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[1][2]

v · d · e


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
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.


  1. Lindeburg, Michael, Civil Engineering Reference Manual for the PE Exam 
  2. Wurbs, Ralph A, Fort Hood Review Sessions for Professional Engineering Exam,, retrieved October 26, 2011 

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