Moment of Inertia Converter
Convert a moment of inertia between kg·m², g·cm², lb·ft², lb·in², and oz·in². Enter a value, then choose the From unit and To unit.
Convert Moment of Inertia Between Units
Moment of Inertia Conversion Formula
Where:
- \(I_{\mathrm{from}}\) — the entered inertia value in the selected From unit
- \(I_{\mathrm{to}}\) — the displayed value in the selected To unit
- \(F_{\mathrm{from}}\) and \(F_{\mathrm{to}}\) — the calculator’s factors for the selected units, expressed relative to kg·m²
The calculator multiplies the entered value by its From unit factor and divides by its To unit factor. Its lb·ft² factor differs from the standard conversion factor; see the limitation below before relying on results involving that unit.
Moment of Inertia – Calculation Example
Example: enter the default Inertia value of 10, keep kg·m² as the From unit, and select lb·ft² as the To unit.
\[ 10\times\frac{1}{1.3558179483314}\approx 7.3756\ \mathrm{lb\,ft^2} \]
Result: the calculator displays approximately 7.3756 lb·ft². This reproduces its output, but it is not the standard physical conversion for lb·ft².
How to use the calculator
- Enter a nonnegative number in Inertia value.
- Choose the unit of that number under From unit.
- Choose the unit you want under To unit.
- Read Converted Inertia, including the unit shown beside the result. If you change a selection, check the updated result before copying it.
The available selections are kilogram square meters (kg·m²), gram square centimeters (g·cm²), pound square feet (lb·ft²), pound square inches (lb·in²), and ounce square inches (oz·in²). The tool converts an existing value; it does not calculate an object’s moment of inertia from its dimensions and mass.
What moment of inertia means
Moment of inertia, also called mass moment of inertia, describes how an object’s mass is distributed around a chosen axis of rotation. Mass farther from the axis contributes more: for a set of point masses, \(I=\sum m_i r_i^2\), where \(r_i\) is each mass’s perpendicular distance from the axis. This gives moment of inertia units of mass multiplied by length squared, such as kg·m².
A larger moment of inertia means more torque is needed to produce the same angular acceleration about the same axis, according to \(\tau=I\alpha\). For example, moving a flywheel’s mass toward its rim increases its moment of inertia even if its total mass stays the same. You can use the torque converter when the torque in a rotational calculation is given in a different unit.
Converting units changes only how a known moment of inertia is expressed. It does not account for a change in rotational axis, an altered mass distribution, or a different object. Before comparing two values, confirm that both refer to the same axis and that neither is a different quantity, such as an area moment of inertia used in beam bending.
Conversion factors and limitations
The following factors are the values used by this calculator. In its formula, each factor represents the number of kg·m² assigned to one unit in the first column.
| Selected unit | Calculator factor |
|---|---|
| kg·m² | 1 |
| g·cm² | 0.0000001 |
| lb·ft² | 1.3558179483314 |
| lb·in² | 0.0002926397 |
| oz·in² | 0.00001827 |
Important: the calculator’s lb·ft² factor is not the standard factor for pound-mass square feet. The standard value is approximately \(1\ \mathrm{lb\,ft^2}=0.04214011\ \mathrm{kg\,m^2}\); the calculator instead uses approximately \(1.35581795\ \mathrm{kg\,m^2}\), a value associated with slug·ft². Thus, the default example’s 10 kg·m² is approximately 237.30 lb·ft² by standard conversion, not the displayed 7.3756 lb·ft². Do not use results involving the lb·ft² selection where an accurate physical conversion is required.
The oz·in² factor is also rounded differently from a conversion based on standard ounce-mass and inch definitions, so it can introduce a smaller discrepancy. The displayed result is rounded to ten decimal places. For very small values, that display rounding may hide significant digits; keep more precision in a separate calculation if your application needs it.
Enter mass-based inertia units only. A pound-force is a unit of force, not the pound-mass assumed by lb·in² and lb·ft². If you are relating inertia to a rotation rate, the frequency converter can help align frequency units, but frequency alone does not determine moment of inertia.
Frequently Asked Questions
How do I calculate moment of inertia for a simple object by hand?
Choose the rotation axis first, then use a formula for the object’s shape. A uniform solid disk rotating about its central axis has \(I=\tfrac12 mr^2\), while a thin hoop about its central axis has \(I=mr^2\). Use mass in kilograms and radius in meters to obtain kg·m². These formulas assume uniform mass distribution.
What is a normal or good moment of inertia?
There is no universal good value. The useful value depends on the object, its size, and the axis of rotation. A lower moment of inertia makes an object easier to accelerate rotationally with a given torque; a higher one can help it resist changes in rotational speed. Compare values only for the same intended application and axis.
How do I convert kg·m² to g·cm² without a calculator?
Multiply by ten million: \(1\ \mathrm{kg\,m^2}=10^7\ \mathrm{g\,cm^2}\). A kilogram contains 1,000 grams, and squaring the conversion from meters to centimeters contributes another factor of 10,000. To convert back, divide by ten million. Remember to square the length conversion—multiplying by just 100 is a common mistake.
How many lb·in² are in 1 lb·ft²?
One pound-mass square foot equals 144 pound-mass square inches because \(1\ \mathrm{ft}=12\ \mathrm{in}\) and \(12^2=144\). This direct relationship is useful for checking imperial-unit calculations. Do not rely on this converter’s lb·ft² selection for that check: its factor does not represent the standard pound-mass square-foot unit.
How does moving the rotation axis change moment of inertia?
Changing the axis generally changes the value even when the object stays the same. For an axis parallel to one through the center of mass, the parallel-axis theorem gives \(I=I_{\mathrm{cm}}+md^2\), where \(d\) is the distance between the axes. Convert units only after finding the moment of inertia about the axis you actually need.
Is mass moment of inertia the same as area moment of inertia?
No. Mass moment of inertia describes rotational motion and has units such as kg·m². Area moment of inertia, also called the second moment of area, describes a cross-section’s geometry in bending calculations and has units of length to the fourth power, such as mm⁴. Do not enter an area moment of inertia into a mass-inertia converter.
Can moment of inertia be zero or negative?
A mass moment of inertia about a real axis cannot be negative: mass is nonnegative, and each distance is squared. It can be zero in an idealized model where all mass lies exactly on the axis, such as a point mass located on that axis. A negative result usually signals an input, formula, or sign-convention mistake.
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