The absolute centimeter-gram-second system is a system of mechanical units. The centimeter is the base unit of length or distance, the gram is chosen to be a unit of mass, and the second is the base unit of time. All other mechanical quantities, and specifically force, are expressed in terms of combinations of these three units. In absolute systems, Newton's second law is expressed as F = ma, and since acceleration is the second derivative of a distance with respect to time, if the unit of length or distance is denoted by L, the unit of mass by M, and the unit of time by T, the unit of force becomes a derived unit of dimensions MLT−2, in this case gram·centimeter/second2, which is known as the dyne.

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

Prior to the adoption of the SI, the most commonly used system of mechanical units in physics was the absolute centimeter-gram-second system, and electrical units were defined for use with this system by the use of laws of physics in the same way that Newton's second law was used to relate force and mass. However, two different laws were used: Coulomb's law, defining the "electrostatic system," and Ampère's law, defining the "electromagnetic system." These two systems led to two quite differently-sized sets of units for describing electrical and magnetic quantities, and even the dimensionalities of the units in these two systems.

See also


  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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