Free · Rotational and periodic motion calculators 🌎

Angular Momentum for a Particle or Fixed-Axis Body

Calculate angular momentum from mass, tangential velocity and radius, or from moment of inertia and angular velocity.

  • Formula & worked example
  • Private in your browser
  • No signup
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A 2 kg particle moving tangentially at 3 m/s at radius 4 m has angular momentum 24 kg·m²/s about that axis.

Particle: L = mrvₜ; fixed-axis body: L = Iω

Worked example

Enter these known values and leave the other values blank.

Mass (m)
2 kg
Signed tangential velocity
3 m/s
Radius from the chosen axis
4 m
Particle angular momentum
24 kg⋅m²/s

Assumptions and limitations

  • Particle mode uses the tangential velocity component perpendicular to the radius. It is not the general three-dimensional cross product.
  • Rigid-body mode uses moment of inertia about the chosen fixed axis. Velocity, angular velocity and momentum may be signed consistently with that axis.
  • Mass, radius and moment of inertia are positive. A zero speed gives zero momentum; inverse calculations with a zero divisor are not unique.

Common questions

Can I enter the total velocity at any angle?

Use its tangential component. Radial motion contributes no angular momentum about the chosen origin.

Does a negative result mean negative mass?

No. It describes the direction of angular momentum along your chosen axis.

References

Rotational inertia in pound-force foot seconds squared uses exact international pound-force and foot definitions. Pound-mass square feet use the exact international pound and square international foot, replacing a rounded inertia factor. Bookify uses the exact relationship one revolution = 2π radians instead of the captured rounded angular-speed factor.

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