# Pound (force)

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Pound (force)

The pound force (symbol: lb, lbf, lbf) is a unit of force in some systems of measurement including English engineering units and British gravitational units.[1]

## Definitions

The pound-force is 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.[2]

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 with the General Conference on Weights and Measures, standard gravity is usually taken to be 9.80665 m/s2 (32.174 049 ft/s2).[3][4]

The acceleration of the standard gravitational field (gn) and the international avoirdupois pound (lbm) define the pound-force as:[5]

\begin{align} 1\,\mathrm{lb}_f &= 1\,\mathrm{lb}_m \cdot g_n \\ &= 1\,\mathrm{lb}_m \cdot 32.174049\,\mathrm{\tfrac{ft}{s^2}}\\ &= 32.174049\,\mathrm{\tfrac{ft\cdot lb_m}{s^2}}\end{align}
\begin{align} or\end{align}
\begin{align} 1\,\mathrm{lb}_f &= 0.45359237\,\mathrm{kg} \cdot 9.80665\,\mathrm{\tfrac{m}{s^2}}\\ &= 4.4482216152605\,\mathrm{N} (\mbox{exact})\end{align}

This definition can be rephrased in terms of the slug. A slug has a mass unit equivalent of 32.174049 lbm. A pound-force is the amount of force required to accelerate a slug at a rate of 1 ft/s2, so:

$1\,\mathrm{lb}_f = 1\,\mathrm{slug} \cdot 1\,\mathrm{\tfrac{ft}{s^2}}$
$= 1\,\mathrm{slug}\,\mathrm{\tfrac{ft}{s^2}}$

## Conversion to other units

Units of force
v · d · e 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.

## Foot-pound-second systems of units

In some contexts, 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 otherwise be ambiguity, the symbols "lbf" and "lbm" and the terms "pounds-force" and "pounds-mass" can be used to distinguish.

Three approaches to mass and force units[6] v · d · e
Base force, length, time weight, length, time mass, length, time
Designations gravitational, technical colloquial, pre-newtonian absolute, scientific
Type coherent incoherent coherent
Force (F) $F = m\cdot {a} = w\cdot\tfrac{a}{g}$ $F = m\cdot\tfrac{a}{g_c} = w\cdot\tfrac{a}{g}$ $F = m\cdot {a} = w\cdot\tfrac{a}{g}$
Weight (w) $w = m\cdot g$ $w = m\cdot\tfrac{g}{g_c} \approx m$ $w = m\cdot g$
System BG GM EE EM AE CGS MTS SI
Acceleration (a) ft/s2 m/s2 ft/s2 m/s2 ft/s2 gal m/s2 m/s2
Mass (m) slug hyl lbm kg lb g t kg
Force (F) lb kp lbF kp pdl dyn sn N
Pressure (p) lb/in2 (PSI) at lbF/in2 (PSI) atm pdl/in2 Ba pz Pa

In the gravitational systems, the weight of the mass unit (pound-mass) on Earth's surface is approximately equal to the force unit (pound-force). This is convenient because one pound mass exerts one pound force due to gravity. Note, however, unlike the other systems the force unit is not equal to the mass unit multiplied by the acceleration unit[7]—the use of Newton's Second Law, F = m·a, requires another factor, gc, usually taken to be 32.174049 lbm·ft/lbf·s2 = 32.174049 lbm/slug. "Absolute" systems are coherent systems of units: by using the slug as the unit of mass, the "engineering" FPS system avoids the need for such a constant. The SI is an "absolute" metric system with kilogram and meter as base units.

## Notes and references

• Obert, Edward F., “THERMODYNAMICS”, D.J. Leggett Book Company Inc., New York 1948; Chapter I, Survey of Dimensions and Units, pages 1-24.
1. ^ The Engineering ToolBox
2. ^ 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.
3. ^ 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.

4. ^ Barry N. Taylor, Guide for the Use of the International System of Units (SI), 1995, NIST Special Publication 811, Appendix B note 24
5. ^ The international avoirdupois pound is defined to be exactly 0.45359237 kg.
6. ^ Lindeburg, Michael, Civil Engineering Reference Manual for the PE Exam
7. ^ The acceleration unit is the distance unit divided by the time unit squared.

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### Look at other dictionaries:

• pound force — noun 1. The gravitational force of 1lb weight and mass 2. A unit of such force (abbrev lbf) • • • Main Entry: ↑pound * * * pound force, = poundal. (Cf. ↑poundal) Abbr: lbf (no periods) …   Useful english dictionary

• Pound-Force —   [ paʊndfɔːs], Einheitenzeichen lbf, Einheit der Kraft in Großbritannien, definiert als die Kraft, die einem Körper mit der Masse 1 Pound (lb) die Normalfallbeschleunigung erteilt, 1 lbf = 4,4482216 Newton …   Universal-Lexikon

• Pound-force — 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… …   Wikipedia

• pound force — (lbf or lb)    a traditional unit of force. Traditional measuring systems did not distinguish between force and mass units. A force of one pound is simply the gravitational force experienced at the Earth s surface by a mass of one pound. To… …   Dictionary of units of measurement

• Pound-force — Einheit Norm Angloamerikanisches Maßsystem Einheitenname Pound force Einheitenzeichen lb, lbf, lbf Dimensionsname Kraft Dimensionssymbol F In …   Deutsch Wikipedia

• pound force — Force applied to a 1 lb. mass; has an acceleration of 32.173 ft/s2 …   Dictionary of automotive terms

• pound-force — /pownd fawrs , fohrs /, n. Physics. a foot pound second unit of force, equal to the force that produces an acceleration equal to the acceleration of gravity when acting on a mass of one pound. Abbr.: lbf [1895 1900] * * * …   Universalium

• pound-force — /pownd fawrs , fohrs /, n. Physics. a foot pound second unit of force, equal to the force that produces an acceleration equal to the acceleration of gravity when acting on a mass of one pound. Abbr.: lbf [1895 1900] …   Useful english dictionary

• pound-force — /paʊnd ˈfɔs/ (say pownd faws) noun a unit of force in the f.p.s. system, equal to the gravitational force acting on a mass of one pound, approx. equal to 32.174 pdl or 4.45 newtons. Symbol: lbf …   Australian English dictionary

• pound-force — noun A unit of force equal to a mass of one avoirdupois pound times a standard acceleration of gravity, equal to about 4.44822 newtons. Symbol lbf or lb …   Wiktionary