The foot–pound–second system or FPS system is a system of units built on three fundamental units: the foot for length, the (avoirdupois) pound for either mass or force (see below), and the second for time..
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Gaussian units existed before the CGS system. The British Association report of 1873 that proposed the CGS contains gaussian units derived from the foot–grain–second and metre–gram–second as well. There are also references to foot–pound–second gaussian units.
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The electrostatic and electromagnetic systems are derived from units of length and force, mainly. As such, these are ready extensions of any system of containing length, mass, time. Stephen Dresner gives the derived electrostatic and electromagnetic units in both the foot–pound–second and foot–slug–second systems. In practice, these are most associated with the centimetre–gram–second system.
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The foot-poundal (symbol: ft-pdl) is a unit of energy that is part of the foot-pound-second system of units, in Imperial units introduced in 1879, and is from the specialized subsystem of English Absolut Edward F. Obert, Thermodynamics, McGraw-Hill Book Co., 1948. (a coherent system). The foot- poundal is equal to 1/32.174049 that of the more commonly used foot-pound force.
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The SI unit of force is the newton (symbol N), which is the force required to accelerate a one kilogram mass at a rate of one meter per second squared, or . The corresponding CGS unit is the dyne, the force required to accelerate a one gram mass by one centimeter per second squared, or . A newton is thus equal to 100,000 dynes. The gravitational foot-pound-second English unit of force is the pound-force (lbf), defined as the force exerted by gravity on a pound-mass in the standard gravitational field of .
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The United States Code refers to these units as "traditional systems of weights and measures". Other common ways of referring to the system in the U.S. are: "customary", "standard", or, erroneously: "English", or "imperial" (which refers to the post-1824 reform measures used throughout the British Empire). Another term is the foot–pound–second (FPS) system, as opposed to centimeter–gram–second (CGS) and meter–kilogram–second (MKS) systems. Tools and fasteners with sizes measured in inches are sometimes called "SAE bolts" or "SAE wrenches" to differentiate them from their metric counterparts.
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If a system of units has both equations and base units, with only one base unit for each base quantity, then it is coherent if and only if every derived unit of the system is coherent. The concept of coherence was developed in the mid-nineteenth century by, amongst others, Kelvin and James Clerk Maxwell and promoted by the British Science Association. The concept was initially applied to the centimetre–gram–second (CGS) in 1873 and the foot–pound–second systems (FPS) of units in 1875. The International System of Units (1960) was designed around the principle of coherence.
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The pound-force provides an alternative unit of mass: one slug is the mass that will accelerate by one foot per second squared when acted on by one pound-force. An alternative unit of force in a different foot- pound-second system, the absolute fps system, is the poundal, defined as the force required to accelerate a one-pound mass at a rate of one foot per second squared. The units of slug and poundal are designed to avoid a constant of proportionality in Newton's Second Law. The pound-force has a metric counterpart, less commonly used than the newton: the kilogram-force (kgf) (sometimes kilopond), is the force exerted by standard gravity on one kilogram of mass.
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Before SI units were widely adopted around the world, the British systems of English units and later imperial units were used in Britain, the Commonwealth and the United States. The system came to be known as U.S. customary units in the United States and is still in use there and in a few Caribbean countries. These various systems of measurement have at times been called foot-pound-second systems after the Imperial units for length, weight and time even though the tons, hundredweights, gallons, and nautical miles, for example, are different for the U.S. units. Many Imperial units remain in use in Britain, which has officially switched to the SI system—with a few exceptions such as road signs, which are still in miles.
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