KEVOS® MAKEOS · Units
Moment of Inertia, Section Modulus and Momentum Converter
What is this mass moment of inertia, second moment of area, section modulus or momentum in other units?
Converts the four quantities of the handbook’s moment of inertia and momentum tables between SI, metric and US customary units: mass moment of inertia (kg·m², lb·ft², lb·in², slug·ft², lbf·in·s² and others), second moment of area (m⁴, cm⁴, mm⁴, in⁴, ft⁴), section modulus (m³, cm³, mm³, in³, ft³) and momentum (kg·m/s, lb·ft/s, lb·in/s), showing the value in every unit of the same kind.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Value to convert | The number exactly as written on the data sheet, section table or calculation. | |
| Unit of the entered value | choice | The unit printed beside the value; the tool shows the value in every other unit of the same kind. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Value to convert
- What it is
- The moment of inertia, section modulus or momentum you want to convert, as written in the source.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Every converted value is proportional to it.
- Get it right
- WR² on motor data sheets is a mass moment of inertia in lb·ft².
What this means: Unit of the entered value
- What it is
- The unit the value was given in, which also sets the kind of quantity converted.
- Units and format
- Choose one of 21 options from the list: kg·m² (mass moment of inertia); g·cm² (mass moment of inertia); kg·mm² (mass moment of inertia); lb·ft² (mass moment of inertia); lb·in² (mass moment of inertia); oz·in² (mass moment of inertia); slug·ft² = lbf·ft·s² (mass moment of inertia); lbf·in·s² (mass moment of inertia); m⁴ (second moment of area); cm⁴ (second moment of area); mm⁴ (second moment of area); in⁴ (second moment of area); ft⁴ (second moment of area); m³ (section modulus); cm³ (section modulus); mm³ (section modulus); in³ (section modulus); ft³ (section modulus); kg·m/s (momentum); lb·ft/s (momentum); lb·in/s (momentum).
- Example
- The form opens with “lb·ft² (mass moment of inertia)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Chooses the kind of quantity and the factor applied.
- Get it right
- in⁴ and mm⁴ are second moments of area for bending; kg·m² and lb·ft² are mass moments of inertia for rotation.
Method and formulas
- Value in the SI unit = entered value × factor of the entered unit; value in each other unit = SI value ÷ that unit’s factor.
- Factors are built from 1 in = 0.0254 m, 1 ft = 0.3048 m, 1 lb = 0.45359237 kg and standard gravity 9.80665 m/s², all exact; they reproduce the handbook’s Tables 57 and 58.
- Mass moment of inertia in lb·ft² (often written WR² or WK²) is a mass times a radius squared; slug·ft² and lbf·in·s² are the gravitational units used in dynamics.
- Example: 1 lb·ft² = 0.04214011 kg·m².
Limitations
- Mass moment of inertia (resistance to angular acceleration) and second moment of area (resistance to bending) are different quantities; the tool converts only within a kind.
- Some data sheets give WR² in lb·ft² but GD² in kgf·m², which is four times the kg·m² value.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Convert motor and load inertias from a US data sheet
- Convert section properties from an inch steel table
- Check a calculation that mixes unit systems
Who it is for
- Engineers
- Technicians
- Buyers and estimators
What you get
- The value in each unit of the same kind
- Value in the SI unit of that kind
Interpreting the result
- Keep the original unit on record and round to the precision of the source.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2699. Topic reference; no source tables or recommended settings are reproduced.
- BIPM: The International System of Units (SI brochure) — https://www.bipm.org/en/publications/si-brochure
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
Built-up rotors and datasheet units
In Inertia and Flywheels by the Numbers
What it covers: How to add the parts of a built-up rotor into one inertia with its stored energy, and how to convert the inertias on motor and servo datasheets, including WR² and GD², without a factor-of-four error.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
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