m² = 0.01 g•cm²

• Pound-foot² (lb•ft²): The pound foot squared is a unit commonly used in engineering systems that employ the Imperial system. One pound foot squared is defined as the moment of inertia of a mass of one pound rotating in a circular path with a radius of one foot.
  Conversion factor: 1 lb•ft² = 144 lb•in² = 0.04214 kg•m²

• Pound-inch² (lb•in²): Pound inch squared is another unit frequently encountered in engineering systems using the Imperial system. One pound-inch² is defined as the moment of inertia of a mass of one pound rotating in a circular path with a radius of one inch.
  Conversion factor: 1 lb•in² = 1/144 lb•ft² = 0.00029264 kg•m² = 2.9264 kg•cm²

• Ounce-inch² (oz•in²): Ounce inch squared is a unit commonly used for smaller moment of inertia values in systems employing the Imperial system. One ounce inch squared is defined as the moment of inertia of a mass of one ounce rotating in a circular path with a radius of one inch.
  Conversion factor: 1 oz•in² = 1/16 lb•in² = 0.00001829 kg•m² = 18.29 kg•mm²

• Slug-foot² (slug•ft²): Slug foot squared is a unit primarily used in engineering applications in the United States. One slug foot squared is defined as the moment of inertia of a mass of one slug rotating in a circular path with a radius of one foot.
  Conversion factor: 1 slug•ft² = 32.174 lb•ft² = 1.3558 kg•m²

Frequently asked questions

Is this the same as the area moment of inertia in m⁴?

No. The mass moment of inertia, in kg·m², is about rotation. The area moment of inertia, or second moment of area, in m⁴ or mm⁴, is about how a beam's cross-section resists bending. They can't be converted into each other.