Calculator Inputs
Use density mode to calculate mass from geometry, or switch to direct mass mode when the cylinder mass is already known.
Formula Used
Hollow cylinder volume: V = πL(Ro2 − Ri2)
Mass from density: m = ρV
Mass moment about the longitudinal axis: Iz = 0.5m(Ro2 + Ri2)
Mass moment about a transverse centroidal axis: Ix = Iy = (m/12)[3(Ro2 + Ri2) + L2]
Rotational kinetic energy: KE = 0.5Iω2
Use consistent units. This page converts entered values into SI units internally, performs the physics calculations, then converts results into your selected display units.
How to Use This Calculator
- Select whether mass should come from density or be entered directly.
- Choose the length unit for inner radius, outer radius, and cylinder length.
- Enter the hollow cylinder dimensions carefully so the outer radius exceeds the inner radius.
- Provide density or mass, depending on your selected calculation mode.
- Pick the desired inertia output unit and the axis used for rotational energy.
- Enter an angular speed if you also want rotational kinetic energy.
- Set the decimal precision and optionally enable thin-wall comparison.
- Press Calculate Inertia to show the result above the form, chart the values, and export data.
Example Data Table
| Inner Radius | Outer Radius | Length | Density | Mass | Iz | Ix = Iy |
|---|---|---|---|---|---|---|
| 4 cm | 6 cm | 30 cm | 7.85 g/cm³ | 14.7969 kg | 0.0385 kg·m² | 0.1302 kg·m² |
| 2 in | 3 in | 18 in | 0.284 lb/in³ equivalent | 80.1858 lb | 3.6195 lb·ft² | 16.8446 lb·ft² |
| 25 mm | 40 mm | 240 mm | 2,700 kg/m³ | 1.9849 kg | 0.0022 kg·m² | 0.0106 kg·m² |
FAQs
1. What is mass moment of inertia for a hollow cylinder?
It measures how strongly a hollow cylinder resists angular acceleration about a chosen axis. The value depends on mass placement, not only total mass. Material farther from the axis increases inertia significantly.
2. Why are Iz and Ix different?
Iz uses the central longitudinal axis, so radius dominates. Ix and Iy use centroidal transverse axes, so both radius and length influence the value. Long cylinders often have much larger transverse inertia.
3. When should I use density mode?
Use density mode when you know the material density and geometry but not the finished mass. The calculator finds volume first, then computes mass and all inertia values automatically.
4. When is direct mass mode better?
Direct mass mode is better when the real component has holes, coatings, fittings, or manufacturing differences that make theoretical density-based mass less accurate than an actual measured mass.
5. What does the thin-wall comparison show?
It compares the exact longitudinal inertia with the thin-wall approximation based on mean radius. This helps you judge whether a quick hand estimate is close enough for preliminary design work.
6. Does unit choice change the physics?
No. The physical result stays the same. Only the displayed number changes because the calculator converts your inputs to SI units internally, then converts outputs into your selected units.
7. Can I use this for rotational kinetic energy?
Yes. Enter an angular speed and select the relevant axis. The calculator applies the rotational kinetic energy equation, using the matching inertia value for the selected axis.
8. What input mistakes cause wrong results?
Common mistakes include swapping inner and outer radius, mixing units, entering diameter instead of radius, and using direct mass with a value that already includes unrelated attached parts.