Pound (force)

The pound of force or pound-force (symbol: lbf,^[1] sometimes lb_f,^[2]) is a unit of force used in some systems of measurement, including English Engineering units^{[lower-alpha 1]} and the foot–pound–second system.^[3]

"lbf" redirects here. For the airport in Nebraska, see LBF (airport).

For other uses, see Pound (disambiguation).

Pound-force
Unit system	English Engineering units, British Gravitational System
Symbol	lbf
Conversions
1 lbf in ...	... is equal to ...
SI units	4.448222 N
CGS units	444,822.2 dyn
Absolute English System	32.17405 pdl

Pound-force should not be confused with pound-mass (lb), often simply called "pound", which is a unit of mass; nor should these be confused with foot-pound (ft⋅lbf), a unit of energy, or pound-foot (lbf⋅ft), a unit of torque.

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 equator to pole by up to half a percent) can safely be neglected.^[4]

The 20th century, however, brought the need for a more precise definition, requiring a standardized value for acceleration due to gravity.

Product of avoirdupois pound and standard gravity

The pound-force is the product of one avoirdupois pound (exactly 0.45359237 kg) and the standard acceleration due to gravity, approximately 32.174049 ft/s² (9.80665 m/s²).^[5][6][7]

The standard values of acceleration of the standard gravitational field (g_n) and the international avoirdupois pound (lb) result in a pound-force equal to 32.174049 ⁠ft⋅lb/s²⁠ (4.4482216152605 N).^{[lower-alpha 2]}

$${\displaystyle {\begin{aligned}1\,{\text{lbf}}&=1\,{\text{lb}}\times g_{\text{n}}\\&=1\,{\text{lb}}\times 9.80665\,{\tfrac {\text{m}}{{\text{s}}^{2}}}/0.3048\,{\tfrac {\text{m}}{\text{ft}}}\\&\approx 1\,{\text{lb}}\times 32.174049\,\mathrm {\tfrac {ft}{s^{2}}} \\&\approx 32.174049\,\mathrm {\tfrac {ft{\cdot }lb}{s^{2}}} \\1\,{\text{lbf}}&=1\,{\text{lb}}\times 0.45359237\,{\tfrac {\text{kg}}{\text{lb}}}\times g_{\text{n}}\\&=0.45359237\,{\text{kg}}\times 9.80665\,{\tfrac {\text{m}}{{\text{s}}^{2}}}\\&=4.4482216152605\,{\text{N}}\end{aligned}}}$$

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

$${\displaystyle {\begin{aligned}1\,{\text{lbf}}&=1\,{\text{slug}}\times 1\,{\tfrac {\text{ft}}{{\text{s}}^{2}}}\\&=1\,{\tfrac {{\text{slug}}\cdot {\text{ft}}}{{\text{s}}^{2}}}\end{aligned}}}$$

Conversion to other units

Units of force

v t e	newton	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 (9.80665 m/s2) as used in the official definition of the kilogram-force is used here for all gravitational units.

Foot–pound–second (FPS) systems of units

Main article: Foot–pound–second system

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. The international standard symbol for the pound as a unit of mass is lb.^[8]

Three approaches to units of mass and force or weight^[9][10]

v t e Base	Force		Weight		Mass
2nd law of motion	m = ⁠F/a⁠		F = ⁠W ⋅ a/g⁠		F = m ⋅ a
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	pound-mass	kilogram	pound	gram	tonne	kilogram
Force (F), weight (W)	pound	kilopond	pound-force	kilopond	poundal	dyne	sthène	newton
Pressure (p)	pound per square inch	technical atmosphere	pound-force per square inch	standard atmosphere	poundal per square foot	barye	pieze	pascal

In the "engineering" systems (middle column), 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^[11]—the use of Newton's second law, F = m ⋅ a, requires another factor, g_c, usually taken to be 32.174049 (lb⋅ft)/(lbf⋅s²). "Absolute" systems are coherent systems of units: by using the slug as the unit of mass, the "gravitational" FPS system (left column) avoids the need for such a constant. The SI is an "absolute" metric system with kilogram and meter as base units.

Pound of thrust

Further information: thrust

The term pound of thrust is an alternative name for pound-force in specific contexts. It is frequently seen in US sources on jet engines and rocketry, some of which continue to use the FPS notation. For example, the thrust produced by each of the Space Shuttle's two Solid Rocket Boosters was 3,300,000 pounds-force (14.7 MN), together 6,600,000 pounds-force (29.4 MN).^[12][13]

See also

• Foot-pound (energy)
• Ton-force
• Kip (unit)
• Mass in general relativity
• Mass in special relativity
• Mass versus weight for the difference between the two physical properties
• Newton
• Poundal
• Pounds per square inch, a unit of pressure

Notes and references

1. Despite its name, this system is based on United States customary units and is only used in the US.
2. The international avoirdupois pound is defined to be exactly 0.45359237 kg.

1. IEEE Standard Letter Symbols for Units of Measurement (SI Units, Customary Inch-Pound Units, and Certain Other Units), IEEE Std 260.1™-2004 (Revision of IEEE Std 260.1-1993)
2. Fletcher, Leroy S.; Shoup, Terry E. (1978), Introduction to Engineering, Prentice-Hall, ISBN 978-0135018583, LCCN 77024142, archived from the original on 2019-12-06, retrieved 2017-08-03.^: 257
3. "Mass and Weight". engineeringtoolbox.com. Archived from the original on 2010-08-18. Retrieved 2010-08-03.
4. Acceleration due to gravity varies over the surface of the Earth, generally increasing from about 32.1 ft/s² (9.78 m/s²) at the equator to about 32.3 ft/s² (9.83 m/s²) at the poles.
5. BS 350 : Part 1: 1974 Conversion factors and tables, Part 1. Basis of tables. Conversion factors. British Standards Institution. 1974. p. 43.
6. In 1901 the third CGPM Archived 2012-02-07 at the Wayback Machine 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.
7. Barry N. Taylor, Guide for the Use of the International System of Units (SI), 1995, NIST Special Publication 811, Appendix B note 24
8. IEEE Std 260.1™-2004, IEEE Standard Letter Symbols for Units of Measurement (SI Units, Customary Inch-Pound Units, and Certain Other Units)
9. Comings, E. W. (1940). "English Engineering Units and Their Dimensions". Industrial & Engineering Chemistry. 32 (7): 984–987. doi:10.1021/ie50367a028.
10. Klinkenberg, Adrian (1969). "The American Engineering System of Units and Its Dimensional Constant g_c". Industrial & Engineering Chemistry. 61 (4): 53–59. doi:10.1021/ie50712a010.
11. The acceleration unit is the distance unit divided by the time unit squared.
12. "Space Launchers - Space Shuttle". www.braeunig.us. Archived from the original on 6 April 2018. Retrieved 16 February 2018. Thrust: combined thrust 29.36 MN SL (maximum thrust at launch reducing by 1/3 after 50 s)
13. Richard Martin (12 January 2001). "From Russia, With 1 Million Pounds of Thrust". wired.com. Archived from the original on 25 September 2019. Retrieved 25 November 2019.

General sources

• Obert, Edward F. (1948). Thermodynamics. New York: D. J. Leggett Book Company. Chapter I "Survey of Dimensions and Units", pp. 1-24.