Moment of Inertia Calculator

Moment of inertia is to rotation what mass is to straight-line motion: it measures how strongly an object resists having its spin changed, and this calculator works it out for the rigid shapes you meet most in physics and engineering. Choose a shape, a solid sphere, hollow sphere, solid cylinder or disc, hollow hoop, or a thin rod spun about its centre or its end, enter the mass and the relevant dimension, and it returns the moment of inertia about the standard axis, updating as you type. What makes the quantity so interesting is that it depends not just on how much mass an object has, but on how that mass is arranged relative to the axis of rotation. Mass far from the axis counts far more than mass near it, because the distance enters the formula as a square, which is why a hollow hoop, with all its mass at the rim, has a larger moment of inertia than a solid disc of the same mass and radius, and why figure skaters spin faster when they pull their arms in. Each shape carries its own neat coefficient in front of mass times the dimension squared, from two fifths for a solid sphere to one half for a disc and one twelfth for a rod about its centre, and the calculator applies the right one for your choice. That makes the tool genuinely useful for physics and engineering students learning rotational dynamics and checking homework, and for designers working with flywheels, rollers, shafts, wheels and gears, where the moment of inertia sets how much torque is needed to spin something up or slow it down. Using kilograms and metres gives a result in kilogram metres squared. The formulas and a worked example are explained clearly below.

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