Flywheel Inertia and Energy Calculator

The moment of inertia and stored energy of a flywheel, and the energy given up when it slows.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

A flywheel stores kinetic energy, E = ½ I ω². For a solid disc the moment of inertia is ½ m r², and for a ring it is ½ m (ro² + ri²) (a thin rim approaches m r²). Energy grows with the square of the speed, so speed is the cheap way to store more energy.

The energy given up when the flywheel slows from one speed to another is the difference of the two kinetic energies. The rim speed matters too: the rim stress rises with its square, so a high-speed flywheel needs a stress check against bursting.

Formulas used

  • I = \tfrac{1}{2} m (r_o^2 + r_i^2)
  • E = \tfrac{1}{2} I\omega^2
  • \Delta E = \tfrac{1}{2} I(\omega_1^2 - \omega_2^2)
  • C_s = \frac{2(N_1 - N_2)}{N_1 + N_2}

Worked example

With the default numbers in the calculator above:

  1. Moment of inertia (solid disc or ring): 9 kg m²
  2. Kinetic energy at the starting speed: 111 kJ
  3. Energy given up in slowing to the end speed: 21.1 kJ
  4. Coefficient of speed fluctuation: 10.53 %
  5. Rim speed at the start (a bursting limit check): 47.12 m/s

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is the coefficient of speed fluctuation?

How much the speed varies as a fraction of the mean speed during a cycle. A smaller value needs a bigger flywheel.

Why is a ring better than a disc?

For the same mass, more of the mass is at a larger radius, so the inertia is larger.

Is there a speed limit?

Yes. The stress in the rim grows with the rim speed squared, so there is a bursting limit set by the material.

Related calculators

Further reading: Shigley, Mechanical Engineering Design (flywheels); Meriam and Kraige, Engineering Mechanics: Dynamics; Hibbeler, Engineering Mechanics: Dynamics; Rao, Mechanical Vibrations.

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