Angular Momentum Calculator
Angular momentum (L) is a fundamental quantity in rotational mechanics, representing how much rotational motion a body has. For a rigid body rotating about a fixed axis, it is calculated as L = I × ω, where I is the moment of inertia (kg m²) and ω is the angular velocity in radians per second. Angular momentum is conserved in the absence of external torques, which explains phenomena from spinning tops to planetary orbits. Enter the moment of inertia and angular velocity below to find the angular momentum. You can convert RPM to rad/s by multiplying by 2π/60.
Angular momentum formula
L = I × ω
Where I is the moment of inertia in kg m² and ω is the angular velocity in rad/s. To convert RPM to rad/s: ω = RPM × 2π / 60.
Moment of inertia for common shapes
- Solid disk or cylinder: I = (1/2) m R²
- Thin rod about center: I = (1/12) m L²
- Solid sphere: I = (2/5) m R²
- Thin spherical shell: I = (2/3) m R²
- Point mass at radius R: I = m R²
Angular momentum: frequently asked questions
What is angular momentum?
Angular momentum L is the rotational analog of linear momentum. For a rigid body rotating about a fixed axis, L = I omega, where I is the moment of inertia and omega is the angular velocity in rad/s. Its SI unit is kg m² / s.
How do I find the moment of inertia?
The moment of inertia depends on the mass distribution. Common values: solid disk I = (1/2)mR²; thin rod about center I = (1/12)mL²; solid sphere I = (2/5)mR²; point mass at radius R: I = mR². Use the appropriate formula for your object, then multiply by omega.
What is the unit of angular momentum?
In SI units, angular momentum is measured in kilogram square meters per second (kg m² s or kg m² / s). This is equivalent to joule-seconds (J s) or newton meter seconds (N m s).
Is angular momentum conserved?
Angular momentum is conserved when no external torques act on the system. This is why a spinning ice skater speeds up when pulling in their arms: reducing I while L stays constant forces omega to increase.
What is the difference between angular momentum and torque?
Torque is the rate of change of angular momentum: tau = dL/dt. A net torque changes angular momentum, just as a net force changes linear momentum. If torque is zero, angular momentum is constant.
Official sources
- NIST Reference on Constants, Units, and Uncertainty: NIST Physics.
- OpenStax University Physics Volume 1: Angular Momentum.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.