Angular Momentum Calculator (L = Iω)

This angular momentum calculator solves the equation L equals I omega, the rotational equivalent of mass times velocity, for any one of its three variables. Angular momentum describes how much rotational motion a spinning object carries, combining the moment of inertia, how its mass is spread out from the axis of rotation, with the angular velocity, how fast it spins, measured in radians per second. It matters in physics and engineering because angular momentum is conserved when no external torque acts, so pulling mass closer to the axis forces the spin rate to increase, which is why a figure skater speeds up when they draw their arms in and why a flywheel resists changes to its rotation. To use the tool, pick the variable you want from the dropdown, angular momentum, moment of inertia or angular velocity, then enter the other two values in SI units, kilogram metres squared per second, kilogram metres squared, and radians per second. The calculator instantly returns the solved value with its unit, along with a results card confirming the figure and which variable it solved for. It suits physics students, teachers and engineers who need a fast, accurate rearrangement of the formula rather than working through the algebra by hand. Figures are rounded for display, so treat the output as a close approximation rather than a certified engineering value.

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Angular momentum (kg·m²/s)

Moment of inertia (kg·m²)

Angular velocity (rad/s)

Solve for

Value

Result

The formula

Angular momentum is L = I times omega, where I is the moment of inertia and omega is the angular velocity in radians per second. Rearranged: I = L / omega and omega = L / I.

Worked example

A flywheel with moment of inertia 2 kg m squared spinning at 3 rad/s has angular momentum L = 2 times 3 = 6 kg m squared per second. Solve for L with I = 2, omega = 3 to confirm.

Frequently asked questions

What is angular momentum?

The rotational analogue of momentum, equal to the moment of inertia times the angular velocity.

Why is it conserved?

With no external torque, angular momentum stays constant, so reducing the moment of inertia increases the spin rate.

What units is it in?

Kilogram metres squared per second in SI.

Who this calculator is for

This calculator is for physics students, teachers and engineers.

What this calculator assumes

You enter SI units as labelled.
One variable is solved from the others.
Results are rounded for display.

Formula and sources

Related calculators

Kinetic Energy Calculator: energy of motion.
Momentum Calculator: mass times velocity.
Projectile Motion Calculator: range and height.

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