Rotational Kinetic Energy Calculator
Calculate rotational kinetic energy from inertia and angular velocity.
LIVE 2D EXPLANATION
KE = ½ × I × ω²The geometry, arrow and label respond to the current calculation state.
PRIMARY RESULT
Live calculation ready for review
This is an educational or preliminary result. Apply relevant standards and engineering judgement before use.
ENGINEERING PRINCIPLE
A rotating body stores energy based on inertia and the square of angular velocity.
Calculate rotational kinetic energy from inertia and angular velocity.
FORMULA & VARIABLES
KE = ½ × I × ω²
- KE = rotational kinetic energy (J)
- I = mass moment of inertia (kg·m²)
- ω = angular velocity (rad/s)
CALCULATION STEPS
How this result is assembled
- Convert the entered values to the SI basis required by the formula.
- Apply KE = ½ × I × ω² using the current inputs.
- Present the result as 9,000 J and review the stated assumptions.
FORMULA VERIFICATION
Units, scope and reference
Reference: NIST SP 811 for unit relationships; standard classical mechanics and strength-of-materials derivations for the stated scalar relation.
Internal basis: All inputs are converted to the calculator’s SI base before the formula is evaluated.
Valid conditions: Positive finite scalar input values in the current calculator model.
Limitations: The inertia is about the stated rotation axis. Speed is treated as constant at the calculation instant.
ASSUMPTIONS
Use this result in context
- The inertia is about the stated rotation axis.
- Speed is treated as constant at the calculation instant.
Results must be verified by a qualified engineer and checked against applicable engineering standards, material properties, loading conditions and design requirements.
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OPTIONAL ENGINEERING HELP
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