⚙️ Rotational Kinetic Energy Calculator
Calculate rotational kinetic energy KE = ½Iω² for spinning objects.
Result
How to Use This Calculator
This calculator finds the kinetic energy of a spinning object. Enter the moment of inertia and the angular velocity in radians per second.
Enter the moment of inertia I in kg m^2. For common shapes, use the site's moment of inertia calculators to find it first.
Enter the angular velocity in radians per second. Convert from rpm by multiplying by 0.1047.
Click Calculate. The rotational kinetic energy appears in joules.
For a rolling object, remember this is only the spin part. Add 1/2mv^2 for the total.
Rotational Kinetic Energy
Every spinning thing carries energy, and this formula counts it. Moment of inertia measures how the mass is distributed, angular velocity measures how fast it turns, and the 1/2w^2 structure mirrors linear kinetic energy exactly. The square on w is the whole story of flywheels: spin twice as fast and you store four times the energy, which is why energy-storage flywheels run at tens of thousands of rpm.
Like all kinetic energy, this is relative to a frame: it is the energy in the rotation itself, independent of any translational motion. A figure skater's spin energy, a turbine's fury, and a hard drive platter's hum are all 1/2Iw^2, differing only in the numbers.
Worked Example
Where This Comes Up
Flywheel energy storage, from race-car KERS to grid backup, is sized with this formula. Rotating machinery safety uses it in reverse: engineers calculate the burst energy of a grinding wheel or turbine rotor to design containment housings, because a rotor failure releases all 1/2Iw^2 at once. Sports physicists apply it to discus, hammer throw, and figure skating.
Radians versus rpm is the classic unit trap: entering 3,000 rpm as w gives an answer nearly 100 times too big after squaring. Always convert first. The other mistake is using the wrong moment of inertia for the shape or axis. A solid disk and a hoop of equal mass and radius differ by a factor of two, and that factor squares into every energy number downstream.
Frequently Asked Questions
How do I convert rpm to radians per second?
Multiply by 2π/60, which is about 0.1047. A motor spinning at 3,000 rpm is therefore about 314 rad/s.
Why does this formula look like 1/2mv^2?
It is the rotational twin. Moment of inertia I plays the role of mass m, and angular velocity w plays the role of linear velocity v. The derivation is identical, just in angular coordinates.
Can an object have translational and rotational kinetic energy at once?
Yes. A rolling wheel has both: 1/2mv^2 for its center of mass plus 1/2Iw^2 for the spin. The total is the sum, which is why a rolling ball beats a sliding block in a ramp race.
What are the units?
Joules, like all energy. I in kg m^2 and w in rad/s multiply out to kg m^2/s^2, which is the joule.
Why do flywheels store energy this way?
They spin a heavy rim fast, and since energy grows with w^2, doubling the spin speed quadruples the stored energy. That is why flywheel bursts can deliver huge power for short times.