Moment of Inertia Converter
Convert mass moment of inertia (kg·m², lb·ft²) and area second moment (m⁴, mm⁴) instantly with our dual-domain simulator. Features real-time flywheel kinetic energy simulation, commercial steel profile rigidity matching (HEB, IPE), Euler-Bernoulli deflection analysis, and CAD spec export.
Unit ConvertersPhysics Domain
Mass moment of inertia for rotating bodies, flywheels, shafts, and rotor dynamics.
Flywheel Kinetic Energy Simulator
Dynamic rotational energy, rim tip speed, and vehicular impact momentum equivalence.
Copy calculated inertia, kinetic energy, and structural rigidity data to clipboard for engineering documentation.
How to Use the Moment of Inertia Converter & Dynamics Simulator
Dual-domain guide to converting rotational mass inertia and structural bending stiffness, simulating flywheel energy, and matching steel profiles.
Select Engineering Domain (Rotational Mass vs. Structural Area)
Choose between Mechanical Rotational Inertia (kg·m², for rotating shafts, flywheels, and robotics) or Structural Bending Inertia (m⁴, for beam cross-sections and deflection).
Input Value in Any Preferred Unit
Enter your inertia value in SI base units (kg·m² or m⁴), metric multiples (g·cm², cm⁴, mm⁴), or imperial/AISC standards (lb·ft², slug·ft², in⁴).
Inspect the Omni-Grid Matrix
View instant zero-latency conversions across all engineering units simultaneously, formatted with clean scientific notation to prevent precision loss.
Simulate Flywheel Kinetic Energy & Car Equivalence
In mechanical mode, adjust rotation speed (RPM) to compute stored kinetic energy (Ek = 0.5·I·ω²), rim velocity, and equivalent linear momentum of a 2,000 kg vehicle.
Cross-Reference Standard Steel Profiles & Deflection
In structural mode, check automatic matching against commercial steel profiles (IPE, HEA, HEB) and verify Eurocode mid-span deflection (δ) under 10 kN load against L/200.
Apply Industrial Presets & Export CAD Specs
Load quick industry presets (from drone rotors and industrial pumps to transfer girders) and click 'Copy Engineering Spec' to export formatted CAD/FEA parameters.
Frequently Asked Questions
Physical definitions, unit conversion formulas, flywheel kinetic energy, and structural flexural rigidity standards.
Q:What is the fundamental difference between mass moment of inertia and area moment of inertia?
Mass moment of inertia (I, in kg·m²) measures an object's resistance to angular acceleration about a rotational axis (τ = I·α). Second moment of area (Ix, in m⁴) is a purely geometric cross-sectional property that measures resistance to bending deflection under transverse loads (M = E·I·κ). Although both share the name 'moment of inertia', mass inertia governs rotating machinery, while area inertia governs structural beam stiffness.
Q:How do I convert between imperial (lb·ft², slug·ft²) and metric (kg·m²) mass moment of inertia?
Multiply pound-foot squared (lb·ft²) by 0.0421401 to obtain kg·m² (1 lb·ft² = 0.04214011 kg·m²). One slug·ft² equals exactly 32.174 lb·ft² ≈ 1.355818 kg·m². Conversely, 1 kg·m² ≈ 23.7304 lb·ft² ≈ 0.737562 slug·ft².
Q:How do I convert between in⁴, cm⁴, and mm⁴ for structural steel sections?
1 in⁴ = (25.4 mm)⁴ = 416,231.4 mm⁴ = 41.62314 cm⁴ = 4.162314 × 10⁻⁷ m⁴. To convert US AISC beam shapes (in⁴) to European Euronorm catalog values (cm⁴), multiply in⁴ by 41.623. To convert cm⁴ to in⁴, divide by 41.623.
Q:How does rotational speed (RPM) relate to stored kinetic energy in a flywheel?
Stored kinetic energy is given by Ek = 0.5·I·ω², where ω = (2π·RPM)/60 rad/s. Because energy scales quadratically with angular velocity (ω²), doubling rotational speed quadruples stored kinetic energy, whereas doubling moment of inertia only doubles stored energy.
Q:What is flexural rigidity (EI) and how does area moment of inertia determine beam deflection?
Flexural rigidity is the product of Young's modulus of elasticity (E, typically 210 GPa for structural steel) and the second moment of area (I). In Euler-Bernoulli beam theory, center deflection under a point load is δ = (F·L³)/(48·E·I). Increasing I (e.g. choosing a deeper HEB beam) drastically reduces deflection without adding proportional weight.
Q:Why do units of moment of inertia differ between mechanical and structural engineering?
Mass moment of inertia integrates mass elements times distance squared (∫ r² dm, mass × length² → kg·m²). Area moment of inertia integrates cross-sectional area elements times distance squared (∫ y² dA, area × length² → length⁴ → m⁴). Both measure distribution relative to an axis, but one measures mass distribution while the other measures geometric area distribution.
Mechanical: Mass Moment of Inertia
- Solid Cylinder Flywheel: I = ½ m r2
- Thin-Walled Cylindrical Rim: I = m r2
- Stored Kinetic Energy: Ek = ½ I ω2
- Parallel Axis Theorem: I = Icm + m d2
Structural: Second Moment of Area
- Solid Rectangle (b × h): Ix = (b · h3) / 12
- Euler-Bernoulli Bending: σ = (M · y) / I
- Parallel Axis Theorem: Ix = Ix̄ + A d2
- Center Deflection (Point Load): δ = (F L3) / (48 E I)
Moment of Inertia Converter Table
| Unit | kg·m² | kg·cm² | g·cm² | lb·ft² |
|---|---|---|---|---|
| 1 kg·m² | 1 | 10,000 | 10,000,000 | 23.7303660884 |
| 1 kg·cm² | 0.0001 | 1 | 1,000 | 0.0023730366 |
| 1 g·cm² | 0.0000001 | 0.001 | 1 | 0.000002373 |
| 1 lb·ft² | 0.0421401 | 421.401 | 421,401 | 1 |
What is Moment of Inertia Converter?
Practical Calculation Example
Reference Zones
| Interface Element | Physics Function | Practical Application |
|---|---|---|
| Scientific Omni-Grid | Base Conversion | Switches fluidly between mass inertia for rotors and area moment for beam deflection. |
| Flywheel Kinetic Energy | Mechanical Simulation | Calculates the exact rotational energy (Joules) stored in a spinning mass at a specific RPM. |
| Structural Rigidity Matcher | Civil Engineering | Compares a calculated area moment (m⁴) to commercial steel beams like HEB or IPE. |
| Euler-Bernoulli Deflection | Stress Analysis | Determines the mid-span bend of a supported beam under a centralized structural load. |