Mass Moment of Inertia Calculator
Select a shape and enter dimensions to compute I about common axes.
How to Use This Calculator
1
Select the shape
Choose from common geometries and the default rotation axis.
2
Enter mass and dimensions
Use SI units for consistent results (kg, m).
3
Get I
The calculator outputs the moment of inertia for the chosen axis.
Formula
Disk: I = ½ m r²; Ring: I = ½ m (r² + rᵢ²); Sphere: I = 2/5 m r²
Rod center: I = 1/12 m L²; Rod end: I = 1/3 m L²; Plate: I = 1/12 m (w² + h²)
These are standard results for uniform density and the specified rotation axes.
Frequently Asked Questions
Can I change the rotation axis?
Use the parallel axis theorem: I = I_cm + m d², where d is the distance from CM axis.
What about non-uniform objects?
These formulas assume uniform density. For complex shapes, integrate or approximate with parts.