Flywheel Energy Calculator

Formula

• I = k × m × r²
• KE = ½ I ω²
• Cs = (N1 − N2) / N_mean
• ΔE = KE(N1) − KE(N2)

About this calculator

Part of our Mechanical Calculators collection. Beams, bolts, springs, gears, bearings, and core ME calculations.

How it works

Moment of inertia equals shape factor times mass times radius squared. Kinetic energy uses I times omega squared over 2. Speed fluctuation coefficient compares speed swing to mean speed. Energy fluctuation shows how much kinetic energy changes between N1 and N2.

Enter your values in the inputs above and click CALCULATE. Results appear on the right without a page reload. No login and no server upload.

Worked example

Solid disk (k = 0.5), 50 kg, r = 0.3 m, speed 300 → 280 rpm.

1. I = 0.5 × 50 × 0.09 = 2.25 kg·m²
2. ω1 = 31.42 rad/s, ω2 = 29.32 rad/s
3. ΔE = 0.5 × 2.25 × (31.42² − 29.32²) = 143 J

Result: Energy fluctuation 143 J, speed fluctuation coefficient 0.069.

When to use

• Sizing flywheel inertia to limit speed variation
• Checking energy storage between speed limits
• Machine design and punch-press energy balance

Limitations

• Shape factor k must match geometry (0.5 solid disk, 1.0 thin ring)
• Assumes rigid body rotation about central axis
• Does not include bearing or windage losses

FAQ

What is the speed fluctuation coefficient?

Cs compares speed swing to mean speed: (N1 − N2) / N_mean. Lower Cs means smoother speed.

Solid disk vs ring k factor?

A uniform solid disk uses k = 0.5. A thin ring with mass at the rim uses k = 1.0.