Pound (force)
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Poundforce  

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 
The pound of force or poundforce (symbol: lbf^{[1]}, sometimes lb_{f},^{[2]}) is a unit of force used in some systems of measurement including English Engineering units^{[a]} and the Foot–pound–second system.^{[3]} Poundforce should not be confused with footpound, a unit of energy, or poundfoot, a unit of torque, that may be written as "lbf⋅ft"; nor should these be confused with poundmass (symbol: lb), often simply called pound, which is a unit of mass.
Contents
Definitions
The poundforce 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 lowprecision 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.^{[4]}
The 20th century, however, brought the need for a more precise definition. A standardized value for acceleration due to gravity was therefore needed.
Product of avoirdupois pound and standard gravity
The poundforce is the product of one avoirdupois pound (exactly 0.45359237 kg) and the standard acceleration due to gravity, 9.80665 m/s^{2} (about 32.174049 ft/s^{2}).^{[5]}^{[6]}^{[7]}
The standard values of acceleration of the standard gravitational field (g_{n}) and the international avoirdupois pound (lb) result in a poundforce equal to 4.4482216152605 N:^{[8]}
This definition can be rephrased in terms of the slug. A slug has a mass of 32.174049 lb. A poundforce is the amount of force required to accelerate a slug at a rate of 1 ft/s^{2}, so:
Conversion to other units
newton (SI unit) 
dyne 
kilogramforce, kilopond 
poundforce  poundal  

1 N  ≡ 1 kg⋅m/s^{2}  = 10^{5} dyn  ≈ 0.10197 kp  ≈ 0.22481 lbf  ≈ 7.2330 pdl 
1 dyn  = 10^{−5} N  ≡ 1 g⋅cm/s^{2}  ≈ 1.0197 × 10^{−6} kp  ≈ 2.2481 × 10^{−6} lbf  ≈ 7.2330 × 10^{−5} pdl 
1 kp  = 9.80665 N  = 980665 dyn  ≡ g_{n} ⋅ (1 kg)  ≈ 2.2046 lbf  ≈ 70.932 pdl 
1 lbf  ≈ 4.448222 N  ≈ 444822 dyn  ≈ 0.45359 kp  ≡ g_{n} ⋅ (1 lb)  ≈ 32.174 pdl 
1 pdl  ≈ 0.138255 N  ≈ 13825 dyn  ≈ 0.014098 kp  ≈ 0.031081 lbf  ≡ 1 lb⋅ft/s^{2} 
The value of g_{n} as used in the official definition of the kilogramforce 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⋅s^{2}/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.^{[9]}
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/s^{2}  m/s^{2}  ft/s^{2}  m/s^{2}  ft/s^{2}  Gal  m/s^{2}  m/s^{2} 
Mass (m)  slug  hyl  poundmass  kilogram  pound  gram  tonne  kilogram 
Force (F), weight (W) 
pound  kilopond  poundforce  kilopond  poundal  dyne  sthène  newton 
Pressure (p)  pounds per square inch  technical atmosphere  poundsforce per square inch  atmosphere  poundals per square foot  barye  pieze  pascal 
In the "engineering" systems (middle column), the weight of the mass unit (poundmass) on Earth's surface is approximately equal to the force unit (poundforce). 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^{[12]}—the use of Newton's Second Law, F = m ⋅ a, requires another factor, g_{c}, usually taken to be 32.174049 (lb⋅ft)/(lbf⋅s^{2}). "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
The term pound of thrust is an alternative name for poundforce 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 is 3,300,000 poundsforce (14.7 MN), together 6,600,000 poundsforce (29.36 MN).^{[13]}^{[14]}
See also
 Footpound (energy)
 Tonforce
 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
 ^ Engineering in England has not used this system for many years. This system is used today only in the US.
 ^ IEEE Standard Letter Symbols for Units of Measurement (SI Units, Customary InchPound Units, and Certain Other Units), IEEE Std 260.1™2004 (Revision of IEEE Std 260.11993)
 ^ Fletcher, Leroy S.; Shoup, Terry E. (1978), Introduction to Engineering, PrenticeHall, ISBN 9780135018583, LCCN 77024142. ^{:257}
 ^ "Mass and Weight". engineeringtoolbox.com.
 ^ Acceleration due to gravity varies over the surface of the Earth, generally increasing from about 9.78 m/s^{2} (32.1 ft/s^{2}) at the equator to about 9.83 m/s^{2} (32.3 ft/s^{2}) at the poles.
 ^ BS 350 : Part 1: 1974 Conversion factors and tables, Part 1. Basis of tables. Conversion factors. British Standards Institution. 1974. p. 43.

^ 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/s^{2}, value already stated in the laws of some countries.
This value was the conventional reference for calculating the kilogramforce, a unit of force whose use has been deprecated since the introduction of SI.
 ^ Barry N. Taylor, Guide for the Use of the International System of Units (SI), 1995, NIST Special Publication 811, Appendix B note 24
 ^ The international avoirdupois pound is defined to be exactly 0.45359237 kg.
 ^ IEEE Std 260.1™2004, IEEE Standard Letter Symbols for Units of Measurement (SI Units, Customary InchPound Units, and Certain Other Units)
 ^ Comings, E. W. (1940). "English Engineering Units and Their Dimensions". Industrial & Engineering Chemistry. 32 (7): 984–987. doi:10.1021/ie50367a028.
 ^ 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.
 ^ The acceleration unit is the distance unit divided by the time unit squared.

^ "Space Launchers  Space Shuttle". www.braeunig.us. Retrieved 16 February 2018.
Thrust: combined thrust 29.36 MN SL (maximum thrust at launch reducing by 1/3 after 50 s)
 ^ Richard Martin (12 January 2001). "From Russia, With 1 Million Pounds of Thrust". wired.com. Retrieved 25 November 2019.
Sources
 Obert, Edward F., “THERMODYNAMICS”, D.J. Leggett Book Company Inc., New York 1948; Chapter I, Survey of Dimensions and Units, pages 124.