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What does this calculator estimate?
A 3 kg object moving at 4 m/s on a 2-meter radius has 24 kg-m^2/s of angular momentum: L = 3 x 4 x 2 = 24 kg-m^2/s. Angular momentum = mass x velocity x radius.
- Angular momentum (kg-m^2/s) = mass x velocity x radius.
- Angular momentum is conserved when no external torque acts.
- Skaters speed up when pulling arms in because radius shrinks (NIST).
What angular momentum is
Angular momentum is the rotational counterpart of linear momentum — how much 'spin' an object carries around an axis. It's conserved when no external torque acts, which explains why a spinning skater speeds up when pulling in their arms.
Limitations to watch for
The formula assumes motion perpendicular to the radius at a single radius — planets and point masses. For extended objects, use L = I × ω (moment of inertia × angular velocity). The tool reports magnitude; direction is along the axis.
How to use it in practice
Use it to analyze orbiting bodies, spinning systems, and collision problems. Remember conservation: reducing r increases v (skater effect). For solid objects, use the moment-of-inertia form instead.
['Enter the mass in kilograms.', 'Enter the tangential velocity in m/s.', 'Enter the radius in meters; the tool computes L = mvr.']
How this calculator works
Formula
Angular momentum L = m × v × r, where m is mass (kg), v is tangential velocity (m/s), and r is the radius (m). Units: kg·m²/s.
Worked example
A 2 kg object moving at 3 m/s at a radius of 0.5 m: L = 2 × 3 × 0.5 = 3.0 kg·m²/s.
Assumptions to verify
- The mass moves at constant radius.
- Velocity is perpendicular to the radius.
- A point-mass model applies (no rotation of the object itself).
Frequently asked questions
What is angular momentum?
The rotational quantity of motion: L = mvr for a point mass orbiting at radius r, measured in kg·m²/s.
How do I calculate it?
Multiply mass × velocity × radius. A 2 kg mass at 3 m/s and 0.5 m radius has L = 3 kg·m²/s.
Why is it conserved?
Without external torque, nothing changes the angular momentum — which is why figure skaters spin faster when pulling their arms in (r decreases, v increases).
What's the difference from linear momentum?
Linear momentum p = mv is straight-line motion; angular momentum is motion around an axis. Both are conserved in their respective systems.
What is the moment of inertia form?
For extended objects, L = I × ω — moment of inertia times angular velocity. The mvr form works for point masses and planets.
What is torque?
The rotational equivalent of force — it changes angular momentum, just as force changes linear momentum.
Does this apply to planets?
Yes — Earth's orbital angular momentum around the Sun follows the same conservation laws, keeping the orbit stable.
Cite this tool
BoringToolsKit. “Angular Momentum Calculator.” boringtoolskit.com/angular-momentum-calculator/ (reviewed 2026-08-25). Free to reference in articles, syllabi, and answer posts with a link.
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