In the unit force-mass foot-pound-second system, the base unit of length (equivalently, of distance) is the foot, and the base unit of time is the second. The name pound 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 pound-mass and the pound-force, as base units of the unit force-mass foot-pound-second system.

This system is actually in accord with the way the term pound is used by most people who are not physical scientists nor engineers, and even in some engineering applications. The pound-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 pound-mass of the system.

In the absolute foot-pound-second system, it was required to create a unit of force with a new, unfamiliar name, and similarly, in the gravitational foot-pound-second system, it was required to create a unit of mass with a new, unfamiliar name. This is unnecessary in the unit force-mass foot-pound-second system, which is an advantage to some. However, the fact that the term pound has two different meanings, the pound-mass and the pound-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 poundf·second2/poundm·foot, where the subscripts f and m refer to the force and mass units designated by the name pound. 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

Common usageEdit

As the term pound is used in the United States, and has been used as well in the countries employing the British Imperial system of units, to denote both a unit of mass and a unit of force, the common system in use in the US and formerly in the other countries is by implicaton the unit force-mass FPS system.

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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