### Pound-Force

"Klbf" redirects here. For the airport in North Platte, Nebraska, assigned the ICAO code KLBF, see North Platte Regional Airport.
For the unit of mass, see Pound (mass). For the basis weight of paper, see Paper density.

The pound or 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\left\{align\right\}

1\,\mathrm{lbf} &= 1\,\mathrm{lbm} \times g_{\rm n} \\ &= 1\,\mathrm{lbm} \times 32.174049\,\mathrm{\tfrac{ft}{s^2}}\\ &= 32.174049\,\mathrm{\tfrac{ft {\cdot} lbm}{s^2}}\end{align}

\begin\left\{align\right\}

or\end{align}

\begin\left\{align\right\}

1\,\mathrm{lbf} &= 0.45359237\,\mathrm{kg} \times 9.80665\,\mathrm{\tfrac{m}{s^2}}\\ &= 4.4482216152605\,\mathrm{N} \text{ (exact)}\end{align}

This definition can be rephrased in terms of the slug. A slug has a mass 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:

$1\,\mathrm\left\{lbf\right\} = 1\,\mathrm\left\{slug\right\} \times 1\,\mathrm\left\{\tfrac\left\{ft\right\}\left\{s^2\right\}\right\}$
$= 1\,\mathrm\left\{slug\right\}\,\mathrm\left\{\tfrac\left\{ft\right\}\left\{s^2\right\}\right\}$

## Conversion to other units

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.

## Foot-pound-second (FPS) 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][7]
Base force, length, time weight, length, time mass, length, time
Force (F) F = m·a = w·Template:Sfrac F = m·Template:Sfrac = Template:Sfrac F = m·a = w·Template:Sfrac
Weight (w) w = m·g w = m·Template:Sfracm w = m·g
System BG GM EE M 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 at PSI atm pdl/ft2 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[8]—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...