Moment of Inertia Calculator
Enter a mass and its distance from the axis to get the moment of inertia in kg·m² — and see why distance from the axis matters far more than mass.
Point-mass formula
Enter the mass and the radius and the calculator returns the moment of inertia (I = m·r²) in kilogram square metres.
Use SI units
Mass in kilograms and the radius in metres give the moment of inertia in kg·m² — convert grams and centimetres before you start.
What is the moment of inertia?
The rotational equivalent of mass
This moment of inertia calculator finds how strongly an object resists a change in its rotation about a chosen axis. The moment of inertia is the rotational equivalent of mass: just as mass measures resistance to a change in straight-line motion, the moment of inertia measures resistance to a change in spinning. For a single point mass it depends on two things — how much mass there is and, far more strongly, how far that mass sits from the axis of rotation. The calculator turns the mass in kilograms and the radius in metres into the moment of inertia in kilogram square metres, the number behind flywheels, spinning wheels, and how quickly a skater or a turntable speeds up.
Enter a mass in kilograms and a radius in metres to get the moment of inertia in kg·m² instantly.
The moment of inertia of a point mass is the mass multiplied by the square of its distance from the axis of rotation.
I = m × r²The radius is squared, so it dominates the result: a small change in distance from the axis produces a large change in the moment of inertia. Use kilograms for the mass and metres for the radius and the moment of inertia comes back in kg·m².
Suppose a 2 kg mass sits 0.5 m from the axis of rotation. Square the radius first: 0.5² = 0.25. Then multiply by the mass: 2 × 0.25 = 0.5. The moment of inertia is 0.5 kg·m². Move the same mass out to 1 m and the radius squared becomes 1, so the moment of inertia quadruples to 2 kg·m² — the same mass, four times harder to spin up, purely because it is twice as far from the axis.
The formula is exact for a point mass, but a couple of practical points are worth keeping in mind.
Point mass only — extended bodies use shape factors
This calculator uses the point-mass formula I = m·r², which treats all the mass as concentrated at a single radius. Extended bodies spread their mass out, so they use shape-specific factors instead: a solid disk is ½mr², a solid sphere is ⅖mr², and a thin rod about its centre is one-twelfth mL². Keep your units consistent — kilograms for mass and metres for the radius — or the kg·m² will be wrong, and remember the moment of inertia always depends on which axis you measure it about.