Moment of Inertia Calculator
Looks up the standard formula for a shape and applies it. All shapes are uniform.
Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
The formula
point or hoop: I = mr² disc: I = ½mr² solid sphere: I = ⅖mr² hollow sphere: I = ⅔mr² rod: I = mL²/12 at the centre, mL²/3 at the end plate: I = m(a² + b²)/12 shifted axis: I + md²
The further the mass sits from the axis, the harder it is to spin up. The shifted axis uses the parallel axis theorem, which is strictly valid when starting from an axis through the centre of mass.
What to watch out for
For objects built of several parts, work out each about the same axis and add them up.
Frequently Asked Questions
What is the moment of inertia of a 5 kg, 20 cm radius disc?
0.1 kg·m². As a hoop, it would be 0.2 kg·m².
Why do a hoop and a disc roll differently?
A hoop has its mass further out, so more of its energy goes into spinning and it rolls down a slope more slowly.