Radius of Gyration Calculator
Calculate radius of gyration with transparent engineering inputs and the displayed formula.
Run deterministic checks for missing or mixed units, physical bounds, detectable out-of-range values and formula applicability. This is not an engineering approval or a complete code/compliance check.
Export the current calculation inputs and outputs with formula, assumptions, confirmed source credits, automated verification status, tool version and timestamp.
PROFENG Pro unlocks calculation-record exports. The calculation itself remains free.
PROFENG provides this tool for engineering screening and educational use. Check the calculation basis, units, physical assumptions, applicable standards, safety factors, equipment data and project-specific requirements before design, procurement or operation.
Turn this result into a calculation record
Carry the tool context into the PROFENG calculation-check and record workspace without implying certification or engineering approval.
Why use this radius of gyration calculator?
Calculate radius of gyration with transparent engineering inputs and the displayed formula. The displayed relationship is r = √(I/A).
What this calculation does
This calculator determines radius of gyration from second moment of area, cross-sectional area. Use it for first-pass mechanics and machine-design calculations with explicit loads, geometry and material inputs.
Formula and engineering variables
r = √(I/A)
| Variable | Definition | Unit | Working guidance |
|---|---|---|---|
inertia | Second moment of area | mm⁴ | Illustrative screening band: 0 to about 8.000000e+7 mm⁴. This is not a design limit. |
area | Cross-sectional area | mm² | Illustrative screening band: 0 to about 20,000 mm². This is not a design limit. |
Ranges above are screening guidance or physical bounds where stated. They are not code limits or manufacturer ratings.
Calculated outputs
- Radius of gyration (mm): Math.sqrt(inertia/area)
Worked example
- Second moment of area (inertia) = 8,000,000 mm⁴
- Cross-sectional area (area) = 2,000 mm²
Math.sqrt((8000000)/(2000)) = 63.246 mmRadius of gyration: 63.246 mmAssumptions
- Loads and geometry are represented by the idealized relationship shown.
- Material behavior is treated according to the simple formula, typically linear-elastic where relevant.
- Units and section properties are consistent with the displayed equation.
Limitations
- Stress concentrations, fatigue, dynamics, buckling interaction, tolerances and manufacturing effects may require dedicated analysis.
- Apply appropriate design factors and the governing component or machinery standard before final design.
- I and A must refer to the same cross section and axis.
- Units for I and A must be consistent so the resulting radius has the intended length unit.
- The displayed default values are a worked example only; replace them with traceable project or measurement data.
Formula source and acknowledgement
Relationship used: r = √(I/A) for section radius of gyration about the selected axis.
The relationship used here follows Ferdinand P. Beer, E. Russell Johnston, John T. DeWolf, David F. Mazurek, Mechanics of Materials 8th edition (2020), McGraw Hill.
Credit for the underlying method belongs to the cited author(s). PROFENG presents its own implementation and wording and is not affiliated with or endorsed by the authors or publishers.
Limits of use for this relationship
- I and A must refer to the same cross section and axis.
- Units for I and A must be consistent so the resulting radius has the intended length unit.
Read the PROFENG methodology for formula sourcing and automated checks →
How to use it
Start with the inputs shown above, review the assumptions or options, then generate the result. Where the tool creates a file, keep the original until you have opened and checked the downloaded output.
Frequently asked questions
What does Radius of Gyration Calculator calculate?
This calculator determines radius of gyration from second moment of area, cross-sectional area. Use it for first-pass mechanics and machine-design calculations with explicit loads, geometry and material inputs.
What formula does Radius of Gyration Calculator use?
The calculator uses r = √(I/A). Every input used by the implementation is listed in the variable table on this page.
How is the worked example for Radius of Gyration Calculator checked?
PROFENG substitutes the displayed default values into the implemented relationship and compares the result against automated verification cases where an independent verifier is available.
What assumptions matter most for Radius of Gyration Calculator?
Loads and geometry are represented by the idealized relationship shown. Material behavior is treated according to the simple formula, typically linear-elastic where relevant. Units and section properties are consistent with the displayed equation.
Can I use this result for final design or procurement?
Use it as an engineering screening calculation. Final design, procurement, operation or compliance decisions require project-specific data and the applicable engineering method, standard or manufacturer information.
QA, changelog and corrections
Last QA update: 30 September 2026.
Automated verification passed – 30 September 2026 – six numerical cases checked, with dimensional checks, independent cross-checks for calculators, and unit round-trip checks for converters where applicable.
Changelog
30 September 2026 – source/indexation status, metadata and correction pathway reviewed. Engineering tools display the automated verification label only when they are inside the passing Part 3 verification scope.