# Pound-force

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This article deals with the unit of force. For the unit of mass see Pound (mass).

The pound-force or simply pound (abbreviations: lb, lbf, or lbf) is a unit of force.

## Definitions

The pound-force is approximately equal to the gravitational force exerted on a mass of one avoirdupois pound on the surface of Earth. Since the 18th century, the unit has been used in low-precision measurements, for which small changes in Earth's gravity (which varies from place to place by up to half a percent) can safely be neglected.[1]

The 20th century, however, brought the need for a more precise definition. A standardized value for acceleration due to gravity was therefore needed. Today, in accordance the General Conference on Weights and Measures, standard gravity is usually taken to be 9.80665 m/s² (approximately 32.17405 ft/s²)[2][3] but other values have been used, including 32.16 ft/s² (approximately 9.80237 m/s²).[4]

From the acceleration of the standard gravitational field and the international avoirdupois pound, we arrive at the following definition:[5]

 1 pound-force ≡ 0.45359237 kg × 9.80665 m/s² = 4.4482216152605 N (exactly)

Sixteen avoirdupois ounces (as a unit of mass) are equal to one avoirdupois pound (as a unit of mass). Similarly one ounce-force is equal to a sixteenth of a pound-force.

Units of force
newton
(SI unit)
dyne kilogram-force,
kilopond
pound-force poundal
1 N ≡ 1 kg·m/s² = 105 dyn ≈ 0.10197 kp ≈ 0.22481 lbf ≈ 7.2330 pdl
1 dyn = 10−5 N ≡ 1 g·cm/s² ≈ 1.0197×10−6 kp ≈ 2.2481×10−6 lbf ≈ 7.2330×10−5 pdl
1 kp = 9.80665 N = 980665 dyn gn·(1 kg) ≈ 2.2046 lbf ≈ 70.932 pdl
1 lbf ≈ 4.448222 N ≈ 444822 dyn ≈ 0.45359 kp gn·(1 lb) ≈ 32.174 pdl
1 pdl ≈ 0.138255 N ≈ 13825 dyn ≈ 0.014098 kp ≈ 0.031081 lbf ≡ 1 lb·ft/s²
The value of gn as used in the official definition of the kilogram-force is used here for all gravitational units.

## Use of pound as a unit of force

In some contexts, such as structural engineering applications, the term "pound" is used almost exclusively to refer to the unit of force and not the unit of mass. In those applications, the preferred unit of mass is the slug, i.e. lbf·s²/ft. In other contexts, the unit "pound" refers to a unit of mass. In circumstances where there may be ambiguity otherwise, the symbols "lbf" and "lbm" and the terms "pounds-force" and "pounds-mass" can be used to distinguish.

Three common, equally valid foot-pound-second (fps) systems of units for doing calculations with mass and force are summarized in the table below, which also includes the corresponding metric units.

In the "engineering" fps system, the weight of the mass unit (pound-mass) on Earth's surface is approximately equal to the force unit (pound-force). The price for this convenience is that the force unit is not equal to the mass unit multiplied by the acceleration unit[6]—the use of Newton's Second Law, F = ma, requires another factor, gc, usually taken to be 32.17405 lb·ft/(lbf·s²). The "gravitational" fps system is a coherent system of units: by using the slug as the unit of mass, it avoids the need for such a constant. The "absolute" system is similarly coherent; the SI units are those of the "absolute" metric system.

## Notes and references

1. Acceleration due to gravity varies over the surface of the Earth, generally increasing from about 9.78 m/s² (32.1 ft/s²) at the equator to about 9.83 m/s² (32.3 ft/s²) at the poles.
2. In 1901 the third CGPM declared (second resolution) that: "The value adopted in the International Service of Weights and Measures for the standard acceleration due to Earth's gravity is 980.665 cm/s², value already stated in the laws of some countries." This value was the conventional reference for calculating the kilogram-force, a unit of force whose use has been deprecated since the introduction of SI.
3. Barry N. Taylor, Guide for the Use of the International System of Units (SI), 1995, NIST Special Publication 811, Appendix B note 24
4. J. Edmond Shrader, Physics for Students of Applied Science, McGraw Hill, 1st ed., 1937, p. 24.
5. The international avoirdupois pound is defined to be exactly 0.45359237 kg.
6. The acceleration unit is the distance unit divided by the time unit squared.
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