The Formula
The rotational equivalent of $KE = \frac12mv^2$.
KE = ½ · I · ω²
- I (Inertia): Resistance to rotation (kg·m²)
- ω (Omega): Angular Velocity (rad/s)
Rotational Kinetic Energy Calculator
Calculate rotational kinetic energy, moment of inertia, or angular velocity with unit conversion.
Rotational K.E.
Calculate the energy stored in rotating mass. Essential for flywheels, turbines, and vehicle dynamics.
KErot = ½ · I · ω²
Rotational Kinetic Energy
Objects that spin possess kinetic energy even if they aren't moving across the floor. This energy depends on how fast they spin ($\omega$) and how hard they are to spin ($I$).
Applications
Flywheels: Devices designed to store rotational energy. By spinning at very high speeds, they can store significant energy in a compact rotating assembly.
Note: Doubling the RPM quadruples the stored energy!
rotational kinetic energy formulas and interpretation
Rotational kinetic energy is the energy carried by an object because it rotates.
It depends linearly on moment of inertia and on the square of angular velocity.
How to use the rotational kinetic energy calculator
- Choose a model: Select the physical relationship that matches the known values.
- Choose the unknown: Select the quantity you need to calculate.
- Enter values and units: Provide every requested measurement using consistent units.
- Calculate: Check the formula, converted result, sign, and units.
Formula and variables
Rotational kinetic energy equals one-half times moment of inertia times angular velocity squared.
KErot = ½Iω²- KErot — Rotational kinetic energy
- Energy of rotation (J)
- I — Moment of inertia
- Rotational inertia (kg·m²)
- ω — Angular velocity
- Rotation rate (rad/s)
Flywheel energy example
A flywheel has inertia 2 kg·m² and rotates at 10 rad/s.
- Moment of inertia
- 2 kg·m²
- Angular velocity
- 10 rad/s
- KErot = ½ × 2 × 10²
- KErot = 100 J
Result: Rotational kinetic energy is 100 J.
The rotating flywheel stores 100 joules of kinetic energy.
Understanding your results
Interpreting the result
Doubling angular velocity increases rotational energy by a factor of four.
A sign indicates direction only when a consistent rotational sign convention is used.
Assumptions
- Rotation is evaluated about a specified axis.
- Inputs are converted through coherent SI units.
- The selected formula adequately represents the physical system.
Limitations
- The calculator does not simulate time-varying inputs.
- Vector directions and multiple axes must be resolved separately.
- Losses such as friction are not added unless represented in the entered net value.
Common mistakes
- Mixing RPM with radians per second.
- Using diameter instead of radius.
- Entering a zero divisor.
- Ignoring the direction represented by a negative value.
Practical use cases
Physics and education
Check rotational kinematics and dynamics exercises.
Machines and mechanisms
Estimate quantities for wheels, shafts, rotors, and rotating equipment.
Frequently asked questions
Why are radians used in rotational formulas?
Radians make angular and linear relationships dimensionally coherent without an extra conversion factor.
Can the result be negative?
Yes. A negative value means the quantity points opposite the direction chosen as positive.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.
Related Calculators
Continue with calculators that answer nearby questions and help compare the next step.
Acceleration Calculator
Use this free acceleration for science calculations. Get instant, accurate results with clear inputs and no signup required.
Angular Acceleration Calculator
Use this free angular acceleration for science calculations. Get instant, accurate results with clear inputs and no signup required.
Angular Impulse Calculator
Use this free angular impulse for science calculations. Get instant, accurate results with clear inputs and no signup required.
Angular Impulse Momentum Calculator
Use this free angular impulse momentum for science calculations. Get instant, accurate results with clear inputs and no signup required.
Angular Momentum Calculator
Use this free angular momentum for science calculations. Get instant, accurate results with clear inputs and no signup required.
Angular Velocity Calculator
Use this free angular velocity for science calculations. Get instant, accurate results with clear inputs and no signup required.