Gravitational meter-gram-second system

The gravitational meter-gram-second system is a system of mechanical units. The meter is the base unit of length or distance, the gram is chosen to be a unit of force, and the second is the base unit of time. All other mechanical quantities, and specifically mass, are expressed in terms of combinations of these three units. In gravitational systems, Newton's second law is expressed as F = ma, but since force is the basic unit rather than mass, it must be written in the form m = F/a, so that if the unit of length or distance is denoted by L, the unit of force by F, and the unit of time by T, the unit of mass becomes a derived unit of dimensions FL⁻¹T², in this case gram·second²/meter, which is known as the hyl.

Three approaches to mass and force units

Base	force, length, time		weight, length, time		mass, length, time
Force (F)	F = m·a = w·a/g		F = m·a/gc = w·a/g		F = m·a = w·a/g
Weight (w)	w = m·g		w = m·g/gc ≈ m		w = m·g
System	BG	GM	EE	M	AE	CGS	MTS	SI
Acceleration (a)	ft/s2	m/s2	ft/s2	m/s2	ft/s2	gal	m/s2	m/s2
Mass (m)	slug	hyl, also called “metric slug” or “TME”	lbm	kg	lb	g	t	kg
Force (F)	lb	kp	lbF	kp	pdl	dyn	sn	N
Pressure (p)	lb/in2	at	PSI	atm	pdl/ft2	Ba	pz	Pa

Note that the term hyl used here refers to a unit 10^-3 as large as the hyl defined as a mass unit in the Gravitational meter-kilogram-second system, which has more commonly been used by European engineers.