In the unit force-mass meter-kilogram-second system, the base unit of length (equivalently, of distance) is the meter, and the base unit of time is the second. The name kilogram is applied to both the unit of mass and the unit of force (equivalently, of weight), though, since these are in fact different quantities, it would be better to refer to two separate units, the kilogram-mass and the kilogram-force, as base units of the unit force-mass meter-kilogram-second system.

This system is actually in accord with the way the term kilogram is used by most people who are not physical scientists nor engineers, and even in some engineering applications. The kilogram-force, the unit of weight, is the weight (at some definite point on the Earth's surface) of an object whose mass is the standard kilogram-mass of the system.

In the absolute meter-kilogram-second system, it was required to create a unit of force with a new, unfamiliar name, and similarly, in the gravitational meter-kilogram-second system, it was required to create a unit of mass with a new, unfamiliar name. This is unnecessary in the unit force-mass meter-kilogram-second system, which is an advantage to some. However, the fact that the term kilogram has two different meanings, the kilogram-mass and the kilogram-force, which need to be distinguished, is a disadvantage.

In such a system, Newton's second law cannot be expressed simply as F = ma, but needs to be written F = kma, where k is a specific constant characteristic of the system. And k is not simply a pure dimensionless constant, but in order to make the equation consistent, if the unit of length or distance is denoted by L, the unit of force by F, the unit of mass by M, and the unit of time by T, k must have dimensions FM−1L−1T2, in this case kilogramf·second2/kilogramm·meter, where the subscripts f and m refer to the force and mass units designated by the name kilogram. The result is also that this value of k appears in a number of other equations.

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


The kilogram-force is sometimes referred to as the kilopond, to make it certain that this is different from the kilogram-mass, the official SI meaning of the term kilogram.

Common usageEdit

In most countries using the metric system, the term kilogram is used to refer both to the kilogram-mass and the kilogram-force. Thus the Unit force-mass system is implied by common usage.

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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