Moment of Inertia Calculator
Pick a shape, enter mass and a length/radius — get the moment of inertia about the standard textbook axis, with a diagram.
Formulas
Point mass: I = m·r²
Thin rod about centre: I = (1/12) m·L²
Thin rod about end: I = (1/3) m·L²
Solid disk/cylinder: I = ½ m·R²
Solid sphere: I = (2/5) m·R²
Hollow sphere: I = (2/3) m·R²
Ring / hoop: I = m·R²
Thin rod about centre: I = (1/12) m·L²
Thin rod about end: I = (1/3) m·L²
Solid disk/cylinder: I = ½ m·R²
Solid sphere: I = (2/5) m·R²
Hollow sphere: I = (2/3) m·R²
Ring / hoop: I = m·R²
Physics behind moment of inertia
The moment of inertia tells you how hard it is to angularly accelerate a body about an axis. It depends not only on the total mass but on how that mass is distributed: mass far from the axis contributes much more than mass close to the axis (I ∝ r²). This is why a figure skater speeds up by pulling her arms in — by shrinking r she shrinks I, and angular momentum L = I·ω is conserved, so ω must grow.
Worked example
Solid sphere, m = 2 kg, R = 0.5 m
I = (2/5) · 2 · 0.5² = 0.2 kg·m²
Related tools
FAQs
What is moment of inertia?
The rotational analogue of mass.
Does the axis matter?
Yes — the same object has different I about different axes.