Dimensional Analysis of Energy and Power

Quantity	Formula	SI Unit	Dimension
Work/Energy	F*d	Joule (J)	[ $ML^{2T}^{-2}$ ]
KE	$\frac{1}{2}$$mv^2$	J	[ $ML^{2T}^{-2}$ ]
PE (gravitational)	mgh	J	[ $ML^{2T}^{-2}$ ]
PE (elastic)	$\frac{1}{2}$$kx^2$	J	[ $ML^{2T}^{-2}$ ]
Power	W/t = Fv	Watt (W)	[ $ML^{2T}^{-3}$ ]
Spring constant	F/x	N/m	[ $MT^{-2}$ ]
Energy density	E/V	J/ $m^3$	[ $ML^{-1}$$T^{-2}$ ]

Unit conversions: 1 kWh = 3.6 * 10^6 J = 3.6 MJ 1 eV = 1.6 * 10^{-19} J 1 HP = 746 W 1 calorie = 4.186 J