Rotational Kinetic Energy Calculator

Use our rotational kinetic energy calculator to calculate rotational kinetic energy from angular velocity and moment of inertia. Includes the rotational kinetic energy formula, unit conversions (lb·ft² to J), a worked example, and when to use rotational kinetic energy.

Angular velocity (ω) (rad/s)
Angular velocity in radians per second (rad/s). Must be ≥ 0.
Moment of inertia (I) (lb·ft²)
Moment of inertia in lb·ft². Converted to kg·m² to compute energy in joules.
Results
Rotational kinetic energy (J)
KE = ½ I ω². Moment of inertia is converted from lb·ft² to kg·m² before computing joules.
Steps: convert I(lb·ft²) → kg·m², then KE(J) = 0.5 × I × ω².
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What Is Rotational Kinetic Energy?

Rotational kinetic energy is the energy an object has because it is rotating. It depends on how fast the object spins and how its mass is distributed around the rotation axis.

For the same angular velocity, an object with a larger moment of inertia has more rotational kinetic energy because more mass is effectively farther from the axis.

This calculator uses angular velocity (ω) in rad/s and moment of inertia (I) in lb·ft², then outputs rotational kinetic energy in joules (J).

Rotational Kinetic Energy Formula

Rotational kinetic energy is calculated using a standard physics formula. Because this calculator accepts moment of inertia in lb·ft², it converts I to SI units (kg·m²) to output energy in joules (J).

Rotational kinetic energy (SI units) =
E = 1/2 × I × ω^2

Use I in kg·m² and ω in rad/s to get E in joules (J).

Convert moment of inertia (lb·ft² → kg·m²) =
I(kg·m^2) = I(lb·ft^2) × 0.04214011

1 lb·ft² ≈ 0.04214011 kg·m².

Combined form used by this calculator =
E(J) = 1/2 × (I(lb·ft^2) × 0.04214011) × ω^2

Outputs energy directly in joules when I is entered in lb·ft².

E
= Rotational kinetic energy (J)
I
= Moment of inertia (lb·ft², converted to kg·m² internally)
ω
= Angular velocity (rad/s)
Rotational kinetic energy example
I = 10 lb·ft², ω = 20 rad/s → I = 10×0.04214011 = 0.4214011 kg·m² → E = 0.5×0.4214011×20² = 84.28 J

Energy scales with ω², so doubling angular velocity increases energy by 4×.

How to Calculate Rotational Kinetic Energy

  1. 1

    Enter angular velocity (ω) in rad/s.

  2. 2

    Enter moment of inertia (I) in lb·ft².

  3. 3

    The calculator converts I to kg·m² and applies E = 1/2 × I × ω².

  4. 4

    Read the result as rotational kinetic energy in joules (J).

Frequently Asked Questions

How to calculate rotational kinetic energy?

Use E = 1/2 × I × ω². If you want energy in joules, use I in kg·m² and ω in rad/s. This calculator converts lb·ft² to kg·m² for you.

What are rotational kinetic energy units?

In SI, rotational kinetic energy is measured in joules (J). Moment of inertia is kg·m² and angular velocity is rad/s.

When to use rotational kinetic energy?

Use it when an object’s motion is primarily rotational (wheels, flywheels, gears, turbines) or when you need total kinetic energy that includes both translation and rotation.

How do I find rotational kinetic energy if I have RPM instead of rad/s?

Convert RPM to rad/s with ω = RPM × 2π ÷ 60, then apply E = 1/2 × I × ω².

Can I calculate the rotational kinetic energy of Earth?

In principle, yes: you would need Earth’s angular velocity and an appropriate moment of inertia about its rotation axis. This calculator can compute energy once you supply ω and I in the required units.