Dimensional Systems

Dimensional systems provide a systematic way to describe physical quantities in terms of fundamental dimensions such as mass, length, time, and force. In engineering and physics, the most commonly used frameworks are the MLT (Mass–Length–Time) and FLT (Force–Length–Time) systems. These systems are widely applied in dimensional analysis, unit conversion, and the formulation of governing equations across mechanical, fluid, and thermal engineering disciplines.

Dimension – Symbol – Unit Table (USCS & SI)

Symbols, dimensions, and USCS/SI units of fundamental physical quantities based on the MLT and FLT dimensional systems.

Symbol	Quantity	MLT	FLT	USCS	SI
Geometric
$l$	Length	L	–	ft	m
$A$	Area	L²	–	ft²	m²
$V$	Volume	L³	–	ft³	m³
Kinematic
$t$	Time	T	T	s	s
$\omega$	Angular velocity	T^-1	T^-1	s^-1	s^-1
$f$	Frequency	T^-1	T^-1	s^-1	s^-1
$v$	Velocity	LT^-1	LT^-1	ft/s	m/s
$\nu$	Kinematic viscosity	L²T^-1	L²T^-1	ft²/s	m²/s
$Q$	Volumetric flow rate	L³T^-1	L³T^-1	ft³/s	m³/s
$\alpha$	Angular acceleration	T^-2	T^-2	s^-2	s^-2
$a$	Acceleration	LT^-2	LT^-2	ft/s²	m/s²
Dynamic
$\rho$	Density	ML^-3	FL^-4T²	slug/ft³	kg/m³
$M$	Mass	M	FL^-1T²	slug	kg
$I$	Moment of inertia	ML²	FLT²	slug·ft²	kg·m²
$\mu$	Dynamic viscosity	ML^-1T^-1	FL^-2T	slug/(ft·s)	kg/(m·s)
$\dot{m}$	Mass flow rate	MT^-1	FL^-1T^-1	slug/s	kg/s
$MV$	Momentum	MLT^-1	FT	lbf·s	N·s
$Ft$	Impulse	MLT^-1	FT	lbf·s	N·s
$p$	Pressure	ML^-1T^-2	FL^-2	lbf/ft²	Pa
$F$	Force	MLT^-2	F	lbf	N
$E$	Energy	ML²T^-2	FL	lbf·ft	J
$P$	Power	ML²T^-3	FLT^-1	lbf·ft/s	W
$v$	Specific volume	M^-1L³	F^-1L⁴T^-2	ft³/lbm	m³/kg