How to use the moment of inertia calculator
Estimate moment of inertia for common shapes. Enter mass, radius (or length for rod), shape in the fields above; the moment of inertia is computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “moment of inertia calculator”, “inertia calculator”, “rotational inertia calculator”, “mass inertia calculator”, “rotational inertia of a disk or sphere”.
Formula
Variables
- m — Mass (kg)
- r — Radius (or length for rod) (m)
- k — Shape (—)
Worked example
With mass = 5 kg, radius (or length for rod) = 0.4 m, shape = Solid disk or cylinder, the calculator gives moment of inertia ≈ 0.4 kg·m².
Tips for accurate results
- Choose the shape whose rotation axis matches the one in your problem; the same object has different values for different axes.
- For a rod, enter its length as the radius input, and the factor 1/12 applies only to rotation about the centre.
- Use kilograms and metres to get kg·m².
Common mistakes
- Entering the diameter where the radius is needed, which quadruples the answer.
- Using the centre-axis value for a rod that rotates about one end.
- Forgetting that an object's moment of inertia depends on its mass distribution, not just its mass.
Frequently asked questions
What is the moment of inertia calculator used for?
Estimate moment of inertia for common shapes. It helps with questions such as “moment of inertia calculator”, “inertia calculator”, “rotational inertia calculator”.
What is the formula for the moment of inertia calculation?
Moment of inertia (kg·m²) = k × m × r × r. Here m is mass (kg), r is radius (or length for rod) (m), k is shape (—).
What inputs do I need for the moment of inertia calculator?
You need mass in kg, radius (or length for rod) in m, shape in —. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the moment of inertia calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the moment of inertia result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.