Foot–pound–second system of units

The foot–pound–second (FPS) system uses three base units: the foot for length, the avoirdupois pound for either mass or force, and the second for time. Its variants were the most common system in English-language technical writing until around the mid-20th century.

To avoid errors and ease translation between unit systems, all physical quantities can be labeled consistently with their units. In the FPS context, this approach is sometimes called the Stroud system, after its popularizer William Stroud.

When the pound is treated as a unit of mass, the coherent system works much like the metric MKS and CGS systems. This version is called the Absolute English System, and its derived unit of force is the poundal (1 pdl = 1 lb·ft/s²). The international standard symbol for the pound as a mass unit is lb. In 1861, Joseph David Everett proposed using the dyne and erg as FPS units of force and energy. Latimer Clark’s 1891 dictionary suggested names like celo (acceleration), vel or velo (velocity), and pulse (momentum) for FPS absolute units.

When the pound is treated as a unit of force, the system is known as the technical or gravitational FPS system, or the British gravitational system. Common among US engineers, it takes the pound-force as a fundamental unit, and the derived unit of mass is the slug (1 slug = 1 lbf·s²/ft). In this context, the pound-force is sometimes simply called the pound.

Another variant uses both the pound-mass and the pound-force, but neither the slug nor the poundal. This is sometimes called the English engineering system, though it is based on US customary units and is not used in England.

For molar quantities, the FPS unit of substance is the pound-mole (lb-mol = 273.16×10²⁴). Until SI adopted the gram-mole, the mole was derived directly from the mass unit. A unit of (lbf·s²/ft)-mol also appears in an earlier definition of the atmosphere.

Electromagnetic units in the FPS system derive from length and force. Stephen Dresner gives electrostatic and electromagnetic units for both foot–pound–second and foot–slug–second systems, though these are most associated with the CGS system. The 1929 International Critical Tables uses the symbols fpse (FPS electrostatic) and fpsm (FPS electromagnetic). The 1979 CRC Handbook also lists these abbreviations. For charge: 1 fpsm unit = 117.581866 cgsm unit (Biot-second); 1 fpse unit = 3583.8953 cgse unit (Franklin); 1 fpse unit = 1.1954588×10⁻⁷ abs coulomb.

The candle and foot-candle were the first defined units of light, set in the Metropolitan Gas Act (1860). A foot-candle is the intensity of light one foot from a standard candle. These units were internationally recognized in 1881 and later adopted into the metric system.

Confusion over the pound arises because “weight” can mean gravitational force in technical contexts or mass in commerce and law, and the distinction often doesn’t matter in practice. The pound’s relation to metric units is expressed in kilograms, not newtons, and was historically defined by a mass prototype used with a two-pan balance, which is unaffected by local gravity. In July 1959, national foot and avoirdupois pound standards were replaced by the international foot (exactly 0.3048 m) and international pound (exactly 0.45359237 kg), making conversion simple arithmetic. The poundal converts as 1 pdl = 1 lb·ft/s² = 0.138254954376 N exactly. To convert between absolute and gravitational FPS systems, the standard acceleration g must be fixed, relating pound-mass to pound-force.