Engineering converters
Moment of Inertia Converter
Convert kg·m², lb·ft², slug·ft² and other mass moment of inertia units.
Result
23.7304 lb·ft²
1 kg·m² = 23.7304 lb·ft²
All units for this value
| Unit | Symbol | Value |
|---|---|---|
| Kilogram square meter | kg·m² | 1 |
| Kilogram square centimeter | kg·cm² | 10000 |
| Gram square centimeter | g·cm² | 10000000 |
| Gram square millimeter | g·mm² | 1000000000 |
| Tonne square meter | t·m² | 0.001 |
| Ounce square inch | oz·in² | 54674.8 |
| Pound square inch | lb·in² | 3417.17 |
| Pound square foot | lb·ft² | 23.7304 |
| Slug square foot | slug·ft² | 0.737562 |
About this calculator
Moment of inertia measures how much an object resists changes to its rotational speed, based on how its mass is distributed around an axis. This converter switches between metric units like kilogram square metres and US units like pound square feet and slug square feet, which show up in mechanical design, flywheel calculations, and rotating machinery specs.
How it works in plain English
Every moment of inertia unit combines a mass unit and a squared length unit, so converting between them means rescaling both parts together. The converter treats the kilogram square metre as its common anchor: it multiplies your entered value by a fixed factor to reach that anchor, then divides by another factor to land on your chosen target unit. Because the length term is squared, these factors don't scale the same way ordinary length or mass conversions do.
The US customary side includes both pound square feet, based on pound mass, and slug square feet, based on the slug, which is the US customary unit of mass tied to pound-force and standard gravity. These two look similar but differ by a factor related to standard gravity, so mixing them up is a common source of error in hand calculations. Smaller metric units like gram square centimetres are also included for lightweight rotating parts such as small gears or instrument components.
Pick your source and target units from the from and to menus, type a value, and the converted figure appears immediately. A full reference table lists that same moment of inertia across every supported unit at once, and a precision control adjusts how many decimal places are shown. A swap button reverses the two selected units in a single click.
The formula
- value_in_target = value_in_source × (source factor to kg·m²) ÷ (target factor to kg·m²)
- 1 lb·ft² = 0.042140110093804 kg·m²
- 1 slug·ft² = 1.3558179619 kg·m²
- 1 lb·in² = 0.00029263965243 kg·m²
- 1 kg·cm² = 0.0001 kg·m²
Worked example
Suppose a datasheet lists a rotor's moment of inertia as 5 lb·ft² and an engineering report needs it in kg·m² to match a metric drivetrain analysis. Multiply by the conversion factor: 5 × 0.042140110093804 = 0.2107005505 kg·m², which rounds to about 0.2107 kg·m².
Entering 5 into the lb·ft² field with kg·m² selected as the target shows 0.2107 kg·m² right away. As a quick sanity check, one lb·ft² is a small fraction of a kg·m² since a pound is much lighter than a kilogram and a foot is shorter than a metre, so a result well under one for a modest rotor is expected rather than a sign of an error. The full unit table confirms the same rotor equals roughly 3.686 slug·ft² and 2,107,005.5 g·cm², all generated from that single entered value without running the calculation three separate times.
Moment of inertia unit equivalents
| Unit | Equal to (kg·m²) |
|---|---|
| 1 kg·m² | 1 |
| 1 kg·cm² | 0.0001 |
| 1 g·cm² | 0.0000001 |
| 1 t·m² | 1,000 |
| 1 oz·in² | 0.000018289978 |
| 1 lb·in² | 0.00029263965 |
| 1 lb·ft² | 0.042140110 |
| 1 slug·ft² | 1.3558179619 |
Standard mass and length unit definitions
Frequently asked questions
Why is there a separate unit for slug square feet and pound square feet?
Pound square feet uses pound mass directly, while slug square feet uses the slug, the US customary mass unit that relates to pound-force through standard gravity. One slug equals about 32.174 pounds mass, so slug·ft² and lb·ft² differ by that same factor. Engineering calculations involving force and acceleration in US units often expect slugs, so both are included here.
Why does moment of inertia use squared length units?
Moment of inertia depends on how far mass sits from the rotation axis, and that distance effect grows with the square of the radius, not linearly. That's why units like kg·m² and lb·ft² pair a mass term with a squared length term, unlike simpler quantities such as density that only use length cubed for volume.
Can I convert very small values, like for a small gear or instrument part?
Yes. Units such as gram square centimetres and gram square millimetres are included for lightweight components, alongside larger units like tonne square metres for heavy industrial flywheels. The converter handles the full range the same way, by scaling through the kilogram square metre anchor regardless of magnitude.
How do I see a value in every unit at once?
Type your value into the from field after selecting the from and to units; the results table below updates immediately to show that same moment of inertia expressed in every supported unit simultaneously, so there's no need to run separate conversions one at a time.
Can I adjust how many decimal places are shown?
Yes, a precision control lets you widen or narrow the number of decimal places displayed in both the main result and the full unit table. This is useful when comparing moments of inertia that are close in value or when you need a simplified figure for a quick estimate.
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