Enter the moment of inertia (kg·m²), the angular velocity (rad/s), and the time (s) into the calculator to determine the Flywheel Power. 

Flywheel Power Calculator

Power Energy Inertia (k·m·r²) Inertia (Disc/Ring) Torque/Spin-up

Enter any 3 values to calculate the missing variable

Flywheel Power Formula

The following formula is used to calculate the Flywheel Power.

P_{fw}=\frac{I\omega^2}{2t}

This equation gives the average mechanical power required to accelerate a flywheel from rest to angular speed ω in time t (neglecting losses).

  • Where Pfw is the Flywheel Power (watts)
  • I is the moment of inertia (kg·m²) 
  • ω is the angular velocity (rad/s) 
  • t is the time (s) 

To calculate the flywheel power, multiply the moment of inertia by the angular velocity squared, then divide by 2 times the time.

How to Calculate Flywheel Power?

The following example problems outline how to calculate Flywheel Power.

Example Problem #1

  1. First, determine the moment of inertia (kg·m²). In this example, the moment of inertia is determined to be 4.
  2. Next, determine the angular velocity (rad/s). For this problem, the angular velocity is measured to be 4.
  3. Next, determine the time (s). In this case, the time is found to be 10.
  4. Finally, calculate the Flywheel Power using the formula above: 

Pfw = (I*w^2) / (2*t)

Inserting the values from above and solving yields: 

Pfw = 1/2*4*4^2 /10 = 3.2 (watts)

Example Problem #2

Using the same method as above, determine the variables required by the formula. For this example problem, these are:

moment of inertia (kg·m²) = 56

angular velocity (rad/s) = 7

time (s) = 9

Enter these given values into the calculator above to get: 

Pfw = 1/2*56*7^2 / 9 = 152.44 (watts)