Flywheel Rotational Energy Calculator
Calculate moment of inertia, angular momentum and stored or released rotational energy for an annular disk or thin hoop.
YOUR CALCULATION
Result
—
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Calculate moment of inertia for the selected mass distribution, convert each speed from RPM to radians per second and apply rotational kinetic energy.
Annulus I=m(R²+r²)/2; hoop I=mR²; E=Iω²/2; angular momentum=Iω
Worked example
A 10 kg solid disk of radius 0.5 m has I=1.25 kg m². At 120 RPM it stores 10π²≈98.696 J; slowing to 60 RPM releases 7.5π²≈74.022 J ideally.
Assumptions and input details
Uniform annular disk or ideal thin hoop rotating about its perpendicular central axis. Inner radius must not exceed outer radius; thin-hoop mode ignores the inner-radius value. No spokes, hub, nonuniform density, bearings, losses or torque history. Signed released energy is negative when final speed is higher. These numbers do not establish material stress, containment or a safe rotational speed.
References: OpenStax: rotational kinetic energy
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
The 19 mass definitions distinguish avoirdupois and troy measures, metric and regional measures. Japanese kin is 600 g; mainland Chinese shijin is 500 g.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Find translational kinetic energy, mass or speed from the other two values. Choose explicit units, compare energy equivalents and see how energy changes with speed.
Convert rpm, angular speed and tangential rim speed using a radius or diameter. Find frequency, period and centripetal acceleration with explicit units.
Calculate an ideal blackbody’s wavelength-density peak and frequency-density peak without confusing the two maxima.
Reserved advertising space.